High performance vibration isolation techniques for the AIGO gravitational wave detector

Transcription

1 High performance vibration isolation techniques for the AIGO gravitational wave detector Eu-Jeen Chin 2007 This thesis is presented for the degree of Doctor of Philosophy of The University of Western Australia

2

3

4

5 Abstract Interferometric gravitational wave detectors are being built around the world with continually improving measurement sensitivities. Noise levels from sources that are intrinsic to these detectors must be reduced to a level below the gravitational wave signal. Seismic noise in the low frequency range, which is within the gravitational wave detection bandwidth, is a concern for earth-based detectors. This thesis presents research and development of a high performance vibration isolation system that is designed to attenuate seismic noise. The final design will be used as part of a fully working interferometer at the Australian International Gravitational Observatory (AIGO). Pendulums and springs are conventionally used for the horizontal and vertical vibration isolation components respectively. A complete system comprises of a cascade of these components, each stage dramatically improving the level of isolation. The residual motion at the test mass level is thus reduced but is dominated by the normal mode resonances of the chain. A simple and effective method to reduce residual motion further is to add ultra-low frequency pre-isolation stages which suspend the chain. The Roberts Linkage is a relatively new and simple geometrical structure that is implemented in the pre-isolation stages. Here we present experimental results of improving isolation based on mathematical modelling. The attenuation of seismic noise in the vertical direction is almost as important as that in the horizontal direction, due to cross-coupling between the two planes. To help improve the vertical performance a lightweight Euler spring that stores no static energy was implemented into the AIGO suspension system. Euler springs were first introduced in the year 2000 and offer an improvement over previous systems because they increase the internal resonant modes of the spring elements which, in the past, bypassed their isolation at undesirable low frequencies (a i

6 ii few tens of hertz). The use of Euler springs together with geometrical antispring techniques provides a further reduction of the normal mode frequencies and thus improves the vertical vibration isolation performance. Theoretical and experimental results are presented and discussed. Currently the AIGO laboratory consists of two 80 m length arms. They are aligned along the east and south directions. One of AIGO s top priorities is the installation of two complete vibration isolators in the east arm to form a Fabry-Perot cavity. Assembling two suspension systems will enable more accurate performance measurements of the tuned isolators. This would significantly reduce the measurement noise floor as well as eliminate the seismic noise spectrum due to referencing with the ground motion. The processes involved in preparing such a task is presented, including clean room preparation, tuning of each isolator stage, and local control schematics and methods. The status of the AIGO site is also presented.

7 Acknowledgements First and foremost, I would like to express my deepest thanks to my supervisors David Blair and Ju Li. You have supported me through every step of the way ever since I joined the group. David, your strong passion for science in this field is evident when I look back at just how fast the group and everything around you have grown. My motivation to do well had a lot to do with your strength. Ju Li, I have enjoyed the discussions that we ve had and you ve been extremely helpful in the lab. You always tend to brighten up my mood whenever I hit a rough patch in my project. To Chunnong Zhao who I had the pleasure to work closely with. Thankyou for your guidance and the sharing of your wealth of knowledge. You truly are a great asset to the group. Thanks to all the workshop boys especially Peter, Steve, Ken and Daniel. You never stop to amaze me. You guys turn raw metal into works of art. My project could not have progressed this far without you all. I would never have made it through without the fun company of my colleagues, especially the wit of Jean-Charles Dumas who I ve spent insanely large amounts of time with. You have kept me sane numerous times and I am extremely grateful to have worked beside you. Also to Andrew I, Andrew II, Ben, Fan, Florin, Jerome, Kah-Tho, Pablo, Sascha, Slavek and Yan, you have made my journey very memorable. Lastly, I have my wonderful group of friends and family outside the world of my research to thank. Thankyou all so much for your support and the times when iii

8 iv you were just there for me. I never stop telling myself just how lucky I am to have all of you in my life.

9 Preface The layout of this thesis is done such that it attempts to provide an easy understanding of the topics presented. This thesis is a collection of journal papers with relevant supporting sections not covered in the formatted papers presented in the main body of the text. The order of the chapters does not correspond to the progress in which development and research took place and in which the papers were written. Instead the chapters are ordered to maintain a smooth and logical flow. The first chapter introduces the concepts involved in gravitational wave detection including a brief description of gravitational radiation. The chapter later describes the importance of seismic isolation for successful detection and leads on to discuss the principles and methods used to build high performance vibration isolators with the required level of noise attenuation. Chapters 2, 3 and 4 each include a paper. Chapter 2 describes the advantages of installing pre-isolation stages that suspend the main 3D isolation stack. Specifically the chapter reports on work done on the relatively new concept of including a pre-isolation stage called the Roberts linkage. Following this, Chapter 3 discusses and highlights the advantages of using Euler springs as the main form of vertical isolation after the pre-isolator. The paper presents results on the application of geometric anti-springs in the Euler stages to further reduce their normal mode frequencies. Chapter 4 includes an overview paper of the complete vibration isolator system to be installed at the Australian gravitational wave detector at AIGO. Chapter 5, the Discussion and Conclusion, summarises the status of the seismic vibration isolation system at AIGO and proposes some further work. The Appendices provide further details on the topics mentioned in the main thesis body and includes three more published papers in which the author contributed. v

10 vi

11 Contents Abstract Acknowledgements Preface i iii v 1 Introduction Gravitational Waves Astrophysical Gravitational Wave Sources The Detection of Gravitational Waves Network of Interferometric Gravitational Wave Detectors Noise Sources in Interferometric Detectors Seismic Vibration Isolation Overview Design Concepts Anti-springs Center of Percussion The UWA Design Philosophy Vibration Isolation Stages of AIGO The Roberts Linkage Preface Introduction to the Roberts linkage Roberts Linkage Mathematical Analysis Paper Introduction The Roberts Linkage Analysis Tuning Modelling vii

12 viii Discussion Acknowledgments Postscript Control system of the Roberts linkage Vertical Euler Spring Isolation Preface Introduction to Euler springs Vertical Euler Stage Paper Introduction Euler Buckling and Non-Linearities Spring Coefficient Reduction The Performance of the Euler Stage Discussion and Conclusion Acknowledgements Postscript AIGO Seismic Vibration Isolator Preface Vacuum Clean Environment at AIGO Vibration Isolator Tuning The 3D Vibration Isolation Stack The Roberts Linkage The LaCoste Stage The Inverse Pendulum - Wobbly Table Control of the Isolator Preparation and background Pre-isolation Control Suspension System of AIGO Paper Introduction Isolation Techniques Experimental and theoretical results Isolator Progress in AIGO

13 ix Acknowledgments Postscript Status of the AIGO Vibration Isolators Discussion and Conclusion Summary Future Work Conclusion Bibliography 147 Appendices 157 A Roberts Linkage ANSYS Modelling 157 A.1 Preface A.2 Harmonic Analysis Model of the Roberts Linkage A.3 Roberts Linkage ANSYS code B Ring down curve and Q-factor 169 C Review Paper for the Astronomical Society of Australia 171 C.1 Preface C.2 ACIGA Review Paper C.2.1 Introduction C.2.2 Astronomical Sources of GW s C.2.3 Principles of Laser-Interferometric GW Detection C.2.4 ACIGA Research Activities C.2.5 AIGO High Optical Power Test Facility C.2.6 Summary C.2.7 Acknowledgements D Local Pre-isolation Control Paper 221 D.1 Preface D.2 Pre-isolation Control Paper D.2.1 Introduction

14 x D.2.2 Experimental Setup D.2.3 Experimental Results D.2.4 Conclusion D.2.5 Acknowledgements E Euler Spring Vibration Isolator Paper 233 E.1 Preface E.2 Euler Spring Paper E.2.1 Introduction E.2.2 Vertical Euler Stage with Reduced Spring Coefficient E.2.3 Experimental Results and Discussion E.2.4 Acknowledgements F Publication List 241

15 List of Figures 1.1 The effect of a gravitational wave propagating through a ring of test masses Schematic diagram of a simple Michelson interferometer The map of the world showing the locations of interferometric detectors Graphs showing the importance of having AIGO as a fully functional gravitational wave detector Graph showing the typical noise sources in interferometric detectors Displacement spectrum at AIGO main lab Schematics of the basic concepts for passive vibration isolation Diagram of a simple pendulum for the center of percussion effect Transfer functions showing the center of percussion effect The schematic of the entire AIGO vibration isolator chain Diagrams of the inverse pendulum and the LaCoste linkage Figure showing the wobbly table Schematic of the LaCoste stage Schematic of the self-damping pendulum The improvement achieved by including one stage of pre-isolation The Watt s linkage and the Scott-Russel Top view of the Roberts linkage shadow sensor The transfer function at the Roberts linkage stage while suspending the full isolation stack Experimental setup on the pre-isolator Roberts Linkage diagrams Diagram showing the Roberts linkage as a pendulum xi

16 xii 2.8 Roberts linkage as a compound pendulum Typical frequency response of a compound pendulum Graph showing the effect of changing the height of the suspension point Graph showing the effect of adding small masses on the frame Graph showing tuning of the COP independently of the resonany frequency The control schematic of the Roberts linkage isolation stage Electrical wiring diagram showing the method of controlling the suspension wires of the Roberts linkage Graph showing internal mode frequencies of pendulum and spring Force versus displacement plot of conventional springs Force versus displacement plot of Euler springs The Euler vertical stage configuration Magnetic anti-spring and torsion crank concepts Photograph and diagram of Euler spring clamps The force-displacement curvatures of the Euler stage Diagram of the Euler system with inverse pendulum Diagram showing the modelling parameters The force-displacement curves with varying h values An assembly drawing of the vertical Euler stage A force vs. displacement graph with an h value of 22 mm A plot showing strong inverse pendulum tuning of the Euler stage Plot of the resonant frequency as a function of mass in the Euler stage with different values of the inverse pendulum height h The force-displacement curves for experimental launch angle θ = radians The force-displacement curves for experimental launch angle θ = radians The progressive improvement of the Euler stage transfer functions Clean tents

17 xiii 4.2 Washing basins and ultrasonic baths Vacuum ovens Seismic noise at AIGO Roberts linkage and 3D stack assembly stand The full vibration isolation system at UWA Self-damp pendulums The assembly of the Euler stage Euler stage loaded Isolation stack with dummy control mass stage The Roberts linkage in the clean room View of the top of the Roberts linkage Wire supports for the Roberts linkage The assembled LaCoste stage LaCoste horizontal springs to tune anti-spring effect The pre-isolator assembled at AIGO Picture of the top of the pre-isolator The inverse pendulum leg plate Pictures of the wiring methods installed on the isolator A pair of magnetic/coil actuators The shadow sensor and actuator for the LaCoste linkage The control shelf The control loop for the inverse pendulum Unity gain plot of pre-isolation control - magnitude Unity gain plot of pre-isolation control - phase Spectral density of the inverse pendulum stage RMS residual motion of the inverse pendulum Theoretical horizontal residual motion Schematic of full vibration isolation system Roberts linkage diagram Self-Damping diagram Euler Spring vertical stage diagram The combined 3D isolator stage

18 xiv 4.34 Roberts linkage frequency response Transfer function theoretical curve RMS residual motion theoretical curve Picture of the assembled vibration isolator The input test mass vibration isolator sitting in the base section of the vacuum tank A.1 Schematic of the Roberts linkage model in ANSYS A.2 An example of a harmonic analysis plot done in ANSYS A.3 ANSYS animation of the Roberts linkage B.1 Ring down plot of the Euler stage C.1 Effect on relative amplitudes of adding a very low frequency preisolation stage C.2 The basic Michelson configuration C.3 Optical layout of a second generation laser interferometer C.4 A power recycled Michelson interferometer showing where a squeezed vacuum state is injected C.5 Signal-noise curves with and without squeezing C.6 Top view of the side-pumped Nd:YAG slab laser C.7 Method of scaling stabilised laser power through injection locking of successive master-slave lasers C.8 The Niobium flexure suspension concept C.9 Computing facilities of ACIGA C.10 Aerial photo of the AIGO site 80 km north of Perth C.11 The first three experiment stages for HOPTF C.12 Graph of typical noise sources of an interferometer gravitational wave detector C.13 Typical simulated transfer functions of the horizontal and vertical directions of isolation C.14 One stage of loaded Euler springs C.15 A schematic diagram of the vibration isolation stack for AIGO.. 213

19 xv D.1 Pre-isolator designed by ACIGA D.2 Coil-magnet actuator and shadow sensor D.3 Experimental control setup on the inverse pendulum D.4 Top view of inverse pendulum D.5 Experimental setup on the vertical stage D.6 Front view of coil-magnet mounting D.7 The open loop gain of the horizontal control loop D.8 Performance of the horizontal stage, residual motion and RMS D.9 Performance of the vertical stage, residual motion and RMS D.10 The theoretical horizontal residual motion of the full suspension isolation chain using the experimental pre-isolator results D.11 Time responses to control gains E.1 Schematics of the vertical Euler stage E.2 A force-displacement plot E.3 A plot of transfer functions showing the progressive reduction in the resonant frequency of the vertical Euler stage E.4 Latest Euler stage design and its transfer function

20 xvi

21 Chapter 1 Introduction 1.1 Gravitational Waves From Albert Einstein s theory of general relativity, gravitational waves exist and are created by non-symmetrical acceleration of mass-energy distributions [1]. These waves are perturbations of space-time and propagate at the speed of light. The direct detection of these waves has not been accomplished. An indirect indication of their existence was made by Taylor and Hulse while observing the loss of energy monitored from the in-spiraling binary pulsar PSR , which accurately resembles the emission of gravitational waves [2, 3]. Today, gravitational wave detectors are being built across the globe which aim to measure the small perturbations caused by gravitational waves, and to use these measurements as a basis for a new branch of astronomy called gravitational wave astronomy. A gravitational wave travels through space-time and contains information about the source it comes from. According to Einstein s theory of general relativity, if space-time is a two-dimensional sheet, propagation is possible because of the finite stiffness of the sheet. Conversely in Newtonian physics, space-time is infinitely stiff so gravitational waves would have infinite velocity and infinite energy density, and therefore could not exist. The stiffness of space-time in general relativity can be described by the relationship between the curvature of space-time and the mass-energy of the source producing the waves. This can be expressed by: T = c4 8πG G (1.1) 1

22 2 Chapter 1. Here T is the stress energy tensor, G represents the Einstein curvature tensor, c being the speed of light and G is the gravitational constant. The coupling coefficient c 4 /8πG is effectively the stiffness of space-time having a magnitude of the order This high value is evidence that gravitational waves travel with very small amplitudes, thus making the task of direct detection of these waves extremely difficult. Gravitational wave strength is measured in terms of strain or the fractional length change. This value (h) is defined by Equation 1.2 and defines the amplitude of the wave. It is expected that the largest regular events give a strain value of about to Detectors must obtain and exceed this high level of sensitivity to measure such small displacements. h 2 = L L (1.2) Astrophysical Gravitational Wave Sources There are various sources expected to emit gravitational waves with sizeable amplitudes for future interferometers to detect. They fall mainly into three types depending on the characteristics of their waveforms. They are periodic, burst or stochastic gravitational wave sources. Periodic. Sources that radiate a periodic wave pattern can have a monochromatic signal or a ring down signal. Monochromatic sources emit radiation at a single frequency in a long continuous wave. The most common source of monochromatic radiation comes from non-axisymmetric pulsars. Binary in-spirals have ring down signals. These objects include the coalescing of neutron star and/or black hole pairs (NS/NS, NS/BH, BH/BH). As time progresses the orbital period and the distance between the pair decrease due to the loss of kinetic energy in the form of gravitational radiation. As the pair becomes closer together the frequency and amplitude of the gravitational signal increase until the two stars finally merge. Burst. Anticipated burst objects include asymmetrical core collapses in supernovae and the coalescence and merger of intermediate mass black holes and other binary systems.

23 Introduction 3 Fig. 1.1: The effect of a gravitational wave propagating through a ring of test masses. The two arms illustrate how an interferometer can sense a passing wave. Stochastic. This class of gravitational wave signal is sometimes referred to as the analogue to the cosmic microwave background radiation. Expected emitters include both cosmological sources related to the Big Bang as well as astrophysical sources such as white dwarf binaries and supernovae. 1.2 The Detection of Gravitational Waves A passing gravitational wave changes the local metric of space-time and can in principle be detected by measuring the acceleration of test masses. To illustrate the effect of gravitational waves on free masses, consider a set of freely floating mass bodies arranged in a circle as shown in Figure 1.1. When a gravitational wave passes through with its axis of propagation orthogonal to the plane of the circle, it will cause relative displacements between the masses to alter as shown in the diagram. The diagram shows the change in quarter period intervals. As described in Section 1.1, the strength of gravitational waves are measured using strain h. The most promising modern technique to detect these waves is through the use of a Michelson Interferometer. This instrument is designed to sense relative changes in displacements that can be visualised as the shortening and lengthening of the arms illustrated in Figure 1.1. From the definition of strain, (Equation 1.2) the length shift is proportional to the original distance between the masses. It is thus possible to increase the signal to noise ratio of a gravitational wave measurement by increasing the length of the arms of the interferometer and keeping the absolute length sensitivity constant.

24 4 Chapter 1. There are two main types of gravitational wave detectors in use throughout the world today. A resonant mass detector was first developed in the 1960s by Joseph Weber using a large aluminium bar [4]. The main principle of this type of detector is to have the fundamental resonant mode of the mass (usually in the shape of a bar) to match that of a gravitational wave. The detectors naturally have small detection bandwidths and require bars which have high Q-factors 1 to ensure the acoustic signals in the large mass due to the coupling of the gravitational wave to have low loss. Some resonant mass detectors include ALLEGRO, AURIGA, EXPLORER, NAUTILUS and NIOBE [5]. The second type is the interferometric gravitational wave detector which has already been briefly mentioned. A Michelson interferometer is an optical configuration that senses phase difference accumulated in different path lengths (Figure 1.2). The mirrors must be allowed to float in an inertial frame and follow the distortion of space-time. This is usually achieved in practice by suspending the optical components using pendulums. Control systems are implemented into the Michelson interferometer to maintain the position locking of the suspended mirror test masses with respect to each other for the detection of the disturbances caused by passing gravitational waves. The better the passive isolation of seismic noise, the easier it is to lock the mirrors. A high-powered laser beam is injected and splits at the surface of the beam splitter in two orthogonal directions. The arm lengths are set such that the two beams undergo resonance in the two Fabry- Perot arms before recombining back at the beam splitter surface. The intensity of the recombined beam is detected at the photo detector. In other words the interferometer converts length disturbances into power change at the output of the interferometer Network of Interferometric Gravitational Wave Detectors Having several detectors positioned around the world is advantageous, if not essential in detecting gravitational waves. Because it is difficult for a single detector 1 The Q-factor is described towards the end of the Chapter and is defined by Equation 1.9.

25 Introduction 5 erometer. Vibration isolators and suspension systems High powered laser Fabry-Perot cavities Beam splitter Photo detector Test mass mirrors Fig. 1.2: Schematic diagram of a simple Michelson interferometer for use in a gravitational wave detector. to obtain full information of a passing wave, a worldwide collaboration can obtain greater information as well as reduce the rate of false detections caused by local noise to a minimum. More importantly, a network of detectors is necessary to allow for the state of polarisation of the traveling gravitational wave signal and the direction of the source to be accurately determined. The LIGO group in America has two sites with three detectors, a 4 km long detector in Livingston, Louisiana, and a pair of detectors, a 2 km and a 4 km long in Hanford, Washington [6, 7]. The VIRGO group is situated in Pisa, Italy, and has a 3 km long detector [8]. GEO 600 is a 600 m arm length interferometer located near Hannover, Germany [9]. TAMA 300 is a 300 m long detector situated in Tokyo, Japan [10]. Lastly the AIGO project located in Gingin, Western Australia, is currently developing a 80 m arm length high powered optical test facility which is capable of extending to a 5 km long interferometer. Figure 1.3 shows the map of the world and the locations of major interferometric gravitational wave detectors. So far AIGO is the only interferometer in the southern hemisphere. The location at which AIGO is situated plays a crucial role in determining the location of the gravitational wave source in the sky. Modelling by Linqing Wen

26 6 Chapter 1. Fig. 1.3: The map of the world showing the locations of interferometric gravitational wave detectors. and Bernard Schutz from the Albert Einstein Institute in Potsdam, Germany [11], provide evidence that the location of a detector in the southern hemisphere can drastically improve the determination of the direction of the gravitational wave source. A single detector placed in Australia increases the number of possible sources by 270% and increases the directional resolution by an average of 400%. Figure 1.4 illustrates an example of the resolution of detecting a source with and without the AIGO detector. The axes are in equatorial coordinates; where RA is the right ascension (longitude) in degrees and Dec is the declination (latitude) in degrees, and the colour bar is the probability of detecting the gravitational wave source.

27 Introduction 7 Fig. 1.4: Graphs showing the importance of having AIGO as a fully functional gravitational wave detector. Here shows the hypothetical gravitational wave source at 30 deg Dec, 85 deg RA in the sky, appearing as a long arc spanning 20 degrees without AIGO, then reduced to an area within 0.5 degrees with AIGO (modelling by Linqing Wen and Bernard Schutz, Albert Einstein, Potsdam, Germany).

28 8 Chapter Noise Sources in Interferometric Detectors Various noise sources dominate across different frequency bands. Figure 1.5 is a typical noise spectrum that is faced by interferometric gravitational wave detectors. Here we introduce seismic noise, thermal noise, photon shot noise and radiation pressure noise. Fig. 1.5: Graph showing the typical noise sources that are inherent in interferometric gravitational wave detectors. Seismic Noise. This type of noise dominates the noise spectrum of Earth-based gravitational wave detectors at low frequencies which typically spans from sub-hertz to a few hertz or until the pendulum thermal noise level is reached. It is noted that many pulsars or coalescing binaries are expected to emit in this range of low frequencies. For this reason considerable effort has been made to improve the minimum sensitivity limit in this frequency band. To achieve this, it is necessary to isolate the mirrors from the seismic noise coming from the ground. The motion from the ground is transmitted through mechanical connections between the ground and the test mass and will perturb the separation of the test masses in the interferometer. The ground is constantly vibrating with a continuous background noise

29 Introduction 9 with an RMS amplitude of x s αf 2 m/ Hz, where α is typically between 10 6 and 10 9 [12]. This level of noise greatly exceeds that of gravitational wave signals. Thus it is extremely important for earth-based detectors to isolate the seismic noise background from the test masses. This is achieved by installing high performance vibration isolators to suspend these test masses. A plot showing the seismic noise recorded at the AIGO site compared with the typical noise level is shown in Figure 4.4. Seismic motion is caused by natural phenomena such as macro-seismic, oceanic and atmospheric activities, as well as by human activities. Equipment mounted on the earth surface experiences the continual background of seismic activity. It is important to determine the level of vibration an operating interferometer at AIGO is exposed to before implementing vibration isolation systems onto the complex. The central laboratory has an area of approximately m 2 which is supported below by a concrete foundation 100 mm thick. The two end stations located at the ends of the interferometer arms are 6 m 2 in area each and are also supported by 100 mm thick concrete foundations. At AIGO, it is expected that much of the background noise will be coming from the equipment used for the vacuum systems (see Section 4.2) as well as the equipment used to maintain the clean environment particularly in the laser injection room. Seismic noise monitoring systems are in placed at the site and these frequently confirm the noise levels at particular locations in the lab. Studies have shown the importance of selecting the right location to place gravitational wave detectors in reducing background noise. The physical location and soil properties of the AIGO site is excellent for its purpose because the ground on which it sits is highly effective in attenuating seismic waves in the 2-20 Hz band [13]. However, seismic noise spectrums collected at various locations indicate undesirable coupling of mechanical vibrations to the laboratory structures. Another significant finding was the significant reduction in the background noise level after slowing the fan speed of the fine particle air filters used for the clean room. Figure 1.6 shows the ground displacement spectrum recorded in the main lab of AIGO with and without human activity. It is plotted with a 10 7 /f 2 background seismic noise model.

30 10 Chapter 1. Fig. 1.6: Displacement spectrum at AIGO main lab showing the difference in the noise level with and without cultural activity along with the background noise model. The human activity data spans five minutes when people were active in the main lab (plot taken from [13]). Location has been an important consideration in choosing the site for a future Japanese earth-based gravitational wave detector that can detect sources as far as 200 Mpc in space. The new detector, called the Large Scale Cryogenic Gravitational Wave Telescope (LCGT), is to be built in the Kamioka underground mine site, approximately 1000 m beneath the top of a mountain. It has been proven that the seismic noise inside the mine is two orders of magnitude less than that at the TAMA site at frequency 1 Hz [14]. The increased stability of the site comes from a decreased level of seismic activity due to surrounding hard rock, as well as from having very stable temperatures in the tunnel. Having a stable foundation for LCGT is beneficial to the detector and will result in the improvement of the sensitivity of the detector. This may mean less stringent requirements on the design of vibration isolation systems and control systems. It is planned that construction of LCGT will start in the year 2009.

31 Introduction 11 This thesis focuses on reducing seismic noise in gravitational wave detectors. In section 1.3 the concepts and techniques used in passive vibration isolators to reduce seismic noise are introduced and discussed. Thermal Noise. Thermal noise fluctuation plays an important role in advanced detectors where ultra-sensitive displacement sensing devices are used, such as the optical cavities in gravitational wave detectors [15]. Thermal noise is due to two separate sources: the thermal noise of the test mass suspension, and the thermal noise of the mirror test mass. This noise is due to the random fluctuations of atoms, also referred to as Brownian motion. In gravitational wave detectors this type of noise is caused by the thermal motion of the individual particles in the material of the mirror, the mirror coating and the mirror suspension system. Thermal noise dominates from a few hertz to several hundred hertz. At low frequencies suspension thermal noise limits the strain sensitivity of interferometers where seismic motion has been sufficiently filtered. Advanced detectors use ways to improve the sensitivity in this low frequency range by reducing thermal noise down to the shot noise limit. The main method to reduce thermal noise is by using material that has a high quality factor (high Q) or has a low intrinsic loss. In this case most of the thermal energy will appear in narrow frequency bands instead of dispersed across the band. Ideally the thermal noise peaks should locate outside of the detection band. There is constant flow of thermal energy between the internal modes of the suspension/mirror system and the motion of the mirror surface. Random motion of the atoms, ie. kinetic energy, is dissipated to the heat bath or the internal friction of the system. The thermal energy from the bath can also be transferred to cause mechanical motion of the atoms. The energy exchange is described by the Fluctuation-Dissipation Theorem which shows the relation between the amount of fluctuation of the mirror surface and the dissipation of the system (Equation 1.3 [16]). This theorem describes that the energy exchange is strictly

32 12 Chapter 1. related to the impedance of the system. S x (f) = k BT Re[Y (f)] (1.3) π 2 f 2 where S x (f) is the power spectral density of fluctuations in a degree of freedom x, k B is Boltzmann s constant, T is the temperature of the system, f is the frequency of the motion and Y (f) is the complex mechanical admittance (inverse of impedance) of the system. Suspension thermal noise is described by the Fluctuation-Dissipation Theorem (Equation 1.3) and is contributed by two types of thermal noise: pendulum mode and violin mode thermal noise. At the lower end of the frequency spectrum ranging from a few hertz to several hundred hertz, suspension thermal noise is dominated by pendulum mode thermal noise. In this region the noise rolls off at approximately 1/f 2.5 before reaching the fundamental violin string mode. Above several hundred hertz, high Q violin mode noise dominates. In advanced interferometers, the aim is to improve this region of thermal noise by reducing the amplitude and number of thermal noise peaks. The gravitational wave group of UWA is devising ways to reduce violin string modes in the mirror suspension. One method proposed is to reconfigure the cross-sectional shape of the mirror suspension such that the thermal noise in the direction of the strain readout is reduced, ie. along the cavity axis. The new concept of orthogonal ribbons made from low loss fused silica was modeled and revealed that both the number and the average peak amplitude violin mode were reduced [17]. The orthogonal ribbon had little effect on the pendulum mode thermal noise. A recent research development is the use of orthogonal niobium ribbons for initial testings [18]. Current difficulties with the manufacture of fused silica ribbons of the required thickness make niobium a very suitable material. However, fused silica ribbons have already been proposed by the GEO 600 and VIRGO groups for use in the possible upgrade for VIRGO and for Advanced LIGO detectors [19]. Measurements were made of their losses as well as their breaking stresses which showed promising results [20]. Suspending the mirror with ribbons decreased the violin mode thermal noise in both the cavity directional axis and the axis orthogonal to it. Thermal noise coming from the vibration isolator itself does not play a crucial role. This is because thermal noise of an isolation stage will be filtered by the

33 Introduction 13 stages below so that only the final stage will contribute significant thermal noise to the test mass. Thermal noise fluctuation from the mirror substrate and the mirror coating is also being investigated by the UWA group. Particular attention has been paid to losses located in the equatorial region of the mirror, ie. the plane in which the mirror makes contact with the mirror suspension system [21]. Modelling using computer simulations are being used to obtain an optimal suspension design to minimise suspension losses on the thermal noise of a test mass. Photon Shot Noise and Radiation Pressure Noise. The phase and amplitude of the optical field have an uncertainty relationship whereby their products are constrained to a minimum value. Laser beams in nature are very close to the coherent state. This means equal uncertainty in the phase and amplitude quadratures. The quantum phase fluctuation contributes to a noise component noise called shot noise. Amplitude fluctuation causes the pressure force on the mirrors of the interferometer to vary and thus causes the mirror to move. This type of noise is called radiation pressure noise. The signal to noise ratio of a measurement limited by shot noise is proportional to the square root of the power of the incident laser beam. However, the signal to noise ratio of a measurement limited by radiation pressure noise is inversely proportional to the same power. Hence the noises themselves are proportional to the power according to the following: 1 shot noise P in radiation pressure noise P in (1.4) where P in is the power of the incident light. It can therefore be seen that these two noise sources increase in opposite directions relative to the power of the incident laser beam. Thus it is evident that there is an optimal level where the noise sources are equal. At this level the total noise limited sensitivity is optimal and is called the standard quantum limit, or SQL. Gravitational wave detectors aim to reach this limit of sensitivity and breach it. A means of breaching this limit was proposed in 1980 by Braginsky et al [22] which involves the squeezing of quantum

34 14 Chapter 1. noise. The method does not concern this study so further explanation will not be included in this thesis. 1.3 Seismic Vibration Isolation Overview Vibration isolators are developed to attenuate ground seismic motion to an acceptable level before this noise reaches the suspended test mass. Seismic noise dominates in the sub to low frequency band as was introduced in Section and shown in Figure 1.5. With an effective seismic attenuator, the noise floor at low frequencies should be thermal noise. In this section, the main principles of integrating vibration isolation into gravitational wave detector design are described with emphasis on passive techniques. Passive vibration isolation techniques are the main focus of this thesis Design Concepts There are two main categories of seismic vibration isolation systems used in gravitational wave detection: passive and active techniques of isolation. An active system involves the implementation of servo systems with sensors and actuators. The basic concept is feeding back the error signal from a sensor located at the suspended test mass being isolated to the suspension platform. The aim is to measure the relative motion between the suspension point and the test mass and apply forces to the suspension platform so that it can follow the motion of the test mass. Groups such as LIGO [23, 24] and VIRGO [25, 26] use active forms of vibration isolation together with passive mechanical structures to achieve their required levels of seismic noise attenuation. This type of isolation is usually complex and expensive and can itself introduce noise into the system. However, active control can be used effectively in low frequency responses to correct for thermal drift where minimal forces are required. The baseline design concept for seismic noise isolation for Advanced LIGO includes a two-stage in-vacuum active isolation platform that is supported by an external actuation stage [23, 27]. The Stanford group has built and tested the two-stage active platform and has shown adequate noise performance and actuation bandwidth [28]. Two other key

35 Introduction 15 techniques are also used to reduce the transmission of seismic noise: feed-forward correction which is based on environmental motion measurements, and feedback servo loops which try to null motion sensed at the payload. Data demonstrating the coexistence of the two techniques shows promise for the improvement in active isolation platform performance. At AIGO, local and global controls are planned to be implemented into the predominantly passive vibration isolation system. In Chapter 2, local control schemes that were undertaken to control the Roberts Linkage stage are presented. This isolation stage will be introduced in Section 1.4. In Chapter 4, an overview of the control system of the vibration isolator is presented. In the remainder of this Chapter, the principles of passive vibration isolation are discussed. The vibration isolation system of AIGO stands 2.5 m high and consists of a 3D isolation stack which suspends off the pre-isolation stages of a sub-hertz resonant frequency range. Other gravitational wave groups with high performance suspension systems include VIRGO which is developing a 9 m isolation system called the Super Attenuator [29, 30, 31]. The attenuation system has been built and tested at INFN (Istituto Nazionale di Fisica Nucleare) Pisa laboratories and is currently in use at the VIRGO observatory. This system consists of a tall inverted pendulum which suspends the seven-stage cascaded vibration filters and uses triangular spring blades for the vertical component. A system similar to the Super Attenuator is the Seismic Attenuation System (SAS) developed by the collaboration of LIGO [32] and TAMA [33]. It also uses an ultra-low frequency inverted pendulum which includes sensitive accelerometers and voice coil actuators. Monolithic geometric anti-springs are used for the vertical isolation stages. Passive mechanical vibration isolation systems work by attenuating seismic noise that is transmitted from the ground to the test mass to a sufficient noise level. The design of the suspension system is such that the normal modes are below that of the antenna frequency and its higher internal mode frequencies are above the detection bandwidth. To clarify this, lets look at just one stage of vibration isolation. This stage will have its suspended test mass move with its support at frequencies below resonance. Above resonance, the test mass motion will be attenuated due to its inertia before reaching the higher internal modes.

36 16 Chapter 1. l l mass mass a) Pendulum b) Spring Fig. 1.7: Schematics of the basic concepts for passive vibration isolation; a) pendulum for horizontal vibration isolation; and b) the coil spring for the vertical component. This concept is effectively a mechanical low pass filter. It is then said that passive vibration isolators are good at attenuating noise between frequencies above its resonant modes and its higher internal frequency modes [15]. Each stage of isolation with resonance frequency f 0 will attenuate noise by a factor (f 0 /f) 2 above the resonant mode until the internal modes are reached. In general, pendulums and springs follow these behavioural characteristics and are thus commonly used for vibration isolation systems. Pendulums are used for horizontal passive vibration isolation. A pendulum is good in attenuating noise above its resonant frequency as well as having high internal mode frequencies. The proportionality behaviour of the isolation performance with frequency allows for greater isolation as the resonant frequency is reduced. The transfer function follows a 1/f 2 attenuation after first resonance. The resonant frequency is given by ω = g l (1.5) where g is the gravitational constant and l the pendulum length. Figure 1.7a illustrates the schematic for the pendulum. In the vertical domain, springs are used to momentarily store energy from the vertical vibrations transmitting from the suspension point before reaching down to the suspended test mass. As illustrated in Figure 1.7b the extension of the

37 Introduction 17 spring determines the resonant frequency and extends proportional to the applied force represented by the mass. The amount the spring stretches per unit mass determines the stiffness of the spring. Static energy is defined as the energy put into the spring system by the initial loading of the mass. The vibrational energy in the system is termed dynamic energy. In general, the amount of dynamic energy needed to be stored in the spring system is small compared to the static energy. It is also known that the energy required to be stored is proportional to the available spring mass. The large amount of spring mass required to bring the resonant frequency down introduces the undesirable property of lowering the higher order internal modes of the spring system, which consequently deteriorate the isolation performance. Although gravitational wave detectors are mainly concerned with horizontal vibrations, there is a degree of cross-coupling between the two degrees of freedom, hence vertical vibration isolation is important. This is due to various reasons such as the earth curvature, mechanical imperfections and the orientation of the mirror. Also, the local vertical plane will not be exactly perpendicular to the long laser baseline beam. One aspect that vertical isolators cannot avoid is the support of the entire mass which basically means using large energy storing elastic devices. In the past, the group at UWA has used leaf springs or cantilever springs for their vertical vibration isolation stages [34]. Using this type of spring system, a relatively low resonant frequency of 1.8 Hz was achieved. Today, cantilever springs are still used in the gravitational wave detectors such as VIRGO. Researchers at UWA found that the higher order internal modes stated at about 30 Hz because of the large spring mass that was required to suspend the test masses in the isolation system. This low frequency value prompted them to look for other means of vertical suspension that would see this value rise. They have since developed and implemented Euler springs into their vibration isolation system. The concepts of using these springs are discussed more thoroughly in Chapter 3. We will introduce the spring mechanism in the next section where we describe the vibration isolation design philosophy for AIGO. With the implementation of Euler springs, several other concepts are employed to further improve the isolation performance. Below is a discussion on the concept

38 18 Chapter 1. of anti-springs, which play a vital role in the reduction of the resonant frequency of both horizontal and vertical vibration isolation components. The methods used to implement the anti-spring effect into the physical system will be discussed in later chapters where the particular isolation stages are described. Along with anti-spring, the center of percussion plays another crucial role in the performance level. This concept is especially important in defining the isolation floor or limit in a noise attenuating system. Center of percussion tuning is vital for the Roberts Linkage stage which will be first discussed in section 1.4, then later in more detail in Chapter Anti-springs The concept of anti-springs has been widely used in vibration isolation systems for gravitational wave detectors including at TAMA (Seismic Attenuation System), VIRGO (Superattenuator) as well as at AIGO. The principle of an anti-spring is just that, a mechanism that behaves in an opposite way to a spring, namely, an anti-spring has a negative spring constant. This means that if a constant force is applied onto the mechanism to displace a body, it becomes easier as more of it is displaced, ie. the force that is required to move a certain amount of displacement decreases. Intrinsically the concept of an anti-spring is unstable. However, by combining structures of positive spring constants with the anti-spring mechanism, very low resonant frequencies can be achieved. At AIGO, the pre-isolation stages incorporate the anti-spring concept to obtain sub-hertz resonant frequencies including the inverse pendulum (the so-called wobbly table ) and the LaCoste stage in the horizontal and vertical directions respectively. These pre-isolation stages will be introduced in Section and will be examined throughout the thesis, in particular Chapter 4 which includes our paper, which presents an overview and current status of the AIGO vibration isolation system. Geometric anti-springs are incorporated into the vertical Euler stages to reduce the resonant frequencies. This work is presented in Chapter 3. The main concept is the inclusion of an inverse pendulum into the suspension configuration

39 Introduction 19 of each stage. The effect of the anti-spring is controlled by lowering or increasing the effective height of the inverse pendulum Center of Percussion The center of percussion is an important concept in vibration isolation but is sometimes difficult to understand. Various stages in the AIGO vibration isolation system make good use of center of percussion tuning to achieve the satisfactory and required level of noise attenuation at various frequencies. A simple way to explain the center of percussion effect is by visualising a compound pendulum (Figure 1.8). The point of center percussion is the point at which there is momentarily no motion when the system is excited at its point of suspension. This point is usually somewhere along the length of the pendulum. The center of percussion point can also be explained by a rigid body being accelerated by a force not in line with its center of mass, whereby the body undergoes both translational and rotational motion. Here, the center of percussion point is where it undergoes no acceleration. Fig. 1.8: Diagram of a simple pendulum illustrating the concept of the center of percussion effect. The transfer function isolation floor depends on the position of measurement point A.

40 20 Chapter 1. Figure 1.9 shows the effects of different measurement points along the length of our pendulum. In this case the resonant frequency is set at 1 Hz. The equations used for this theoretical graph are shown in the following which is based on work done by Garoi [35]. The sign convention of A is shown in Figure 1.8. For a thin rigid rod suspended by one end, the transfer function obtained is shown by the following: where X 2 X 1 = 2πf (1 A( f res ) 2 ) 2 f + ( fresq 2 )2 (1.6) (1 ( 2πf f res ) 2 ) 2 f + ( fres 2 Q)2 A = 1 3l p l (1.7) Here X 2 is the motion amplitude at the output point (at test mass), X 1 is defined as the motion amplitude at the input (suspended end of the rod), f res is the resonant frequency of the system and Q is the Q-factor of the system. The value A is defined in Equation 1.7 and is dependent on the difference in length of the center of mass of the rod and the point of measurement l p and the length of the rod itself l. The sign of l p will be positive when the point of measurement is on the side of the center of mass away from the suspension point. As shown in the graph, the test mass which is to be vibration isolated should coincide with the center of percussion point, ie. where A has the value of 0. At this point, only rotation is observed and if further systems are suspended from this point, then almost no motion is coupled. A disadvantage of the center of percussion effect is that it has a flat floor isolation level at frequencies higher than the corner frequency, at which performance cannot be exceeded. The 1/f 2 fall-off after the resonance joins this either by a smooth transition or by a notch (Figure 1.9). The term corner frequency is defined as the last resonance before the fall-off. The general method of tuning the center of percussion is by the addition of mass onto the structure itself which changes the mass distribution. The center of percussion point should be located at either the suspension point, or at the point which it suspends the test mass. The elimination of center of percussion effect on

41 Introduction 21 inverted pendulums include adding counter weights at the supports [30, 12, 36]. Tuning of the Roberts Linkage is presented in the work done in Chapter 2 and is discussed there. Center of percussion effects were observed in the Euler stages, and methods of counteracting this problem have been suggested (Section 3.4). 40 Transfer Function 20 0 db A= A=0.01 A= A=0.001 A= Frequency +Hz / Fig. 1.9: Transfer functions of resonant frequency of 1 Hz showing the center of percussion effect. Center of percussion effects can be seen in the transfer functions that are recorded at each stage. The effect in the Euler stages can be seen in the transfer functions presented in the Euler spring paper in Chapter 3 and it is briefly mentioned and discussed. The most important isolation stage that uses center of percussion tuning is the Roberts Linkage horizontal pre-isolation stage. Work was done previously by the group [35] to investigate the feasibility of incorporating the Roberts Linkage into the suspension system, and preliminary testing was done on a prototype. Results highlighted the importance of center of percussion tuning. Further work on the Roberts Linkage was done by the author and a colleague (see paper presented Chapter 2). Theoretical work and some results of the Roberts Linkage in the isolation stack are presented.

42 22 Chapter The UWA Design Philosophy The vibration isolation system at UWA, which is being built for AIGO, is relatively compact compared to those in other interferometric gravitational wave detectors around the world. The aim at AIGO is to develop a high performance passive vibration isolator. In the past, the research focus has been design and the manufacture of a fully operable suspension system. Chapter 4 describes the vibration isolator as a whole and presents the current status of AIGO. Some isolator tuning methods and procedures are highlighted. The description of each isolation stage and their working concepts are described in the remainder of this chapter. It is perhaps a good place to acknowledge the large contribution to the success of the high level performance of the current suspension system design is by Dr. John Winterflood [12] who completed his PhD at UWA in Today his ideas are still relevant and form the foundation of the AIGO vibration isolation system. The goal of vibration isolation systems for gravitational wave detectors is to reduce residual motion of the test mass down to a low level for two main reasons. One is to allow for cavity lock. It is extremely difficult to locate and position the test mass to within 10 6 of an optical wavelength [15]. Large forces would be required to decelerate the test mass to within operating range. The second reason is to prevent introducing high levels of electronic noise into the system from the actuators in the control system. Actuation noise is caused by electronic noise which introduces small random fluctuations in the actuating forces. This will accelerate the mirrors which the sensors feed back into the control loop and thus compensates with the added noise. These problems can be solved by implementing advanced control techniques or more complex servo systems. Another solution is by reducing the residual motion by increasing the level of seismic attenuation by passive means. Cascading several stages improves the isolation performance above the corner frequency. The theoretical transfer function can be expressed in the following form where f 1 f 2...f N are the resonant frequencies of the Nth stage: T.F. = Output Input = (f 1f 2...f N f N ) 2 (1.8)

43 Introduction 23 At AIGO, there are effectively four horizontal pendulum stages and three vertical Euler spring stages that are suspending off the ultra-low frequency (ULF) pre-isolation stages. The pre-isolation stages consist of two horizontal stages and one vertical stage. However, cascading stages one after another has adverse effects in the performance. One undesirable effect is the increase in the tension of the suspended wire of a pendulum which consequently increases the restoring force of that stage. This will increase the resonant mode and makes it a less effective vibration attenuation stage [12]. Theoretical models have been done at UWA [37] on the expected transfer function of the full vibration isolation system. Work presented in Chapter 4 shows that the complete isolator is expected to achieve a level of residual motion close to 1 nm at 0.2 Hz. Limited by the noise floor of the measurement devices, the performance of the full vibration isolation system which was installed in the laboratory at UWA could not be directly assessed. This is because of the contribution of various noises coming from the measuring devices, which saw at best a noise floor of about 200 db at the output (test mass level). The main cause of this sensitivity limit is seismic noise because sensing and actuating devices are effectively mounted to the ground. A solution is to build two complete vibration isolation systems to allow for relative measurements with each other eliminating the addition of the seismic noise spectrum due to referencing with the ground motion. A laser beam will be injected into the cavity formed by the two isolation systems where its interference pattern is used as the measuring medium. The AIGO group intends to build the cavity for performance testing in the East arm in the main laboratory at the Gingin site. The construction status is presented in Section Vibration Isolation Stages of AIGO The vibration isolator of AIGO is designed to be a compact, multi-staged, high performance suspension system that attenuates seismic noise down to the required level for the possible detection of gravitational waves. Here we present an overview of each of the isolation stages and their concepts before going into more detail in later chapters. As mentioned earlier, the full vibration isolation system consists of the pre-isolator and the stack, which contains four horizontal pendulum stages

44 24 Chapter 1. and three vertical Euler stages. A photo of the full vibration isolator can be seen in Figure 4.6. Figure 1.10 shows the schematic of the entire isolator chain. The Wobbly Table The pre-isolation stages suspend the conventional isolation stack consisting of the cascade of pendulums and Euler spring stages. Each of the pre-isolation stages has resonant frequencies below 100 mhz. The first of the horizontal pre-isolation stages is referred to as the wobbly table, a platform supported by multiple inverse pendulums. The four inverse pendulums sit on top of the isolator stand which is connected to the ground on aluminium legs. The combination of the inverse pendulums with the positive spring stiffness of the flexures at their ends results in the low structural resonant frequency we see today. The group at UWA were the first to investigate the use of inverse pendulums [38] (schematically shown in Figure 1.11a). As described in Section 1.3.2, they are effectively anti-springs whereby gravity is acting as the applied force on the mass load. The design of the wobbly table is such that the structure does not tilt. The tilt rigid platform is made that way because of its geometry. The platform being supported by the inverse pendulum legs is constrained to move only in the horizontal plane. Figure 1.12 shows a diagram of the 2D wobbly table constructed by inverse pendulums and flexures. The LaCoste Linkage Figure 1.11b diagrammatically shows the concept of the LaCoste linkage. This stage is the first vertical pre-isolation stage and can obtain resonant frequencies of about 100 mhz. The anti-spring effect comes about through the horizontal component of the force provided by the spring which acts in the opposite direction of the gravity pull. A torque is created by the spring which acts against the mass under the force of gravity. The combination of the anti-spring effect with the vertical component of the spring load results in the low resonant frequency of the LaCoste stage. In reality, multiple springs are used to support the load mass of about 300 kg. At each of the four faces of the LaCoste structure, two rigid links with flexures at their ends constrain the movement of the mass load to only the vertical direction. This structure is attached to the inverse pendulums and as

45 Introduction 25 Fig. 1.10: The schematic of the entire AIGO vibration isolator chain showing the main components of the pre-isolator stages, the three Euler vertical stages, the four pendulum stages, and the test mass stage.

46 26 Chapter 1. Fig. 1.11: The two approaches to achieve low resonant frequencies using the concept of anti-springs a) the inverse pendulum; and b) the LaCoste linkage. Fig. 1.12: Diagram representing the tilt rigid 2D wobbly table composed of inverse pendulums and flexures.

47 Introduction 27 Fig. 1.13: The LaCoste linkage forming the first vertical pre-isolation stage. such, does not tilt. Figure 1.13 shows the schematic of the tilt rigid vertical stage that is implemented into the pre-isolation system. The Roberts Linkage The next chapter presents work on the Roberts Linkage, therefore details about the performance and properties of this isolation stage will not be repeated here. The concept of the Roberts linkage stage will be introduced here, and the reasons behind its implementation into the isolation system of AIGO. The Roberts Linkage is the second horizontal vibration isolation stage making up the pre-isolator. It is essentially a 2D compound pendulum and its simple construction, ease of installation and effectiveness are the main reasons the AIGO group use it as part of the suspension system. It has a cube-like frame (Figure 2.6) suspended from wires that are attached to its base and hung from the LaCoste stage. Low resonant frequencies are easily obtainable from this type of linkage. This is because the normal modes depend highly on the geometry of the structure, which is designed to be adjusted easily. The structure achieves near straight-line motion from rigid links and pivots and therefore simulates a long arm pendulum in a rather confined space. As mentioned earlier, center of percussion tuning is important as it effectively defines the isolation floor after the resonant mode.

48 28 Chapter 1. Chapter 2 presents the work done to optimally tune the Roberts Linkage by treating it as a compound pendulum. Euler Springs Research into the use of Euler springs is a major focus of this thesis. The concept of Euler springs was first introduced at UWA in 2000 [12]. An Euler spring is a column of flat spring material that is loaded beyond its buckling load. Chapter 3 describes the Euler buckling concepts and the advantages they have for vibration isolation for gravitational wave detectors. The full description of the vertical Euler stages are discussed in that chapter so it will not be repeated here. Damping and Self Damped Pendulums As discussed, the reduction of the residual motion of the suspended test mass is improved by using N stages of isolation. This means there are N number of normal modes present in the transfer function of the isolation system, some with Q-factors up to 100 times greater than the seismic background noise. The Q- factor is a measure of how much decay is in an oscillating system, a dimensionless measure of the amount of energy the system dissipates at the resonant frequency. The definition is defined below as: Q = f 0 f (1.9) where f 0 is the resonant frequency and f is the full width of the resonance peak in the frequency response of the system, measured at half of the maximum power (ie. at 1/ of maximum amplitude). Since high Q-factors can be seen in the resonant peaks of the various stages, it is important to implement damping into the isolation system. Different techniques have been used to damp out the normal modes, including active and passive techniques. Passive damping systems are more suitable in lower stages and at higher frequencies, where damping forces proportional to velocity are more effective. Active damping using control systems is more appropriate at lower frequencies at the upper stages where large displacements appear. For pendulum style isolation chains, high Q-factor resonances can be damped by active techniques, which senses low frequency motion with respect to the ground.

49 Introduction 29 Low-passed viscous forces are then applied to damp the sensed motion. It is inappropriate to use such a control configuration at a stage of a chain where the noise level is already below seismic [39]. VIRGO uses active control systems to damp the pendulum motion which consists of using position and acceleration sensors and actuators. At AIGO, simple PID (proportional integral derivative) control systems are implemented onto the stages of the pre-isolator. Control schemes for the Roberts Linkage (Chapter 2) and the inverse pendulum (Section 4.4.2, Appendix D) are presented in this thesis. Discussion about the local control scheme is presented in the paper in Chapter 4. In the passive case, damping pendulum modes include using vibration absorbers [40] and eddy current damping [41, 42]. The TAMA group has also developed vacuum-compatible alternating layers of heavy mass and metal-sealed rubber as their form of passive damping for their vibration isolation stack [43, 44]. A simple method to damp normal modes is to just apply viscous damping. However, this method will bypass the isolation in each stage and degrade the performance to 1/f per stage [12]. A method called self-damping was proposed by Winterflood (2001) for AIGO which uses magnetic eddy currents as a form of damping mechanism. It has the advantage of viscously damping against no other structure only on itself. Currently, three stages of self-damped pendulums are on the AIGO vibration isolation system. The basic principle is the viscous crosscoupling of the modes of the same isolation stage, which has different degrees of freedom. The arrangement consists of a rocker mass (or inertial mass) that is supported by a gimbal which itself is attached to the main body of the pendulum. The gimbal acts as a 2D pivot. Strong rare earth magnets and copper plates are positioned closely together and interact with each other to create eddy currents as the pendulum rocks. Figure 1.14 illustrates the concept of the self-damping pendulum. Figure 4.33 in Chapter 4 shows a diagram of one 3D isolator stage where the self-damped mechanisms can be seen. Work done by Dumas [37] revealed that the lowest mode of the four stage horizontal isolation stack of the vibration isolator of AIGO could not be effectively damped. This lowest mode can be visualised as the swinging of the entire 4 stage stack. The reason was because this mode had a frequency that was lower than

50 30 Chapter 1. Fig. 1.14: Schematic of the self-damping pendulum. The rocking motion of the pendulum couples with the inertial mass through the magnet-copper arrangement represented by the dash pots. Magnetic eddy currents are produced to provide the damping mechanism. the resonant frequency of the motion of rocker mass on the 2D flexure. Hence there would be no motion of the copper plates with respect to the magnets and thus the rocker mass motion would couple to the rest of the pendulum. One of the proposed solutions was to increase the inertia of the top self-damping stage which will reduce the resonant frequency of that rocker mass. This was done by rigidly attaching vertical beams of about 1.2 m long which weighed about 7 kg each (shown in Figure 4.29). Good results were obtained that showed a 20 db reduction of that first resonant peak. This concludes Chapter 1, Introduction. Chapter 2 describes research into improving the performance of the second horizontal isolation stage, the Roberts Linkage.

51 Chapter 2 The Roberts Linkage 2.1 Preface Present here is the research on the testing and tuning of the Roberts linkage stage, which led to submission of a paper in the Review of Scientific Instruments. Creation of the analytical models was done jointly by the author and J.C. Dumas, a fellow student. Coding was done with computer packages Mathematica and ANSYS. Results from ANSYS are not presented here but were used as a means of verifying the theoretical model of the Roberts linkage. This finite element modelling software was used to take advantage of its modal analysis using the basic package. A ball and stick model was created which allowed the inputs of the positions of center of mass, probe, suspension load height, as well as the rotary moment of inertia, radius of gyration and all the necessary dimensions required to define our Roberts linkage stage. Harmonic analysis using the package correlated well with the derived mathematical model which was used as the basis of the coding done in Mathematica. The main concepts of the work done using ANSYS is presented in Appendix A. The final model coding in Mathematica was written by J.C. Dumas. The next section gives an introduction to the Roberts linkage. The paper is then presented, which shows the theoretical results that can be achieved by tuning the Roberts linkage by changing some parameters. The Postscript in Section 2.4 discusses the status and implementation of the control system at this isolation stage. 31

52 32 Chapter Introduction to the Roberts linkage The motivation behind the implementation of the Roberts linkage into the AIGO vibration isolation system was its simple structure, which could potentially obtain very low fundamental mode frequencies. The concept was first introduced by Winterflood [12] and was implemented in the pre-isolation stage in 2003 by the author and colleagues at the gravitational wave group of UWA. A high performance vibration isolation system would, ideally, reduce massive amounts of seismic noise and thus minimise the residual motion of the suspended test mass. This would allow cavity lock to be achieved more easily. The residual motion of the test mass can be vastly reduced by the inclusion of preisolation stages with lower resonant frequencies than each individual stage in the stack. The theoretical improvement from the implementation of an ultra-low preisolation stage is illustrated in Figure 2.1. Here a horizontal pre-isolation stage of resonant frequency 0.1 Hz drastically reduces the amplitudes of the normal modes of the system of 2 Hz isolators by about 40 db. Theoretically, high performance vibration isolators can achieve a total RMS motion of about 1 nm above 0.2 Hz [15]. As mentioned in Section 1.4, the AIGO vibration isolation system adopted two horizontal pre-isolation stages; the wobbly table and the Roberts linkage, and one vertical pre-isolator; the LaCoste linkage. In the past, several low frequency passive isolators were proposed, including the crossed wire pendulum isolation system [45, 46], the folded pendulum (Watt s Linkage) [47], and the Scott-Russel Linkage [48]. All three concepts showed good results in the attenuation of seismic noise. The Watt s linkage (Figure 2.2a) achieved about 100 db of isolation at 10 Hz; while the Scott-Russel (Figure 2.2b) reached 100 db at 2 Hz before it faced the undesirable influence of the center of percussion effect which saw the increase of the isolation floor level. Both linkages provided very low resonant frequencies by having the suspension point move in an almost flat horizontal line. Thus the restoring force was extremely low, almost entirely gravitational. In practice, the restoring force was not only from a shallow gravitational hill or well, but also the combination of small spring rates provided by the flexes and strains in the structures.

53 The Roberts Linkage 33 Fig. 2.1: Transfer function curves comparing a vibration isolation system with and without pre-isolation. The dotted curve shows a system of five stages of 2 Hz resonant frequency, while the solid curve shows a system which replaced the first stage with a 0.1 Hz ultra-low pre-isolator [15].

54 34 Chapter 2. Fig. 2.2: Two forms of linkages that can provide low horizontal resonant frequencies; a) the Watt s linkage, and b) the Scott-Russel. One of the main advantages the Roberts linkage has over these other low frequency vibration isolators is its very simple and compact design and operates in 2D quite easily which suits the philosophy behind the construction of the high performance compact AIGO isolation system. One benefit it has over the existing and successful Scott-Russel is the orientation of supporting points which are spread out on the horizontal plane, as opposed to all the points vertically positioned one after another [48]. The construction of the Roberts linkage is much simpler from an engineering point of view. The implementation of the Roberts linkage as being part of the pre-isolation stage of the AIGO suspension system is relatively easy and it is located between the LaCoste linkage stage and the start of the 3D isolation stack. The performance of the Roberts linkage relies heavily on the geometry of the structure. Figure 2.6 in Section shows the schematic of the isolation stage which suspends a load from its top middle position of the rigid structure. As explained in that section, the path of the point of suspension P can be either flat, concave up or convex up, which determines the stability and resonant frequency of the stage.

55 The Roberts Linkage 35 Garoi in 2003 [35] was the first to report successful tuning of the Roberts linkage for gravitational wave detection. A single stage Roberts linkage was tested with no stages suspended from it. The tuning of the fundamental mode frequency of the Roberts linkage was relatively simple, and has achieved a resonant frequency of 0.05 Hz. This was done by adjusting the four suspension wires to a suitable length, then straining each of the suspension wires to equal tension. A total of 60 kg of weights were also placed on top of the structure and distributed such that the center of mass came very close to the height of the Roberts linkage suspension points plane (to achieve low resonant mode frequencies). However, it was found that the isolation floor at frequencies above the fundamental mode did not pass 32 db of noise attenuation. It was predicted that with suitable center of percussion tuning, a 20 db at 1 Hz isolation can be achieved. The main difference of the work done by Garoi and of the work here is that a full isolation stack was suspended off the Roberts linkage. This did not allow for the tuning of the center of mass height by the distribution of the heavy weights that were on top of the previous Roberts linkage. Smaller and much lighter weights were used instead for the adjustment of the radius of gyration and the balance of the structure (described in the next section). The adjustment of the mass load height allowed for the resonant mode frequency tuning. Following the assembly of the full vibration isolation system in the laboratory at UWA, testing of the Roberts linkage with all four stages of horizontal pendulums and three Euler vertical stages suspended from it was carried out. Balancing the entire suspension system was complex and involved observations at each isolation stage to ensure maximum structural travel range for testing. The Roberts linkage currently has about ±50 mm in the horizontal plane before coming into contact with the top frame of the inverse pendulum which makes up the wobbly table. However, the dynamic range of the shadow sensor, located at the corner section of the top frame of the Roberts linkage, is only ±5 mm (Figure 2.3). This sensor was measured with respect to the inverse pendulum frame and not the ground. A shadow sensor commonly used in the sensing of motion of the isolation parts consists of a split diode arrangement together with a shadow piece (attached to the moving part), which partially blocks the light

56 36 Chapter 2. Fig. 2.3: Top view of the Roberts linkage shadow sensor which detects motion with respect to the inverse pendulum platform. beam shining from an LED positioned locally. As the shadow piece moves, the current generated in the diodes changes by detecting the variation in the amount of light received. The balancing of this first horizontal pre-isolation stage involved ensuring all four wires suspending the Roberts linkage were of equal length. A crude way of doing this was to measure that the tension of each wire was equal. Finer balancing was done by distributing small weights on top of the Roberts linkage frame. The later step was surprisingly sensitive, indicating proximity to the desirable state of instability to achieve low resonant frequencies. Preliminary results before fine tuning showed a resonant frequency of about 0.16 Hz (Figure 2.4). (NB. Results above the frequency of 1 Hz are not shown here.) The testings for the center of percussion effect between the frequencies 1 Hz and 10 Hz are shown in Chapter 4 and briefly mentioned in the Postscript later in this chapter. The transfer function shown in Figure 2.4 corresponds to the excitation input at the base of the wobbly table stage, and the output at the corner upper frame of the Roberts linkage. Figure 2.5 illustrates the experimental setup which shows the input signal provided by a large speaker actuator (connected to the ground) and rigidly attached to the inverse pendulum frame by a steel rod. During the time of testing, one 2D shadow sensor was used as

57 The Roberts Linkage 37 Fig. 2.4: The transfer function at the Roberts linkage stage while suspending the full isolation stack. the output. Modelling showed the peak that appeared just before 1 Hz originated from the first mode of the isolation stack which was hung below this pre-isolation stage (Chapter 4). Horizontal transfer functions of the full isolations system are described and seen in Figure 4.35 in Section and also in the paper co-written by the author that appears in Appendix D. The peak at 0.6 Hz is due to the rotational mode of the Roberts linkage, and this was verified in the monitored time signals.

58 38 Chapter 2. Fig. 2.5: The top view of the experimental setup showing the large speaker acting as the input actuator at the inverse pendulum frame. The speaker and frame are rigidly attached by a steel rod. The inertia of the speaker stand is increased by the addition of 10 kg weights evenly distributed on its shelves to maximise the effective input signal amplitude of the speaker actuator.

59 The Roberts Linkage Roberts Linkage Mathematical Analysis Paper Modelling and Tuning of a very low frequency Roberts Linkage Vibration Isolator J. C. Dumas, E. J. Chin, C. Zhao, J. Winterflood, L. Ju, D. G. Blair School of Physics, The University of Western Australia, Nedlands, WA 6009, Australia We present an analytical model for a Roberts Linkage vibration isolator used as a preisolation stage at the Australian International Gravitational Observatory (AIGO). The Roberts Linkage is a structure that simulates a very long radius conical pendulum in a relatively small height. We show through an analytical solution that it is possible to independently tune the center of percussion and the resonant frequency for arbitrary geometrical configurations. The result is shown to enable a practical tuning solution to be devised which allows near ideal vibration isolation to be achieved Introduction Interferometric gravitational wave detectors require high performance vibration isolation systems to isolate test masses from ground motions. In addition to isolating vibration in the gravitational wave detection band it is critical that lowfrequency residual motion be reduced to the lowest possible amplitude as this largely affects the ease with which high finesse cavities can be locked. The main control effort required is in applying large forces to counteract low frequency residual motion which bypass the isolation system below its cut off frequency (a few Hz). Reducing low frequency motion down to nanometre levels for frequencies above 0.2 Hz can greatly reduce the required servo control forces and reduce injected noise [49]. Isolation performance and especially low frequency isolation can be greatly improved by the addition of one or several Ultra Low Frequency (ULF) stages, also called pre-isolators. The need for ULF has led to the development of several designs such as the X-pendulum [46], the folded pendulum (Watt s Linkage) [50], and the Scott-Russel Linkage [48]. The Roberts linkage was first proposed as a ULF stage by Winterflood [12]. It has been investigated recently [35] and has been

60 40 Chapter 2. incorporated into the isolator design currently under development by the UWA gravity group for use in the AIGO High Optical Power Test Facility [51]. The full system consists of a three dimensional pre-isolator followed by the Roberts linkage horizontal pre-isolator from which three 3-dimensional isolation stages are suspended. Preliminary test of the Roberts linkage [35] with no suspended load have shown promising results, with a resonant frequency of 50 mhz. However the high frequency isolation was limited to a floor of 32 db due to poor tuning of the center of percussion effect. In this article we will first introduce a geometrical model for the Roberts linkage. It will then be used to build an analytical model for the performance of such a device used as a isolation stage. Finally we will use the model to determine a suitable procedure for tuning a Roberts linkage using our prototype as an example The Roberts Linkage The principle of the Roberts Linkage lies in a simple geometrical effect that results in point P as shown in Figure 2.6(a) moving in a very shallow arc [12, 35]. The closer this point is to the horizontal plane that contains the suspension points of the Robert Linkage (point A and B) the more shallow the arc. If P is exactly in that plane it moves in a completely flat path. The arc is concave up if P is below the plane, and convex up if it is above the plane. The 1-Dimensional geometry can be extended to a 2-Dimensional horizontal isolator by joining two Roberts Linkages at right angle as shown in Figure 2.6(b). While the structure is over constrained, the intrinsic material flexibility of the suspension wires make it a practical solution. A more elegant design is to use three suspension wires which removes the over constraint. Small scale 3-wire designs have been used by the UWA group with good results [52, 53, 54]. However the 4 wire cubic design was preferred for our isolation design as it is better suited for integration into the orthogonal geometry of a laser interferometer. The frequency of the Roberts Linkage is tuned by arranging the system so that its gravitational potential energy is almost independent of displacement. This leads to a low restoring force and therefore a low resonant frequency. The

61 The Roberts Linkage 41 Fig. 2.6: a) 1-Dimensional Roberts Linkage diagram. b) A 2-dimensional Roberts Linkage design. restoring coefficient must however remain positive to satisfy stability requirements. In practice material stiffness (e.g. suspension wires) adds a small spring like restoring force. To balance this the locus of point P usually needs to be made slightly convex up. With an ideal Roberts Linkage, the frame would be massless and the tuning process would be relatively straight forward. One could either carefully adjust the height of the suspension point to achieve the above requirements, or set the suspension point at the height where it would move in a flat plane thereby eliminating the dependence on the mass load. Then a small mass added at an adjustable height near the suspension point could allow fine tuning. In a realistic system however, the structure such as the cube shown in Figure 2.6(b) has a significant mass. This has two effects on the performance of the Roberts Linkage. The first is that the position of the center of mass of the frame adds to the total gravitational potential. Since the center of mass follows a concave up potential well due to its low height, it increases the restoring force. This can be compensated by either moving the suspension point of the 3D stack higher, or adding mass on top of the Roberts linkage to lift its center of mass. The later is only practical for very low mass designs such as our small three wire units [52, 53]. It is impractical for our relatively heavy pre-isolation stage. The second

62 42 Chapter 2. effect arises from the fact that the Roberts linkage frame has a distributed mass with a significant moment of inertia. This results in a center of percussion effect such as that of a compound pendulum as illustrated in Figure 2.9. The isolation performance at high frequencies will be limited and will depend on the location of the suspension point. The point at which the high frequency isolation approaches infinity is the center of percussion. The amount of isolation and the position of the center of percussion are related to the radius of gyration and the position of the center of mass. Analysis of the center of percussion tuning requirements is simple if one recognises that the Roberts linkage is effectively a compound pendulum folded half-way along. If we consider one half of the Roberts Linkage as illustrated in Figure 2.7(a) we notice that the angle of the two links with respect to the vertical is always equal. If we flip the second link (the frame) upside down we obtain Figure 2.7(b) which has an equivalent horizontal motion. Fig. 2.7: The horizontal motion of the Roberts Linkage is that of a pendulum as illustrated here. Note in (a) that each link forms an equal angle with the vertical; (b) shows an equivalent horizontal motion. It follows that the Roberts Linkage will behave similarly to a compound pendulum with dimensions such as shown in Figure 2.8, with the same mass and the same radius of gyration. The vertical motion would be different which results in the much lower frequency of the Roberts linkage. The horizontal motion however

63 The Roberts Linkage 43 is equivalent, and therefore the center of percussion behaviour would be exactly the same. Fig. 2.8: The Roberts Linkage (a) has an equivalent compound pendulum (b). Since the Roberts linkage is equivalent to a compound pendulum it has a transfer function as illustrated in Figure 2.9. The resonant frequency will be dependent on the mass distribution and the suspension point, and the high frequency isolation floor will depend on the distance between the suspension point and the center of percussion Analysis Because a practical Roberts linkage has symmetry about a central axis, it is possible to model the system in 2D without loss of generality. We take a Lagrangian approach to deriving the frequency of a Roberts Linkage as a function of any variable of the setup. We define the potential energy of the entire structure as a function of the displacement angle θ. To obtain the potential energy we first define the vertical position of the center of mass of the Roberts Linkage frame Y c and the suspension point Y p. From Figure 2.8 we can write the following: Y c = l w cos(φ + θ) + l c cos(α + θ) (2.1) Y p = l w cos(φ + θ) + l p cos(β + θ) (2.2)

64 44 Chapter F requency respons e 40 dbl H Resonant frequency Isolation floors Perfect tuning Frequency HHzL Fig. 2.9: Typical frequency response of a compound pendulum. The high frequency isolation is limited by the tuning of the center of percussion. Here we see several curves for arbitrary configurations of the center of percussion, including one that is perfectly tuned. The gravitational potential energy is simply E g = mgh. If the frame has mass m and the suspended load has mass M, then we can write: E g = mgy c + MgY p (2.3) Now, the torque T produced by the gravitational force is the derivative of the energy T = d dθ E g (2.4) And the angular spring coefficient that corresponds to the gravitational restoring force is the derivative of the torque as: kθ grav = d dθ T (2.5) The total restoring force is the sum of the gravitational force, and that due to the stiffness of the suspension wire. kθ = kθ grav + kθ wire (2.6)

65 The Roberts Linkage 45 Finally we define the Moment of inertia I 0 of the Roberts Linkage about its suspension point using the equivalent pendulum as discussed in the previous section. I 0 = m(r 2 g + (H + h) 2 ) (2.7) Where r g is the radius of gyration. The frequency can then be obtained from the relationship kθ ω = (2.8) I 0 This model allows us to consider the relationship between the resonant frequency and any of the design variables such as the locations of the center of mass, the suspension point, the frame mass, the load mass etc. As previously discussed, we must also tune the Roberts Linkage such that the suspension point is located close to the center of percussion. To determine the amount of isolation that will be obtained at high frequencies we use the compound pendulum transfer function [40, 35] which, as argued in section also applies to the Roberts Linkage Here X p X 0 = (1 A( ω ω r es )2 ) 2 + Q 2 (1 ( ω ω r es )2 ) 2 + Q 2 (2.9) A = r2 g d c d p (2.10) rg 2 + d 2 c Then the isolation floor at high frequency will be X p A (2.11) X 0 For the Roberts Linage, this corresponds to: X p r2 g (H + h)d p (2.12) rg 2 + (H + h) 2 X 0 Therefore the high frequency isolation floor is related to only three variables, the radius of gyration, the position of the center of mass, and the suspension point Tuning Modelling Initial testing of our Roberts linkage pre-isolator has shown that while we can easily tune the resonant frequency to an acceptable 45 mhz, our high frequency

66 46 Chapter 2. isolation floor is very poor. To determine a method of tuning the Roberts linkage and achieve an acceptable performance, we use the theoretical model to predict the effect of changing the various parameters that are accessible. The characteristics of the prototype are summarised in Table 2.1. The frame has a mass of 29.6 kg. It has radius of gyration m and a width of m. The center of mass is m above the bottom of the frame and the vertical height of the suspension wire is m. The mass load is 160 kg. Tab. 2.1: These are the parameters of our Roberts Linkage prototype that will be used here as an example. The symbols are defined in Figure 2.8. Rob. Link frame mass m 29.6 kg radius of gyration r g m center of mass height h m suspension height H m width W m load mass M 160 kg First we consider the effect of changing the height of the suspension point, as shown in Figure Note that the suspension height is scaled such that 0 is in the plane containing the four suspensions of the Roberts Linkage frame. We can immediately see that in the current configuration we will not be able to find a satisfactory compromise by only adjusting the suspension height. Also note that the only effect of introducing a restoring spring force corresponding to the stiffness of the suspension wires is to simply shift the frequency curve to the right. Other variables cannot be changed directly without redesigning the structure. The only practical way of tuning the Roberts Linkage other than adjusting the suspension point is to add small masses on the frame. This changes the mass of the frame, the location of the center of mass and the radius of gyration. It is possible to change the radius of gyration independently of the center of mass, by distributing masses around the center and changing their separation while keeping them in the same horizontal plane. From Figure 2.10 we chose a suspension height of 2.5 cm as it already provides a relatively low frequency. Adding mass on top

67 The Roberts Linkage Isolation Limit Resonant frequency Isolation Floor (db) Resonant Frequency (Hz) Suspension point height (m) Fig. 2.10: Here we show the effect of changing the height of the suspension point. of the Roberts linkage will lower the frequency and will shift the location of the center of percussion. In Figure 2.11 we show the effect of adding mass 15 cm above the plane of suspension of the frame. The added mass is assumed to have a radius of gyration of 20 cm (ie. the masses are distributed on a circle of radius 20 cm). Note that since the distance from the center of mass of the frame to the added mass is less than the radius of gyration, adding mass decreases the total radius of gyration. From Figure 2.11 we chose a value of 4 kg, as any more would bring the system too close to instability. Finally we can tune the center of percussion almost independently of the frequency by changing the separation of the added masses while keeping them in the horizontal plane. This is because changing the radius of gyration of the frame has little effect on resonant frequency but strongly tunes the center of percussion. By carefully adjusting the tuning masses so that they are laid on a radius of 39cm, we are able to tune the center of percussion to achieve an isolation floor

68 48 Chapter Isolation Limit Resonant frequency 0.15 Isolation Floor (db) Resonant Frequency (Hz) Added mass (kg) Fig. 2.11: Adding small masses at an arbitrary height on the frame also tunes the Roberts Linkage.

69 The Roberts Linkage Isolation Limit Resonant frequency Isolation Floor (db) Resonant Frequency (Hz) Radius of gyration of tuning mass (m) Fig. 2.12: By changing the position of the tuning masses while keeping them in the same horizontal plane we can fine-tune the COP almost independently of the resonant frequency.

70 50 Chapter 2. of 60 db. Following this procedure, the Roberts linkage would now be tuned to a resonant frequency of approximately 30 mhz, and a isolation floor of at least 60 db Discussion A geometrical model for a very-low frequency vibration pre-isolator based on the Roberts linkage has been introduced. The model identifies equivalent systems to the Roberts linkage geometry which simplifies calculations of the Roberts linkage isolation performance. A simple analytical model predicts the resonant frequency and the isolation floor of the isolator. Using this model, it can be shown that there is a solution to tuning both the resonant frequency and the center of percussion. We suggest a simple tuning solution using small mass displacements after adjusting the suspension point of the load. It was demonstrated that a cubical Roberts Linkage could be tuned to a resonant frequency of approximately 30 mhz, and a isolation floor of at least 60 db Acknowledgments This work is part of the Australian Consortium for Interferometric Gravitational Astronomy collaboration (ACIGA) funded by the Australian Research Council. The AIGO facility was funded by the DEST Systemic Infrastructure Program.

71 The Roberts Linkage Postscript Work to compare the theoretical with the experimental results of the Roberts linkage pre-isolation stage was not completed in the limited time available for this project. The AIGO group had planned to start implementation of the full vibration isolation system at Gingin during the stage when testing and tuning of the Roberts linkage were underway in the laboratory at UWA. The models presented here were used successfully to guide tuning of the pre-isolation stage. A set of transfer functions showing tuning of the Roberts linkage from the theoretical analysis was done following the submission of this paper. This is shown in Chapter 4 in Figure 4.34, where the potential benefits of center of percussion tuning at the Roberts linkage stage are shown. The tests involved the adjustments of the load suspension height and the addition of masses to the top of the frame structure. Inputting real parameters into the model suggests that we increase the suspension height by a few centimeters to lower the resonant frequency, followed by the addition of masses to improve the isolation floor. The results confirmed the general direction in the variation of the parameters mentioned is correct. However, both the quantitative values of the resonant frequency and the isolation floor became slightly worse than predicted, probably because the parameters of the real system were imperfect. Also, the height at which the Roberts linkage is suspended from on the LaCoste frame is not the true height; the thickness of the wire contributes to a position change of the effective suspension height (as in the case for the Euler stage in Chapter 3). In summary, the test results performed on the verification of the predictions based on the model concluded that qualitatively the model is correct and can be used to approximate the state at which the Roberts linkage structure is at. The model provides a guide for the user to change the various parameters to obtain better performance as illustrated in Figure Control system of the Roberts linkage Control systems applied at the pre-isolation stages rather than further down the isolation chain minimises the transfer of seismic noise through the actuators and

72 52 Chapter 2. sensors mounted on the ground down to the test mass. Efforts were made to control the Roberts linkage stage, mainly to counteract diurnal thermal drifts. Some came from creep of the wires suspending the Roberts linkage, which hold about 260 kg of mass. The Roberts linkage stage is suspended from the LaCoste stage which is a tilt rigid structure (Section 1.4.1). The four wires form the medium that the control system acts upon to influence the Roberts linkage to move in a certain direction. The sensing is done using a shadow sensor (described previously). Position control is done by heating the wires, which increase in length as current is applied. Since diurnal changes are at very low frequencies, a very small integral gain is used in the PID control scheme (Figure 2.13). A small gain means that only small amounts of current are used at one time so the amount of electronic noise that is injected into the system is minimal. A description of the hardware used and the process involved in the setup needed to acquire control is presented later on in Chapter 4 in Section 4.4. Also, control of the pre-isolation stages are discussed in more detail there. Fig. 2.13: The control schematic of the Roberts linkage isolation stage. The position of the Roberts linkage is sensed through a shadow sensor located at the top of the Roberts linkage and fed back to the PID control system. Each of the four wires are heated independently with four power supplies, as shown in

73 The Roberts Linkage 53 Figure 2.14 (ie. there are four output signals). Each wire is responsible for one of the two axes in the horizontal plane. A constant current was initially supplied as this permitted the shortening of the wire (when the current is decreased) as well as lengthening and is controlled by the PID control system 1. Cross-coupling into the other directions is minimised since the layout is designed so that the four suspension wires are either perpendicular or parallel to each other. These suspension wires can withstand higher currents than 2 amps but this value was sufficient because the control system does not require a fast response. In several sections, the electrical wires used to connect from the power supplies to the suspension wires are only 0.25 mm thick, and it was known that any current higher than 2 amps would melt them. These electrical wires are made thin to minimise the transmission of vibrational noise from the upper stages. Motion control is also limited to the resistance and the thermal expansion coefficient of the suspension wires. Fig. 2.14: Diagram showing the suspension wires of the Roberts linkage individually controlled by the current source. 1 Having initially no current in the wires would only allow the suspension wires to lengthen by the increase in current.

74 54 Chapter 2. Response time for the suspension wire to respond to current inputs of the Roberts linkage was measured. Results showed that an input of 2 amps to one single wire caused the Roberts linkage structure to exceed the shadow sensor dynamic range and become unbalanced. A thermistor was attached onto one of the suspension wires and was monitored during the testing. The step input of a 2 amp current increased the wire temperature exponentially and took about 200 seconds before it reached steady state. The temperature of the wire increased about 3.7 C (from 21 C to 24.5 C) and took about 300 seconds to cool back down to room temperature. As mentioned above, the response time to control the position of the Roberts linkage was quite large because we only deal with temperature change diurnally. Hence the wire response to the current input is sufficient for this type of control system to work. Since all the control testing was done in the laboratory at UWA, the results gained served as an upper band in the performance. Human activity in the laboratory at UWA is a main source of noise and will be significantly reduced in the vacuum clean tank up at AIGO. Temperature will be closely controlled at AIGO hence diurnal drifts will be minimal compared to those at the laboratory at UWA. Currently, the vibration isolation system is being assembled at AIGO as Class A 2 vacuum clean parts. When two have been built, completing a one arm Fabry-Perot cavity, testing of the isolation system will continue in the more controlled environment. 2 Hardware included in this category are the interferometric optics, suspension system and all other interferometer hardware that are prepared for installation in vacuum [55].

75 Chapter 3 Vertical Euler Spring Isolation 3.1 Preface The paper presented here was published in Physics Letters A in The experimental setup and fundamental research are included in my Honours thesis along with a few preliminary results. The author thanks Kah Tho Lee, a visiting student who assisted in some of the measurements collected, including some creep measurements. The author is very indebted to Dr. Riccardo DeSalvo from the LIGO group who provided the maraging steel for us to manufacture into Euler springs of the required thicknesses. 55

76 56 Chapter Introduction to Euler springs The gravitational wave group of UWA was the first to propose the use of light weight Euler springs as the main form of vertical vibration isolation [56]. The springs have replaced the cantilever type springs which are commonly used by other groups. This section describes the properties and behaviour of the Euler buckling springs, and serves as an introduction to the uses of these springs for gravitational wave detection. In Section 1.3.1, it was stated that the vertical component vibration isolation is important due to the cross-coupling with the horizontal direction. Conventional methods include the use of elastic elements in the form of mechanical springs to temporarily store the vibrational energy being transmitted from the ground. These elements also support the heavy mass loads from the gravity pull. The amount of this static energy the spring element can store is proportional to the spring mass; heavy loads require heavy springs for support. The disadvantage of this is the presence of low frequency internal modes, as illustrated in Figure 3.1 as compared to the relatively light horizontal pendulum isolators. Cantilever springs have internal modes appearing at a few tens of hertz [12]. It would be desirable to increase the internal modes above the detection bandwidth of gravitational wave detectors. The concept of using other means of isolating the vertical component of seismic noise was suggested by Winterflood 2001 when he showed that the internal mode performance of cantilever springs was unsatisfactory. He described as ideal a spring type mechanism that could store only the dynamic vibrational energy to attenuate the noise and not worry about the static gravitational energy needed to support the mass load. This would reduce the spring mass required to perform the same function as well as increasing the frequencies of the higher order modes. At this stage in time, Euler column buckling springs were mentioned and was soon led to the development of mathematical models, Euler stage designing and experimental testing. As mentioned previously, conventional springs store static energy due to the mass load they support. This is usually large compared to the vibrational energy (dynamic energy) described in the first chapter. A linear spring will have a

77 Vertical Euler Spring Isolation 57 Fig. 3.1: Graph showing internal mode frequencies appearing at lower frequencies than the horizontal pendulums due to heavier spring elements for vertical isolation. Fig. 3.2: Force versus displacement plot of conventional springs, showing a large portion of the energy stored is static (adapted from [56]). typical behaviour shown in Figure 3.2. The resonant frequency is dependent on the extension of the spring as shown in Equation 1.5 in Section The Euler spring is described as a column of spring material that is compressed beyond its buckling load. One advantage the Euler spring has over a conventional one is its property of storing minimal static energy under operation. This is a property of a column of an elastic material, where the material undergoes virtually

78 58 Chapter 3. Fig. 3.3: Force versus displacement plot of Euler springs, showing virtually no static energy being stored (adapted from [56]). no deflection when loaded until a critical load is reached whereby it deforms in a linear fashion. Thus an Euler spring has a force-displacement curve similar to that shown in Figure 3.3. The advantage of minimal stored static energy is that a reduced spring mass is required to support the same mass load. Thus the internal mode frequencies of the vertical stage increase improving the isolation bandwidth. Tests have shown internal frequencies start appearing about Hz [56]. The physical shape of the Euler buckling springs allow compact forms of 3D vibration isolation systems to be built for AIGO. The critical load where the force acts axially along the length of the spring in the pin-ended case is according to Equation 3.1. The critical force is four times as much for the clamp-ended case. Here P cr is the critical force, E the Young s modulus of the spring material, I the area moment of inertia calculated along the bending axis, and l is the length of the spring. P cr = π2 EI l 2 (3.1) An important property of the Euler spring is that the resonant frequency just at the start of buckling is only dependent on the length of the spring. What is remarkable is that there is a factor of two appearing in the denominator, and so the mass moves as if though the Euler spring has effectively extended by twice its length (Equation 3.2 where g is the gravitational constant). The equation can be

79 Vertical Euler Spring Isolation 59 derived from the stiffness k called the spring rate (Equation 3.3) or the constant of proportionality seen as the straight line in the Figures 3.2 and 3.3. k = mg 2l (3.2) ω = k g m = 2l (3.3) For the Euler stage to effectively operate as a vibration isolator, the motion of the springs must be constrained such that their compression is in the desired longitudinal direction in the vertical plane. A configuration consisting of a pair of pivoted rotational arms provides this constraint (Figure 3.4). The mass which loads the springs is suspended from the end of the rotational arm with steel wires that are attached to the arms using a hook method. compressed in the desired fashion as seen in the diagram. The Euler springs are This configuration naturally gives a dual wire suspension which has advantages. The angular flexing spring rate is decreased by a factor 1/ 2 as compared to using a single wire. Also, the maximum swing angle before over-stressing occurs is increased by a factor of 2 1. It is briefly mentioned in the next section, that an Euler spring implemented into the rotational arm configuration can compress in one of two ways: buckling towards the pivot, or away. Studies show the behaviour of the spring differs dramatically in the two different compressed states [56, 57]. The spring with a buckling offset away from the pivot of the rotational arm has low spring rates and states of instability can be achieved. A spring buckling the other way always has positive and high spring rates. Where an equal combination of Euler springs buckling towards and away from the pivot is used, an almost linear spring rate can be achieved, similar to a single axially loaded spring. It is thus theoretically possible to have a combination such that the Euler vertical stage achieves very low resonant frequencies. 1 The diameter of two wires can decrease their diameters by 2 to support the same load as one wire, and the spring rate of an infinite length flexure varies as its diameter squared and the square root of its loading [12].

80 60 Chapter 3. Fig. 3.4: The Euler vertical stage configuration consisting of rotational arms to constrain the motion of the springs to the vertical direction (adapted from [56]). The thickness of the Euler springs required for that stage of vibration isolation, can be calculated according to the following formulae. For the clamp ended case, at the point of buckling, the critical load for one spring is: P crit = 4π2 EI l 2 (3.4) where E is the spring material Young s modulus, I the area moment of inertia, and l the length of the spring. The area moment of inertia (for a rectangular cross section) is defined as: I = wt3 12 (3.5) where w is the width of the spring, and t the thickness. Now from Equation 3.3 and making ω = 2πf, we can re-arrange to find the spring length l to be: l = g 8π 2 f 2 (3.6) Hence, combining Equations 3.4, 3.5 and 3.6, the thickness of the spring t can be obtained in terms of the resonant frequency (f in Hz), the number of springs (N), Young s modulus (E), and the width of the spring (w): 3Nmg t = π 6 Ef 4 w (3.7)

81 Vertical Euler Spring Isolation 61 The previous equation acts as a guide in choosing the required spring thicknesses for each Euler stage and works pretty well. Note that it is assumed that equal combinations of Euler springs that are buckling towards and away from the rotational arm pivots are used since Equation 3.4 assumes an axially loaded case. The group uses four pairs of springs per stage with the same size width of 12 mm, and a Young s modulus of 150 GPa (maraging steel). The main reason for the material choice is because of creep issues observed during testings and is discussed later. One of the issues observed in the testing of the setup is the non-linearities in the force-displacement curves. This is because the springs do not behave in an ideal manner. Thus it is difficult to reach the predicted low resonant frequencies based on theoretical models. One of the main factors contributing to the non-linear behaviour of the Euler spring is the boundary conditions which are dependent on the clamping mechanism. Results of investigating launch angles are presented in the following paper which shows the potential in reducing the curvatures seen in the force-displacement curves and thus improving the dynamic operating range of the Euler stage. Methods to further reduce the spring rate of the Euler vertical stage is by the incorporation of anti-springs. This follows from the discussions above about ways to reduce the fundamental resonant mode by means of using anti-springs, or structures which have negative spring constants. The concept of implementing anti-springs into the vertical isolation stage to reduce the resonant frequency has been adapted by other gravitational wave groups. The VIRGO group has incorporated magnetic anti-springs (Figure 3.5a) whereby the anti-restoring force comes from the repelling magnets which act to push the cantilever away from its operating position [30]. The AIGO group has developed a torsion crank mechanism, which involves pre-stressing the torsion rods and by geometry results in regions of low gradients in the force-displacement plots [58]. Cantilever spring blades have been developed for the new generation seismic attenuation system for LIGO [59, 60]. The springs are made to incline in a curved trajectory generating the desired vertical spring effect. A recent improvement of this type of vertical isolation system is through the use of the geometric anti-spring [61], mainly be-

82 62 Chapter 3. Fig. 3.5: Two anti-spring concepts a) the magnetic anti-spring, and b) the torsion crank. cause of its simplicity by reducing the number of mechanical parts which removed some undesirable low frequency resonances. Research presented here used geometric anti-springs, with the negative spring constant relying on the geometry of the rotational arm. The anti-spring essentially comes from the relative positions of the mass load suspension point, and the upper spring end of the compressed Euler spring. The new structure effectively acts like an inverse pendulum to the suspended mass load. By combining the anti-spring with the positive spring rates contributed by the stiffness in the pivot flexure, the Euler springs, and from the stiffness of the suspending wires, low resonant frequencies of the Euler stage are achieved. Creep. Various spring materials were tested. Initially, springs were from feeler gauge strips because there was a large range of spring thicknesses and they were freely available. The feeler gauge steel was AISI C1095 tool steel. These strips were not intended to be used as the final spring material for use in the detector as they were coated by a non-vacuum compatible layer. A major problem of creep was realised during experimentation. Creep is a process that is triggered by atomic level thermal fluctuations in the material which eventuates to dislocations in the grain boundaries. A point of grain failure is reached when a sufficient level of stress has built up and reaches the yield stress

83 Vertical Euler Spring Isolation 63 of the material. At this moment, stress is released emitting acoustic energy and results in the minute drooping of the spring system. The problem of creep is not new to vibration isolators for gravitational wave detection. The group here at UWA has previously reported the level of creep in cantilever springs [62]. Tests for creep was deemed necessary when the author observed the sagging of the spring was noticeably high, about 30 µm per day in initial testings. Consequently, other Euler spring materials were tested, including tempered CS1075 tool steel and AISI 301. Groups including TAMA, VIRGO and GEO all use maraging steel, which is a martensitic air hardened steel. The UWA group decided to conduct tests with this material for one Euler stage and was soon manufacturing Euler springs out of this material. The VIRGO group showed that this alloy can be easily hardened to a high level due to its composition (mostly of nickel, cobalt, molybdenum and titanium), and is therefore used for their cantilever springs [63]. It stops the propagation of dislocations because of the presence of intermetallic precipitates in its atomic structure, thereby reducing the effects of creep. A paper published by DeSalvo 2005 [64] assessed the problem of creep and its influence on the performance of vertical isolation systems, particularly issues with Q-factors and hysteresis. It is known that the kinetic energy from the spring oscillations decreases as the frequency squared. At the point of critical damping (Q factor is unity) the restoring forces become so weak that lossy frictional forces dominate and the springs fail to function. A method to bring the resonant frequency down further is by using different spring materials that can impede the travel of dislocations, or to use materials that have no dislocations at all. DeSalvo proposed the use of glassy materials which have the characteristic of having no crystal structure (amorphous) and have no dislocations with the advantages of increased strength, and larger elastic strain and toughness. Another way to minimise creep is to avoid the concentration of stresses in the material since excess levels of stress can lead to plasticity, even in precipitation hardened metals [36]. The VIRGO group has performed tests of acoustic emission, caused by the sudden release of strain energy from a localised source, in maraging steel blades [65]. The study of acoustic emission was done to evaluate its relevance as a potential

84 64 Chapter 3. source of non-stationary noise; a creep event causing acoustic emission in the steel may simulate a gravitational wave burst. The group concluded that a method to reduce the ultrasonic acoustic emission is by the application of several stress cycles in the spring material prior to installation.

85 Vertical Euler Spring Isolation Vertical Euler Stage Paper Low Frequency Vertical Geometric Anti-Spring Vibration Isolators E. J. Chin, K. T. Lee, J. Winterflood, L. Ju, D. G. Blair School of Physics, The University of Western Australia, Nedlands, WA 6907, Australia Euler spring vibration isolators can be significantly improved by implementing antispring techniques. Here we report geometric spring coefficient reduction techniques which allow an order of magnitude improvement in the effective spring coefficient, achieving a resonant frequency of 0.3 Hz. In this paper we analyse the various effects which determine the behaviour and stability of low frequency Euler stages Introduction Vibration isolation systems have been greatly improved to meet stringent demands for successful gravitational wave detectors. Their purpose is to attenuate seismic vibrations from the ground to levels below the internal thermal noise of the test masses. This is achieved by using a system of cascaded mass-spring harmonic oscillators in which each mass is suspended with soft restoring forces. The level of isolation improves as the characteristic frequencies are reduced, and as more stages are cascaded. To attenuate vertical seismic motion, vibrational energy between the suspension point and the test mass has to be momentarily stored and then recovered with low loss from a spring or a similar element. Many new techniques have been developed. The gravity group at the University of Western Australia (UWA) first introduced the use of curved cantilever springs in 1990 for gravitational wave applications [34, 66]. These are now widely used for vertical isolation. The superattenuators of VIRGO [30, 31] have sets of triangular cantilever springs. GEO600 uses similar blades [67]. Both VIRGO and TAMA [68, 43], use blade structures combined with anti-spring methods to lower the resonant frequency [33]. LIGO is developing active vibration isolation [23] in which very sensitive seismometers are used to suppress noise by actuation on a relatively stiff isolation structure. In

86 66 Chapter the UWA gravity group introduced Euler springs for vibration isolation [56]. These have significantly improved performance compared with blades due to their low mass and high internal mode frequencies. It is planned that together with a LaCoste linkage [12], three stages of Euler spring isolators will be used for the vertical vibration isolation system for the Australian International Gravitational Observatory (AIGO). In this paper we show that by implementing anti-spring techniques the resonant frequency of Euler springs can be significantly reduced. First we give an introduction to Euler springs including results from previous studies. Then we analyse a configuration in which an anti-spring is included in the suspension structure. In section predictions are compared with experimental results Euler Buckling and Non-Linearities An Euler spring is a column of spring material that has been compressed elastically beyond its buckling load. A major advantage in using this type of spring is that it stores negligible static energy below its working range thereby minimising both the stored elastic energy density and the spring mass required to support the suspended test mass [56]. As a result the resonant frequency of the internal modes of the spring elements is increased, thus broadening the isolation bandwidth. An ideal Euler spring by itself produces an almost constant spring coefficient over a large working range. Also, the spring is small in size compared to its equivalent cantilever spring allowing for the construction of more compact 3D vibration isolators. Preliminary analysis [57] and testing reveal that the performance of Euler springs can be strongly manipulated by their constraining mechanism. Pivoting rotational lever arms (see Figure 3.8) are used to constrain the loading direction and displacement allowing them to be compressed in the longitudinal direction. The spring deformation may be either towards or away from the pivot point. These two alternatives yield quite different force-displacement curves which differ significantly from the ideal behaviour discussed above. It has been shown that an Euler spring buckling towards the pivot has non-linear and much lower effective spring coefficients than buckling away from the pivot [56, 12, 57, 69]. The force-

87 Vertical Euler Spring Isolation 67 Fig. 3.6: a) Photograph of the Euler spring clamps in the vertical isolation stage, b) a diagram of the configuration of a pair of springs using wedges to achieve the desired launch angle θ. displacement curves can have a turning point leading to regions of instability. When the spring bend away from the pivot higher spring coefficients are obtained. In the case of an equally balanced pair of springs buckling towards and away from the pivot (see Figure 3.8), an almost constant spring coefficient is observed. Springs in pairs are usually necessary to permit spring coefficient reduction over a useful operating range. Another non-linearity arises when the launching angle of a spring is nonideal. The launching angle is defined as the angle at which the Euler springs are clamped (see diagrams in Figure 3.6). This value, measured from the vertical, is the effective clamping angle of a set of springs in a single ideal Euler stage. If the launching angle at both ends of a pair of springs are equal and deflected in the same rotational direction (so as to produce an S bend shape on buckling), the non-linear effects cancel out. In other words the launching angle for this pair of springs is zero. In reference [57] a mathematical analysis of the performance of the Euler stage was derived. This involved using parametric equations which describe the shape of the spring, called an elastica. The analysis predicted how differing launching angles in the Euler stage influence the behaviour of the system. A set of force-displacement curves was obtained, reproduced here in Figure 3.7. The graph is labeled with normalised values, with respect to the critical force and spring length. In the plot, it assumes that the radius of the lever arm (the distance from the pivot to the top spring clamp) is equal to the length of the spring. The

88 68 Chapter 3. Fig. 3.7: The force-displacement curves of the Euler stage (adapted from [57]). Note the non-linear behaviour of the curves as the launching angle θ is varied over a range from to radians. The desired working range is located in regions of constant spring coefficients. By varying the amount of launching angle the shape of the force-displacement curve can be manipulated and thus improve the performance of the Euler stage. upper part of the graph corresponds to the spring bending away from the pivot while the lower part corresponds to bending towards the pivot. The two dark lines indicate the zero launching angle case while the shaded lines are achieved by fine adjustments in the launch angles. The symbol θ represents the effective launching angle (in radians) that is applied to the springs, predisposing it to buckle in one sideways direction rather than the other. Negative values represent angles opposing the spring buckling direction. If the proportion of springs bending in each direction is varied any intermediate curve can be obtained. Notice the high sensitivity of the spring constant to the value of θ Spring Coefficient Reduction One method of frequency reduction is through the use of an anti-spring with a negative spring coefficient (ie. producing an anti-restoring or de-stabilising force). When combined with the appropriate positive spring coefficient, a very low spring

89 Vertical Euler Spring Isolation 69 Fig. 3.8: Diagram of the Euler system consisting of two pairs of Euler springs and an inverse pendulum of height h in the rotational arms [56]. coefficient can be achieved. The VIRGO group incorporated anti-springs by using cantilevers fitted with repelling magnets [30]. Another spring coefficient reduction technique was demonstrated using a torsion-crank suspension [58]. Similar systems presented by Bertolini [59] and Cella [60] were termed geometric antisprings. The turning points in Figure 3.7 represent intrinsic anti-spring behaviour, but these offer a very low dynamic range. Figure 3.7 shows that the spring coefficient is approximately constant for relative displacements greater than about 1.5 %. We go on now to present a configuration that implements geometric variation into the Euler stage to reduce the spring coefficient further [56]. Having the mass suspension points located above the top Euler spring clamps provides the geometric anti-spring effect as shown in Figure The value h is defined as the distance between the top of the clamped Euler spring and the bottom of the wire holder which is the suspension point. This h component is essentially an inverse pendulum. 2 The implementation of the geometric anti-spring mechanism into the Euler stage can be seen when comparing this figure to Figure 3.4.

90 70 Chapter 3. Mathematical Model The model presented here considers how the stored energy varies with the height of the mass load using the parameters defined in Figure 3.9 [70]. There are two principle energy storage elements. The first is the compression of the Euler springs. The second is unavoidable and significant: an effective spring due to the various flexures and the suspension wires that bend as the rotational arm moves. The force of the latter varies with angle α and some coefficient K w and is represented by the first term in equation 3.8. The compression force from the Euler spring can be considered as the sum of the critical buckling force F cr and a force which varies as compression distance with an approximately constant coefficient of F cr /2l where l is its unbuckled length. We then obtain the following energy equation: Energy(α) = 1 2 K wα F cr 2 2l r2 (sin(α)) 2 + F cr rsin(α) (3.8) In our case the lever radius r is 64 mm and the springs are assumed to have a total critical load of 380 N with an unbuckled length l of 134 mm. The term K w is typically dominated by the bending stiffness of the suspension wires (as they have to be reasonably strong). As shown in reference [57], K w contributes approximately an additional 6 % of the Euler spring coefficient at this loading. The vertical displacement y at the suspension point is derived through simple geometry. For inverse pendulum height h: y(α) = h r 2 + h 2 sin(arctan( h ) α) βsin(α) (3.9) r The last term in equation 3.9 is due to an extension of the wire holding mechanism, where β is the offset distance in the plane of the rotational arm between the point at which the wire suspends the load and the apex of the Euler spring (see Figure 3.9). Our experimental value for β is 10 mm. From equations 3.8 and 3.9 we can obtain: F y = αenergy(α) α y(α) (3.10) The wire thickness contributes to an addition of stiffness to the system as well as the undesired lowering of the suspension point. A new point of suspension is situated lower than the height of the wire holder due to the bending of the

91 Vertical Euler Spring Isolation 71 Fig. 3.9: Diagram showing the modelling parameters. wire [71]. This undesired contribution to the spring coefficient was investigated and is discussed in section The resulting force-displacement curve is shown in Figure 3.10 illustrating the large effects the value h has on the vertical system. Here the x-axis is the vertical displacement at the suspension point as a function of α. The force is normalised to the critical force which is the force needed to start buckling the springs. The displacement is normalised to the length of the Euler springs. In this particular model the parameters are chosen as close as possible to the real experimental apparatus. The curves on the graph show the effect of incorporating various amounts of inverse pendulum height into the rotational arms. It shows that provided the launch angles are well defined and set, and the correct amount of geometric spring coefficient reduction is added, it is theoretically possible to achieve an arbitrarily low resonant frequency. In practice, the system becomes inoperable when the Q-factor approaches unity. At this point, inelastic and hysteretic effects begin to dominate. For the structural damping expected here the Q-factor decreases proportional to the frequency squared.

92 72 Chapter 3. Fig. 3.10: The force-displacement curves shown here with varying h values suggests that low resonant frequencies can theoretically be achieved by this spring coefficient reduction technique. In reality, the performance of the springs only benefit when operating at small spring buckling deflections, (to about 3 % of their unbuckled length) The Performance of the Euler Stage For experimental purposes the Euler stage was supported by a platform attached to a square central tube. The Euler springs were clamped to the lower end of the central tube as well as to the rotational arms as shown in Figure Suspension wires pass through the tube to a suspended mass below the Euler stage. The adjustment of the inverse pendulum height h was achieved by moving the suspension points in the vertical direction along slotted plates. The Euler spring material used for initial testing was AISI C1095 tool steel in the form of a feeler gauge strip. The reason for the choice of the material was its easy availability in different thicknesses. A constant Euler spring length of 134 mm with the thickness of 0.5 mm was used throughout experimentation for easy comparison between results. Shadow sensors were used for measuring vertical displacement in the Euler stage. A geophone was also used to verify the resonant frequency peaks. Vertical displacement was measured at the rotational arm. Launching angle adjustments

93 Vertical Euler Spring Isolation 73 Fig. 3.11: An assembly drawing of the vertical Euler stage showing the tall geometric inverse pendulum plates. Eight Euler springs are used in the stage and are paired together so four would deflect one way and the other four in the opposite direction [70].

94 74 Chapter 3. were provided by different angled aluminium wedges that were clamped together with the Euler springs (as shown in Figure 3.6). A signal analyser was used to obtain transfer functions across the frequency spectrum. Transfer functions were obtained by suspending the supporting platform, which was attached to the top end of the central tube, by coil springs. A loud speaker voice coil assembly was used to excite the platform. A geophone was placed on top of the platform to measure the input motion while another was placed centrally on the test mass to measure the output response. Results The first results presented here are for springs with zero launching angle. Figure 3.12 shows a typical set of data. It is a force-displacement plot with an h value of 22 mm and a wire diameter of 2 mm. The resonant frequency was recorded simultaneously, determining the gradient lines for each data point. The initial displacement offset of the theoretical straight line is determined using a first order approximation equation describing elastica [57]: y = 2l 2 l 2 b 2 π 2 (3.11) Here y is the vertical change of length from the unbuckled springs, l is the length of the Euler springs and b is half the horizontal buckling displacement of the springs. The contribution of the stiffness of the rotational arm at the flexure point is small; having a spring coefficient of 800 N/m and only becomes significant at very low resonant frequencies. The curvature in the experimental data is immediately apparent when compared with the theoretical straight line. This corresponds with a state of positive θ shown in Figure 3.7. The critical Euler buckling force was determined experimentally. Its value, 403 N (41 kg), was constant and consistent for all the measurements made (further plots are not shown in this publication). Figure 3.13 compares two h values: 18 mm and 81 mm, using 1 mm diameter suspension wire. It is seen that the inverse pendulum has significant effects on the spring coefficient of the system. While Figure 3.13 shows the expected qualitative behaviour, the magnitude of the anti-spring is weaker than expected. It appears

95 Vertical Euler Spring Isolation 75 Fig. 3.12: A force vs. displacement graph with an h value of 22 mm. Note the extreme curvature of the data points approaching the theoretical curve in the ideal case. that the system is sensitive to imperfections in the clamping mechanism, uneven spring lengths and creep. The inverse pendulum height of 81 mm achieved a resonant frequency of 0.67 Hz corresponding to a spring coefficient of 800 N/m. Comparing this with a spring coefficient of 8000 N/m for h = 18 mm, we observe a factor of ten improvement. Figure 3.14 shows the improvement in the resonant frequency as the wire diameter is changed. Here the resonant frequency is plotted against the mass load. There is a distinct gap between the data sets for 1 mm and 2 mm wires. The undesirable non-constant gradients of force-displacement plots seen earlier are also noticeable as a dependence of resonant frequency on displacement. The displacement range of the Euler spring restricts the mass load range. Next we present experimental results involving the implementation of launching angle adjustment together with different values of the inverse pendulum height. The continuous theoretical lines in Figure 3.15 and Figure 3.16 were generated using numerical routines developed in reference [57]. The theoretical curves displayed are made to best fit the experimental data. The horizontal and vertical axes are normalised by the length of the springs (134 mm) and the critical force of the system respectively. The routines have essentially two parameters

96 76 Chapter 3. Fig. 3.13: A plot showing strong inverse pendulum tuning of the Euler stage. With h = 81 mm the slope is reduced substantially compared with the system with h = 18 mm. to optimise for best fit: the adjustments of the launching angle and the critical force. These adjustments were kept constant within each data set. Only a handful of data are shown in this publication. Altogether 25 sets of data were collected. Figure 3.15 and Figure 3.16 show the comparison for a fixed clamping angle (θ = and radians respectively) as the inverse pendulum height is varied. The theoretical values of θ used to produce the curves are given in the captions. Adjustments of the critical force to match experimental data were minimal, with a maximum of 1 % variation. The analysis of these plots suggests that the performance behaves as expected although large deviations are seen between the theoretical and experimental launching angles. These and similar plots show a trend corresponding to the upper part of Figure 3.7. As θ becomes more negative in Figure 3.7, the curves approach the desirable dark curve which has an almost constant spring coefficient. As θ is decreased further regions of instability represented by negative gradients start to appear. The force-displacement curves fitting the experimental data show this trend although negative gradients were not reached. The launching angle discrepancies between theoretical and experimental results were mainly due to non-ideal conditions in the experimental setup. Creep

97 Vertical Euler Spring Isolation 77 Fig. 3.14: Plot of the resonant frequency as a function of mass in the Euler stage with different values of the inverse pendulum height h. The distinct different operating ranges in mass load between the different sized wires clearly suggests the system with the 1 mm wire is softer. and the inelastic performance in the springs due do continual use played a major part. The wedges were difficult to adjust as they were able to slip with respect to one another changing the lengths of the Euler springs. Also, there was error in defining the exact clamping point as the wedges have finite roundness on the edges. Figure 3.17 shows four transfer functions illustrating the progressive improvements made on the Euler vertical stage [70]. The first transfer function (a) is obtained using an older design [56]. Transfer function (b) is obtained from the configuration having a launch angle of rads with h = 75 mm achieving a resonant frequency of 0.92 Hz. An even lower resonant frequency of 0.62 Hz is achieved having a spring coefficient of just over 650 N/m using the configuration of θ = rads at the inverse pendulum height of 81 mm. Following this, several design changes were made. A different spring material was trialled: the AISI 301 having higher yield strength and a lower creep rate. Secondly, a new design which allowed for better clamping and finer launching angle adjustments was installed. A new wire holder suitable for holding 0.5 mm

98 78 Chapter 3. Fig. 3.15: The force-displacement curves for experimental launch angle θ = radians (adjusted to rads), A) h = 45 mm, B) h = 55 m, C) h = 65 mm, D) 75 mm, and E) 81 mm. Fig. 3.16: The force-displacement curves for experimental launch angle θ = radians (adjusted to rads), A) h = 45 mm, B) h = 55 m, C) h = 65 mm, D) 75 mm, and E) 81 mm.

99 Vertical Euler Spring Isolation 79 Fig. 3.17: The progressive improvement in the transfer functions: a) using a previous Euler stage design with a resonant frequency of 2.5 Hz, b) the transfer function of the launching angle θ = rads at h = 75 mm during the experimental investigations with a resonant peak at 0.92 Hz, c) obtained from implementing improved methods into system achieving a resonant frequency of 0.50 Hz, and d) with the latest stage design using maraging steel Euler springs with a resonant frequency of 0.3 Hz.

100 80 Chapter 3. diameter suspension wires was also constructed to further soften the system. The resulting transfer function is shown in Figure 3.17c achieving a resonant frequency of 0.50 Hz. Additional modes were introduced by the modified stage appearing between the resonant peaks of 0.5 Hz to about 6 Hz. In an attempt to eliminate some of the problems discussed above (namely clamping conditions and creep), a new and improved vertical stage configuration was designed [70]. The Euler springs were relocated so that their vertical displacements were co-linear with the suspension points. To further reduce creep, the spring steel was replaced with maraging steel [63]. A creep rate of less than 1µm/day for a 40 kg load was recorded. The transfer function of Figure 3.17d was taken using a test mass of approximately 80 kg with an Euler spring length of 175 mm with thickness 0.8 mm. A resonant frequency of 0.3 Hz was obtained for zero launching angle 3. While obtaining transfer function (c) a Q-factor of 35 was observed at 0.62 Hz. The Q-factor decreases with frequency squared as mentioned previously. This suggests that it may be possible to obtain a resonant frequency of order 0.1 Hz before the losses dominate the system. However, it can be seen that curve (d) in Figure 3.17 suggests that this frequency may be extremely difficult to reach (see footnote). The ring down plot for curve (c) and the calculation for the Q factor are shown in Appendix B Discussion and Conclusion The implementation of inverse pendulums into Euler spring vibration isolators has reduced the resonant frequency of the vertical Euler stage to below 1 Hz. Non-linearities can be reduced by adjusting the spring launching angles. While adjustment of the launching angle is advantageous, it is difficult to reproduce theoretical predictions due to imperfections in the system. Issues concerning the 3 At the time of testing, it was found that at this low frequency state of curve (d) the hysteresis behaviour was problematic. The transfer function spanning a larger frequency range could not be obtained even after rigourous attempts due to the high level of instability. Clean repetitive data above 1 Hz was difficult to produce thus the curve presented here was stopped at this frequency. Thus it is intended that the frequency of the Euler stage be increased slightly to improve the stability in the working system.

101 Vertical Euler Spring Isolation 81 stability of the Euler stage have been identified. A resonant frequency of 0.3 Hz was achieved for a single vertical isolation stage. This is about 100 times softer than a comparable cantilever blade spring. The transfer functions shown in Figure 3.17 show classic center of percussion effects [56, 47, 35]. These effects can be tuned out by adjusting the mass distribution of the rotational arm. This will be necessary to maintain good isolation at high frequency. Theoretical and experimental work on the Euler stage center of percussion tuning will be presented in a future publication Acknowledgements This work is supported by the Australian Research Council, and is part of the Australian Centre for Interferometric Gravitational Astronomy. The authors wish to thank the workshop technicians Peter Hay, Ken Field, and Michael Kemp. We would also like to acknowledge John Jacob for his involvement.

102 82 Chapter Postscript The author believes that the non-linearities observed in the results would have been reduced if the wedges had been made from harder materials (for example steel), and better clamping conditions had been provided, which would result in sharper edges and hence more defined launch angles. The difficulty lay in the manufacturing of harder materials into flat pieces of wedges. A much easier and improved method would be to create a mechanism to fine tune the launch angles, which would allow the resonant frequencies to be finely tuned as well. Such a mechanism was made which involved the flexing of the actual clamps themselves using screws to physically bend the angles of the clamps. Almost immediately after the manufacture of this mechanism, the whole Euler configuration was changed to a more in-line setup with the suspension points to improve functionality, so the mechanism was not re-designed and hence was not included in the final setup. It was concluded that the non-linearities could be compensated by increasing the spring compression, so that the springs operate further up the displacement curve, as well as by varying of the inverse pendulum height h. Another modification that was done in the final design was the change in the method of adjusting the inverse pendulum height h. From a practicality point of view, a stronger structure was to include spacers to define the height, to supersede current method of tightening a screw head along a slot (pictures of new design is shown in Figure 4.8 in the next chapter). This, unfortunately, eliminated the fine adjustment of the height h available in the last setup. However, this loss was not critical because tests showed that this value was not as affective in reducing the spring rate as predicted by the model. Spacers of variable heights were manufactured with a minimum spacer value of 1 mm, which was sufficient. Center of percussion effects can be seen in the transfer functions like the one shown in Figure No center of percussion tuning was done on the Euler vertical stages during the course of this research, although a few ways to improve the isolation performance were suggested. As discussed in previous chapters, to obtain ideal performance, the center of percussion location has to be either at the suspension point, or at the point where the mass load hangs off. The immediate place that can be seen for the Euler stage to implement this improvement is at

103 Vertical Euler Spring Isolation 83 the end of the lever arms where the suspension wires are attached. Small counter weights can be made to attach at those ends. Another way to improve the center of percussion effect is by making the rotational arms as light as possible so that more mass is concentrated at the wire holder end of the rotational arms. This can be done using less dense materials to design lighter lever arms and still maintain the structural integrity.

104 84 Chapter 3.

105 Chapter 4 AIGO Seismic Vibration Isolator 4.1 Preface The goal for the UWA research team during my PhD project was to deliver research outcomes involving the collaboration with other gravitational wave groups around the world. One of the top priorities for the AIGO facility in relation to this thesis is the installation of two complete vibration isolation systems to form a Fabry-Perot cavity in the east arm of the High Optical Power Test Facility (HOPTF). The author was involved in the coordination of the processes involved in the installation of the vibration isolators at the AIGO site. This included the scheduling of manufacturing mechanical parts, parts cleaning, transportation, man power and miscellaneous tasks, which contributed to the installation of the isolators at the AIGO facility. The author also contributed to the research and design of the pre-isolation control system. This included the design of the electrical wiring architecture which involved the design of the connectors and the wiring layout that is installed down the whole isolation chain. However, unforeseen circumstances (mainly funding issues) delayed the installation of the two isolators. Work was continuing at the time of writing this thesis. The paper presented in this chapter was published in the Journal of Physics, and was presented at the Sixth Amaldi Conference, It is included because it provides a good overall summary of the broad task of implementing the vibration isolation system into the AIGO site. The processes involved in tuning 85

106 86 Chapter 4. and installing the isolation system are presented in the Sections 4.2 to 4.4 which include mechanical tuning procedures, the control of the pre-isolation stages, and the cleaning processes involved in preparing the system to be in a vacuum environment for cavity locking. The content on the tuning and assembly procedures for the different stages of the isolation system included in this chapter is that which the author considers to be vitally important for the awareness of the tuner. Very detailed descriptions about each mechanical part and how they are assembled are not discussed. The status of the isolation systems being installed at AIGO is presented in the final section of this chapter. The following section starts with an overview of the AIGO main laboratory environment at Gingin and the cleaning procedures for the isolator parts.

107 AIGO Seismic Vibration Isolator Vacuum Clean Environment at AIGO Gravitational wave interferometers require high powered lasers to illuminate the Fabry-Perot arm cavities. The laser light may partially scatter when traveling between the mirror test masses causing phase disturbances. It is therefore essential for the laser beam to travel inside the cavity with as little disturbance as possible. This is solved by implementing a high vacuum environment for the laser beam to travel through in the arms of the interferometer. LIGO attempts to operate at 10 9 torr in its eight kilometers of vacuum piping of one meter diameter. AIGO is aiming to achieve a vacuum pressure of 10 7 torr [72]. Hydrocarbon is a major contaminant for vacuum environments and has to be eliminated. Some sources include the vacuum vessels, pump, the suspension isolation system, and even from the environment of the laboratory building. Hydrocarbon molecules degrade the high reflectivity of the mirrors and may be forced onto the surface of the optics by radiation pressure. The outgassing of products during operation is to be avoided which may produce deleterious effects on the reflectivity of the mirror surface when these mirrors undergo laser irradiation in the order of kilowatts. Thus it is extremely important that every mechanical part or hardware within the vacuum envelope is thoroughly baked and cleaned before the final installation. Large efforts are made to achieve the high level of cleanliness that is required for success in obtaining the necessary vacuum pressure in the pipes. The cleaning procedure adopted at the AIGO laboratory is presented in an ACIGA internal report and is strictly adhered to [73]. The documents specified by LIGO [55, 74] were used as guidelines during the compilation of the report. Presented is a general overview of the author s contribution in the process of installing the full vibration isolator at the AIGO facility for the first time. The construction and installation of the vibration isolator under clean room condition commenced about halfway through the author s research time-line. Figure 4.1 shows pictures of three clean tents located in the main laboratory of AIGO. The two tents shown in Figure 4.1(a) are housings for the cleaning, assembling and storing of the cleaned isolator parts. Each of the tents have four High Efficiency Particulate Air (HEPA) filters installed in the ceiling for

108 88 Chapter 4. Fig. 4.1: The clean tents up at AIGO.

109 AIGO Seismic Vibration Isolator 89 Fig. 4.2: The views in one of the clean tents, showing the washing basins, which use deionised water, and some ultrasonic clean bath systems located at the rear corner in Figure (b). contamination control of the clean tents. The third tent is installed at the location of one end of the east arm cavity where one full vibration isolator is located. Baking of parts inside the high vacuum environment is beneficial. One main benefit is the reduction of the outgassing rate from the molecules that are present on the surfaces of the parts. The most common outgassing molecule is water but also includes the hydrocarbons that are previously described. The contamination of these molecules which cause outgassing, limits the achievable vacuum pressure. Leaving the pump operating over a long period of time will eventually see the vacuum pressure drop but the time scale of this is usually many years. Raising the temperature by heating the parts causes the molecules to come off at an increased rate and may reduce the time needed to achieve the vacuum level to a number of days. Typically, the rate at which the molecules come off the parts doubles for every 6-8 degrees increase in temperature. The cleaning of parts to be installed inside the high vacuum tanks and pipes is carried out by three washing and rinsing steps, two ultrasonic baths, and finally the baking of the parts in a vacuum oven. Detailed steps, eg. the time needed to rinse each part, the different cleaning steps for different materials, the cleaning garments clothed for each stage, etc. will not be listed here. The first wash

110 90 Chapter 4. Fig. 4.3: The two vacuum ovens of different sizes situated in the clean tent that are used for baking parts. involves cleaning the parts with a degreaser solution and then rinsing with tap water. This stage is usually done by the mechanical workshop after the completion of manufacturing the parts. Following this, the parts are washed and rinsed using deionised water and a plaudit 1 solution before entering into the main laboratory. After the parts have dried, they are wheeled into the laboratory and washed and rinsed again inside the clean tents. This time they are washed with liquinox with ultraclean water from a second deioniser in the basins shown in Figure 4.2. The parts then go through a series of ultrasonic baths, first in a liquinox solution, then they are carefully rinsed before a soak in methanol solution. The parts are then ready to be placed inside the vacuum oven to be baked, generally for 48 hours at elevated temperatures which is dependent on the material type, eg. aluminium is to be baked at 120 C, steel at 200 C etc. During baking, a piston pump is used to continually evacuate the air inside the ovens. Figure 4.3 shows the two vacuum ovens that are used to vacuum bake the parts. After the completion of baking, the parts are carefully wrapped in ultrahigh-vacuum (UHV) quality foil and doubled bagged using UltraLo Plus Poly bags (from AeroPackaging). The air inside both bags was evacuated as much as 1 A water based emulsion cleaner used in the industry for removing grease and oil contamination.

111 AIGO Seismic Vibration Isolator 91 possible and heat sealed. The parts are labeled and finally stored away ready to be used in the clean vacuum compatible environment. 4.3 Vibration Isolator Tuning Fig. 4.4: The seismic noise measured at the Gingin laboratory September The measured seismic noise spectrum at the AIGO site was measured in September 2000 and is shown in Figure 4.4. It can be seen that the level of noise at the Gingin site is about one to two orders of magnitude lower than the typical noise level shown as the dotted line. This provides a safety margin for additional noise such as cultural activities, earthquakes, storms, etc. It is evident that even with this reduced noise level at the quiet AIGO site, several orders of magnitude must still be attenuated to allow for cavity locking. Approximately 200 db of isolation is needed across the detection bandwidth, which is from a few tens of hertz to a few kilohertz. Once locked, the mirrors must be located within a dark fringe where the total RMS differential residual motion at the test mass mirror must not exceed m in the detection bandwidth.

112 92 Chapter 4. The full performance of the completed vibration isolation stack is difficult, if not impossible to obtain directly using conventional methods of measurement due to the various noises which are intrinsic to the measuring devices. These include the noises from the geophones, shadow sensors, electronics (Johnson noise), drivers, actuators and spectrum analysers. One of the big contributors to measurement noise is seismic noise since the actuators and shadow sensors are directly measuring relative to the seismic motion and effectively forms an isolation floor in the frequency spectrum. The most effective method to counteract this problem is by installing two fully assembled tuned isolators in a cavity arm, then detecting the motion by shining a laser beam into the cavity and sensing the change in the fringes caused by the interferences of the laser. (Feedback from the error signals in the global control scheme to lock the cavities can be used.) This effectively results in the relative motion sensing of the two isolators and eliminates any measurements done with respect to the ground. To obtain transfer functions of a fully operational vibration isolator is one of the top priorities of AIGO and the group is continually making progress to achieve this target. The first full prototype vibration isolation system was completed and assembled in the laboratory at UWA by mid During installation, it was found that the best method to put together the multi-stage isolation system, was to assemble the Roberts linkage together with the 3D stack, separate to the assembly of the frame, wobbly table and the LaCoste linkage. It was decided that this method of assembly is the easiest and most practical. The assembly time is slightly reduced because the two separate subassemblies can be assembled concurrently. When both subassemblies are ready, the Roberts linkage and the stack structure are dropped in from the top into the pre-isolator and isolator stand. The attachment of the two separate structures is located at the LaCoste frame where the four suspension wire points support the Roberts linkage. This whole process of assembly requires the construction of a tall stand whereby its main purpose is to suspend the Roberts linkage and the stack while being put together and tuned (Figure 4.5). This stand has wheels and an inbuilt winch to allow for the adjustment of the height of the isolator structure to ease the assembly process. Holes are drilled on the back frame to allow for

113 AIGO Seismic Vibration Isolator 93 Fig. 4.5: Pictures showing the assembly of the Roberts linkage and 3D isolation stack being assembled on the temporary stand. Pictures were taken at the AIGO site. clamping of the Roberts linkage to the stand itself as well as providing a means of attaching the safety frame for the isolation stack. The safety frame doubles as the mechanism for lifting the individual rocker masses of the Euler stages to allow for the off-loading of weights while tuning is done to the upper stages. Tuning the entire vibration isolation system is a tedious task, though over time, the task has become easier. The main difficulty comes from the tuning of individual stages which requires some or all of the other stages to be locked. Locking in this context means that the motion of the isolation stage is impeded either by clamping it to another structure (eg. to a frame that is essentially connected to the ground), the placing of wedged materials between stages to lock it with another isolation stage (eg. the method used to lock the Roberts linkage with the LaCoste stage), or lifting its mass load such that it cannot perform. Once a stage is tuned and the other stages are ready to be unlocked, there is a high chance that this may disrupt the state of the tuned stage thus requiring further tuning in an iterative process. One good example is the balancing of the wobbly table. Balancing this stage which suspends all the other stages will be extremely

114 94 Chapter 4. difficult as it has the heaviest load and its state, in principle, can be affected by any of the other stages. Another example is the tuning of the Roberts linkage. When balancing the Roberts linkage, the wobbly table is first locked. At the time of unlocking, the inverse pendulum is unbalanced and will cause the Roberts linkage to also lose balance. In principle, the tilt rigid structure that the Roberts linkage is attached to should not allow it to become unstable, but in reality it sometimes does. This is contributed by the fact that the structures themselves are close to instability because of their very low resonant mode properties. The physical flexing of non-ideal rigid links in the mechanical structure is enough to sometimes upset this. Various stages must be tuned down to ensure stability. Almost all the tuning done by the author required multiple sessions of locking and unlocking of various individual stages. This also meant that different stages may have been tuned several times in one tuning session in order to obtain a well tuned vibration isolator. Figure 4.6 shows the full isolation system that is assembled in the laboratory at UWA. The aluminium sheets seen at the sides that are attached to the isolator stand are there to prevent accidental contact with the long inertia arms by passers-by (described in Section 1.4.1). These sheets also act as shields from air disturbances from people walking around the lab which can affect the tests and measurements performed on the isolator. At times, measurements and results were collected during the night when there was minimal activity. The laboratory at UWA acts as an upper sensitivity limit in the performance and behaviour of the system. The assembly of the isolator is in a fairly stable environment at UWA while up at AIGO, the environment is much more controlled and the testings would be much easier with less noise in the measurements obtained 2. The rest of this section summarises the various methods of tuning and balancing of the different isolation stages that are used in the vibration isolation system of AIGO. There is an order in which the different stages are to be tuned to minimise the work needed to re-tune or re-balance the individual stages. As 2 However it was found that air filters in the laboratory contribute to some noise. Work is being done to access the frequencies and amplitude levels they give out so the amount of noise they contribute is known.

115 AIGO Seismic Vibration Isolator 95 Fig. 4.6: The full vibration isolation system at UWA.

116 96 Chapter 4. mentioned previously, this is due to the effects that the stages have on each other. Two separate subassemblies are made and while the combination of the wobbly table and isolator stand needs to be built ready for the integration with the other subassembly, the 3D isolation stack which suspends off the Roberts linkage can be tuned independently. Hence the 3D stack which consists of the Euler stages and self-damped pendulums are tuned first then locked. Once combined together with the other subassembly, the Roberts linkage is tuned next, followed by the LaCoste linkage and finally the inverse pendulum or wobbly table. The next few subsections are listed in order of tuning but as mentioned before, multiple sessions of re-tuning of the tuned stages may be required. It is intended that the delicate assembly of the control mass stage holding the sapphire test mass mirror be installed as late as possible. Thus the equivalent weight of the control mass and test mass mirror are attached to the final mass plate of the 3D isolation stack to simulate the correct mass (40 kg). This is to avoid damaging the sapphire test mass as well as preventing readjustments of the upper stages as much as possible The 3D Vibration Isolation Stack As mentioned previously, the 3D isolation stack which consists of three vertical Euler stages and four horizontal pendulum stages, is assembled with the Roberts linkage and together are suspended temporarily by a wheeled stand. This stand measures approximately three meters in height and is designed to support the assembly weight of the Roberts linkage and the isolator stack. This subassembly begins by hanging the Roberts linkage at the top by a winch as well as securely attaching the stand with the Roberts linkage structure by the frame at the rear. Since the Roberts linkage only acts as a platform for the isolator to hang off from, it cannot be tuned until it is suspended from the LaCoste stage in the other subassembly. A dummy mass weighing 40 kg which simulates the control mass stage is rigidly bolted onto the last rocker mass of the self damped pendulum (Figure 4.10). This allows the tuning of the upper stages to be done as closely as possible to the completed vibration isolator minimising the work needed to finely re-tune the system once installed.

117 AIGO Seismic Vibration Isolator 97 The wheeled stand also allows for the attachment of a second frame which acts as a safety or support frame for the mass plates (Figure 4.7). In the final system, this safety frame is attached to the main isolator stand. Aluminium arm-like bars are attached on the sides just above the Al webs that house the copper/magnet combination 3. These bars act as stopping mechanisms with respect to the safety frame should any of the isolation stages fall. It is important that these bars do not come in contact with the safety frame while in operation. This can be avoided by adjusting the height of the support frame. The rotation of the masses in the vertical axis is kept at a minimum. The direction in which the test mass mirror faces is dependent on this twist and must be along the axis of the laser beam. If needed, this rotation can be adjusted by carefully twisting one end of the suspension wire. For bigger adjustments, the upper gimbal which supports the first pendulum stage that hangs from the Roberts linkage stage can be rotated and is mentioned later. The process of loading and unloading the weights is provided by the safety frame and is vitally important for tuning of the upper stages. Height adjustable screws with small flat aluminium platforms at the screw ends are installed at the bottom of each rocker mass on the safety frame to allow for the weights to be lifted off the suspended chain. Small steel masses weighing from a few grams to few hundred grams are manufactured specifically to be placed on top of the rocker masses for balance and thus ensuring the masses are suspended horizontally. The balancing is done with a spirit level and is verified by eye. Having the masses balanced maximises the dynamic range of the rocker masses with the central tube that the Al webs are attached to, thus also maximising the effects of the self-damp mechanisms. In the design stages described by Winterflood [12], each pendulum stage in the 3D stack with the four sets of copper/magnetic combs installed in the system, provides a linear damping coefficient of approximately 5.8 Nm/(rad/s). This is sufficient to optimally damp a 50 kg system. In a multi-stage system, the higher isolation stages do not need as much damping as the lower stages, which have less weight. 3 The assembly of the copper combs and rare earth magnets are carefully put together such that they do not come in contact with each other and have the largest possible dynamic range.

118 98 Chapter 4. Fig. 4.7: One isolation stage: the Euler stage with the self-damped pendulum. The picture on the right shows the safety frame which also acts as a lift to off-load weight for upper stages to be tuned. Having the mass plates balanced will ensure the gimbals (which provide the 2D flexing in each of the pendulum stage) have the maximum amount of dynamic range. The gimbal for each pendulum stage is such that it works in compression; the base section is attached to the central tube and the rocker mass sits on top of the gimbal. The gimbal flexure pivot is made of aluminium and is cut with electric discharge machining (EDM) wire cutting. Values of the flexure sizes and approximate spring rates for supporting different mass loads are described in Winterflood s thesis [12]. Note that the vertical beams or the inertial arms mentioned in Section that are used to damp out the first pendulum mode are also balanced using small masses described above. Before the implementation of Euler springs into the vertical stage assembly, the suspension wires must be bent and measured to length. A number of jigs are built to assist in this process where each pendulum stage is to be about 60 cm in vertical height. As mentioned previously, any rotation of the rocker masses must be minimised and depends on the level of twist the suspension wire has in each stage. The twisting of the wire can be corrected at the attachment points by small clamps on the wire holder.

119 AIGO Seismic Vibration Isolator 99 Fig. 4.8: Pictures of the Euler assembly. Fig. 4.9: The Euler stage when loaded. The jellyfish wiring can also be seen in the second picture.

120 100 Chapter 4. For the control of the test mass mirrors, electrical signals must travel through the entire vibration isolator to finally reach the test mass control stage. This is to avoid short circuiting of seismic noise being transmitted from the ground down the chain through the wires. Altogether, 40 poly-imide coated copper wires of 0.25 mm thickness are installed to run through the inside of the central tubes and can be seen in Figure 4.8(b). To minimise the transfer of seismic noise through the electrical wires, they are organised in a jellyfish arrangement between stages (Figure 4.9(b)). The length of these wire sections is made sufficiently long to reduce the stiffness in the wires to minimise vibration transfer. More details on the general planning of the wiring scheme will be discussed later in Section 4.4. In Chapter 3, it was shown that curvatures in the force-displacement plots of the vertical Euler stages are very pronounced and give large variations in the resonant frequencies. This results in the reduction of the dynamic range of the springs. Since there is no clamping adjustments to tune this non-linearity in the AIGO vibration isolation system as discussed in Section 3.4, the only other method to ensure stability at low resonant frequencies is by the compression of the springs far from the state of when they just start to buckle. In other words, away from the curvatures present in the force-displacement curves like the ones shown in Figures 3.7, 3.12 and 3.13). The installation and tuning of the Euler springs involve prior assembly of the suspension wires that are to be attached to the mass plates and wire holders, and the Euler setup as seen in Figure 4.8. Following this, the unsprung Euler springs can be installed. The lower Euler spring base clamp which is attached to the central tube and supports the base of the springs is adjusted to the correct distance with respect to the top clamp assembly. Unlocking of the mass plates thus suspending the weights which loads the springs can then be followed. The important point to note here is the amount of loading the springs take on. From experience, the springs need to buckle about % of their unloaded lengths (Figure 4.9). This is to ensure the springs operate away from the non-linearities that are seen in Chapter 3 and not loaded too much that it may cause permanent plastic deformation in the springs.

121 AIGO Seismic Vibration Isolator 101 The entire Euler stage configuration can move along the central tube which provides an offset adjustment depending on the amount of loading the springs need. Adjustment of the spring length can be made in situ but it is recommended that the length be finalised before loading, as it is one of the design parameters to determine the resonant frequency of the stage. Safety screws installed in the rotational arms as shown in the Figure 4.8(b) allow for the length adjustment in situ to happen such that all the weights from the lower stages are supported by the upper Euler stage assembly (which is now locked with the central tube) and none on the lower Euler base clamp. Fine adjustments of the position of the lower base clamp can be made with a mechanism located below the base clamp and supports the clamp with the turning of screws. The turning of these screws when the base clamp is free to move along the central tube allows the lowering or lifting of the base clamp hence the adjustment of the length of the Euler springs. Safety mechanisms are also installed on the rotational arms close to the flexure pivots to prevent excess lifting of the arms when the mass plate has been unloaded or for what ever reason should the springs suddenly spring up and cause damage to the thin flexures. The adjustment of the inverse pendulum height is done by spacer blocks placed underneath the wire holding mechanism. Unfortunately, in this design it requires the mass to be lifted before inserting or removing the aluminium blocks. It is important to also note the popping behaviour of the Euler springs when the load has reduced to a certain value and may cause other stages to loose balance or unlock. A sudden mechanical shock will run though the entire system so care should be taken when unloading masses. On one occasion, a suspension wire holding one mass plate stage failed and broke at the immediately occurrence of this snapping action of the Euler springs. This led to the replacement of each suspension wire in the isolation stack with higher margins of load safety factor. Figure 4.10 shows the lower section of the 3D isolation stack assembled on the wheeled stand. Here you can see the final two pendulum stages as well as the dummy control mass stage that is suspended off the final Euler stage. The safety frame is rigidly attached to the rear of the stand as well as to the base of

122 102 Chapter 4. Fig. 4.10: The lower section assembly of the Euler stages and self-damped pendulums with the dummy control mass. the Roberts linkage and supports the 3D isolation stack when stages are being tuned The Roberts Linkage Figure 4.11 shows pictures of the Roberts linkage rigidly attached to the stand as well as supported by the winch. Parts of the safety platform can also be seen in Figure 4.11(a) that is described in the last section. The 3D stack has also been assembled which is suspended off the upper platform of the Roberts linkage. A detailed picture can be seen in Figure The central tube of the first pendulum stage is clamped and sits on the upper section of the gimbal which provides the 2D flexing mechanism for the pendulums to operate. The gimbal sits on a circular swivel which can rotate on the Roberts linkage platform to correct for any rotational displacements that may be present in the isolation

123 AIGO Seismic Vibration Isolator 103 Fig. 4.11: Pictures of the Roberts linkage suspended off the wheeled stand a) fronton view, b) side view. stack. Wiring for the control system at the test mass stage can also be seen. The wiring methods will be discussed in Section 4.4. Once the two subassemblies are ready to combine to form the full vibration isolator, the assembly with the Roberts linkage is lifted by a crane at the attachment points located at the top of the Roberts linkage. While the subassembly is being transported, each of the isolation stages are locked to the safety frame to

124 104 Chapter 4. Fig. 4.12: View of the top of the assembled Roberts linkage in the pre-isolator showing its attachment to the 3D isolation stack below. prevent movement of the stage and reduce damage to the parts. The pre-isolation stages of the inverse pendulum and the LaCoste linkage are also locked during the merging of the two subassemblies. The crane drops the Roberts linkage assembly through the middle of the other subassembly and temporarily supports the stack weight while the suspension wires of the Roberts linkage are attached to the mounting points on the upper frame of the LaCoste linkage (one shown in Figure 4.13(a)). In that picture can be seen the wire holder supporting the suspension wire. The wire is actually pre-bent in a hook like shape and sits snugly in a groove in the top section of the wire holder. The position of that top section can be made to increase or decrease in height with respect to the LaCoste platform to allow for the balancing and tuning of the Roberts linkage. This is done by turning this section on a threaded piece which can also be observed in the Figure. As mentioned in the previous section, a method to determine if the Roberts linkage is balanced is by measuring the tension in each of the suspension wires. A crude way to do this is by lightly plucking each of the wires and analysing their acoustical frequency. This technique gives a good starting indication of the state at which the Roberts linkage is at before fine tuning.

125 AIGO Seismic Vibration Isolator 105 Fig. 4.13: Close up views of the wire supports for the Roberts linkage, a) support at the LaCoste frame, b) at the Roberts linkage base frame. As described in Section 2.13, wire heating is used as a means of controlling the position of the Roberts linkage with respect to the LaCoste frame. To isolate the electrical current that is running through the suspension wires, insulation must be placed in locations on the isolator such that stray currents going into the isolator itself are prevented. A material called PEEK 4 is used to manufacture into bushings and are placed into bolt counter-sunk holes to prevent current from running to other parts the bolts connect with. It can be seen that two sets of electrical copper wires are attached to two locations in Figure 4.13(a) (excluding the wires attached to the connectors which are for test mass control), one set is to an isolated bolt on the left of the picture, and the other to the suspension wire itself. These electrical wires together form the electrical circuit loop that heats the individual suspension wire. In fact, the aluminium piece that is supporting the wire holder is positively charged (if current is flowing down the top wire holder towards the Roberts linkage) and is isolated from the LaCoste frame. The copper wires eventually run back down the pre-isolator and isolator stand to the voltage controlled current supply situated on the control rack (Figure 4.22). A flat PCB board is used for each attachment point at the Roberts linkage end 4 Polyetheretherketones (PEEK), sometimes referred to as polyketones is a thermoplastic with very low outgassing properties and is one of the few plastics compatible with ultra-high vacuum applications.

126 106 Chapter 4. of the suspension wire to insulate the current in the wire going to the Roberts linkage frame. The heating current will make its way back up through the copper wires seen on the left of Figure 4.13(b). Chapter 2 presented work on Roberts linkage tuning methods. It was found that the isolation floor at high frequencies is influenced by center of percussion effects. One key adjustment on the Roberts linkage that can improve this isolation limit is the variation of the attachment point at which the 3D stack is suspended from. More accurately, the height of the suspension point of the isolation stack on the Roberts linkage. Adjustments are made possible by the clamp that is located on top of the gimbal shown in Figure The height at which the central tube that holds the first Euler stage can be moved up and down with respect to the gimbal. The desired position is then clamped. If further height adjustment is required, the platform which the gimbal and clamp sit on top can be modified. There is a physical suspension height limit dictated by the ceiling of the vacuum tank. Currently, the extra allowable height adjustment is approximately 100 mm of gap above the current central tube position. Before any height adjustments can be made, all the weights of the lower stages must be lifted which is made possible by the safety supports. Also, the Roberts linkage can be locked to ease the 3D stack suspension height adjustment by aluminium wedges that fit between the corners of the Roberts linkage frame and the upper part of the LaCoste frame The LaCoste Stage This stage must support a total weight of over 300 kg. Four sets of nickel plated coil springs are used, with 11 springs in each set (Figures 4.14(a) and 4.16). The internal mode frequency of the coil springs is about 17 Hz which is high enough not to concern the operation of the pre-isolation system. It is desirable that these springs are pre-tensioned such that they provide enough upward force that results in the LaCoste frame to begin reaching the upper limit of its travel range. Fine positioning and tuning of the stage can then be provided by placing smaller weights on top of the frame. In fact, the height of the LaCoste stage set passively by the mechanical system should be such that it is near the upper dynamic range. This is because the technique of heating the coil springs used

127 AIGO Seismic Vibration Isolator 107 in the control loop can only stretch the springs, hence an initial current in the coils allows for control of both up and down directions. Thus with this initial current, the height at which the LaCoste stage would be determined by the set point given by the PID. Similar to the control system seen on the Roberts linkage, the LaCoste linkage is controlled through the heating of the springs. When uncontrolled, diurnal drifts of the LaCoste linkage observed in the laboratory at UWA sees that the stage exceeds its entire range of 10 mm. Faster response signals are provided using coil actuators which are installed at the base. More on the control of the LaCoste linkage is described in Section 4.4. As explained previously and shown in Figures 1.11 and 1.13, rigid pivot arms are required to create an anti-spring effect with the combination of springs orientated as shown. Figure 4.14(b) shows a close-up view of the 1D flexure joint that connects one end of the pivot arm with the inverse pendulum frame. There is a flexure joint on each end of the pivot arms where the other end in Figure 4.14(b) is attached to the LaCoste frame. The flexures are made from a monolithic block of aluminium and machined into a crossed flexure type of pivot. Monolithic structures give lower losses (higher Q factors) than equivalent materials being clamped and are beneficial in structures such as the vibration isolator which aims to achieve low resonant frequencies. There are altogether eight pivot arms forming the LaCoste linkage, two on each of the sides of the pre-isolator. Counter weights are attached to four of the eight pivot arms to provide center of percussion tuning [12]. The tuning of the anti-spring effect requires the horizontal component of the springs to be adjusted. Moving the mounting points of one end of a whole set of 11 springs can be a tedious and difficult task. A solution is installing separate sets of horizontal springs [12] dedicated to only tune the anti-spring effect (Figure 4.15). The anti-spring effect produces negative spring constants and by varying the amount at which these springs stretch, the vertical spring rate can be tuned to operate at a very low resonant frequency ( 50 mhz). A plate which is made to slide along slots on the LaCoste frame provides this adjustment. There are two sets of three anti-spring adjusting coiled springs. Locking the LaCoste stage for

128 108 Chapter 4. Fig. 4.14: Pictures of the LaCoste stage a) assembled in the pre-isolator, b) closeup view of the flexure joint which connects the rigid link to the inverse pendulum and the LaCoste frame.

129 AIGO Seismic Vibration Isolator 109 Fig. 4.15: The horizontal springs on the LaCoste linkage used to vary the amount of anti-spring in the stage by adjusting the spring extension on the sliding plate. tuning purposes of other isolation stages is made possible by clamps that attach the LaCoste stage to the top frame of the wobbly table The Inverse Pendulum - Wobbly Table The 3D tilt-rigid ultra-low frequency inverse pendulum is designed to support a load of 1000 kg and measures about one meter on each side of the cube-like frame. This device is the first horizontal isolation stage and is part of the pre-isolation stages of the vibration isolator of AIGO. Note that before balancing the inverse pendulum, all the lower stages should have already been tuned and balanced. Figure 4.16 shows the fully assembled pre-isolation stage. Two cube like frames can be seen interweaved with each other. These are the inverse pendulum and vertical LaCoste stages. Diagonal aluminium support struts are used to reinforce the structures to increase their rigidity. Another view of the pre-isolator is shown in Figure Ignoring all the electrical wiring for the control system in the picture, it can be seen that the inverse pendulum, LaCoste, Roberts linkage as well as the first few stages of the 3D isolation stack combination, are neatly packaged in a compact form. Cylindrical steel masses are placed on top and at

130 110 Chapter 4. Fig. 4.16: The pre-isolator in the AIGO main laboratory. the sides of the wobbly table for additional weight for resonant frequency tuning. A total of 360 kg is added to the stage. The inverse pendulum stage is termed the wobbly table since four inverse pendulums legs are used to support the platform (like a table). The over constraint of having four legs rather than the ideal three does not pose a problem as adjustments are incorporated into the base plates (Figure 4.18). These adjustments ensure that each leg supports the same amount of load 5.The inherent elasticity in the material will also make up for the irregularities and imperfections in the final structure dimensions. The height of the leg can be adjusted by a bolt accessed from underneath the upper support platform where the leg sits. The adjusting screws shown in the picture together with the height adjustment of 5 This is because the isolator support stand is leveled with the horizontal plane before the installation of the parts.

131 AIGO Seismic Vibration Isolator 111 Fig. 4.17: Another view of the pre-isolator, showing the extra masses on top, wiring and the Roberts linkage upper platform supporting the 3D isolation stack.

132 112 Chapter 4. the inverse pendulum leg forms effectively a triangular platform. This provides freedom for tilt in all directions as well as height offsets in each inverse pendulum leg. Balancing the inverse pendulum stage first requires the legs to be parallel with each other. Then subsequent leveling of the leg plates is required to set the frame in the center. The working range of the wobbly table is at maximum ±12 mm in every horizontal direction before hitting motion limiters. These limiters comprise of screws that are located close to each base leg plate. The limiting screws are mounted on the isolator stand with an aluminium bracket and can be adjusted for the amount of allowable travel of the horizontal pre-isolation stage. Locking of this pre-isolation stage is done by installing clamps which connect the frame to the flexure, eliminating any motion relative to the stand. Diurnal thermal drifts almost always cause the wobbly table to hit the motion limiters because of the very low frequency state the stage is at. Control at this isolation stage is essential to damp and control the motion of this isolator frame. The control system consists of an actuator and shadow sensor mounted on each of the four sides of the inverse pendulum frame to influence the movement of the isolation stage with respect to the support stand. The control scheme will be discussed more in the next Section. 4.4 Control of the Isolator The vibration isolation system of AIGO will provide adequate seismic noise attenuation in the frequency band of interest for gravitational wave detection. However, resonant modes in the mechanical system enhance the motion of the suspended test mass mirror and hence need to be damped. The suppression of residual motion of the isolator parts yields advantages, including the improvement of the robustness of the interferometer operation, and also the reduction of the mirror actuator range which results in the improvement of the noise performance. For a typical set of parameters of a Fabry-Perot cavity, the maximum allowable residual velocity of the test mass is in the order of 10 7 m/s for rea-

133 AIGO Seismic Vibration Isolator 113 Fig. 4.18: A picture of the inverse pendulum leg plate for balancing the wobbly table. sonable lock acquisition time 6. Additionally, local control is implemented into the pre-isolation stages to suppress large low frequency test mass displacements caused by diurnal thermal drifts and creep in the mechanical structure. This type of motion has time constants in the order of hours. In this section, the work done by the author on the control of the pre-isolator is discussed. The design of the control system would be different to the test mass stage as the parts involved in the upper stages are large and require larger forces to control their positions. However, since the control is done on the upper stages, the noise injected by the control system is attenuated by the passive isolation chain, hence the noise is less effective in being transmitted through to the bottom test mass. Part of the control work on the inverse pendulum was jointly done by C.Y. Lee who was a researcher from Edith Cowan University, Perth, who was with the group for a short period of time. The results of this research are presented in the paper in Appendix D. The real and simulated data represented in the 6 Threshold velocity is estimated using v = λf/f, where λ is the laser wavelength 1 µm, F the finesse of the cavity 3000, and f the length of the control bandwidth 300 Hz.

134 114 Chapter 4. graphs that are shown in this Section (and in Appendix D) were measured and computed by the author and are significant results of the control experiment that was done on the inverse pendulum. These tests and results were completed prior to the commencement of the huge task of preparing and assembling the vibration isolators in the clean laboratory at the AIGO site Preparation and background Considerable effort was placed in designing the wiring architecture for the control of the vibration isolator. These electrical wires must be attached progressively down the isolator chain to avoid seismic noise short circuiting from upper stages. The wiring layout was designed to meet each of the appropriate isolation stages control requirements as they individually have different methods of sensing and actuating. The requirement for each of the pre-isolation stages will be described later. Assembly procedures of the entire isolator were taken into account during the placements of wires, as well as performance compromises and material vacuum compatibility. Custom made socket and plug clips are installed in places of assembly joints and where parts move relative to their neighbouring parts (Figure 4.19). The reason for using these connectors is the ease of reattachment of wires and to eliminate the need to solder or re-solder in situ in the clean environment. Plug connectors were installed near shadow sensors and actuators for easy detachment and attachment of the control hardware (Figure 4.21). The clips are made from individual female and male pins soldered onto various small-sized boards made out of circuit board material. Research was done to ensure that each material used is vacuum compatible. The solder itself is called HydroX which is a flux cored solder where its flux is washable in water. All soldering work is done outside of the clean AIGO laboratory to prevent contamination. The flux is washed away during the cleaning processes before being brought in and installed under the clean tents. Test mass control requires about 20 electrical wires to be sent down the entire vibration isolator chain. Electrical wiring running along the central tubes require connectors that are rigidly attached to the top and bottom ends of the central

135 AIGO Seismic Vibration Isolator 115 Fig. 4.19: Pictures of the wiring methods installed on the isolator, a) at the breakout pallet on the isolator stand, b) plug connectors at the inverse pendulum leg plate where the flexure joint is located.

136 116 Chapter 4. tubes of the 3D isolation stack. They are connected to the other isolation stages by wires soldered to clips that are made to attach and re-attach themselves to the plugs on the central tubes. To reduce the stiffness of the wires which minimises the transfer of vibrational noise from the upper stages, long thin wires placed in a jellyfish arrangement is used, as previously described in Section At the test mass level, the mirrors must be locked to within a dark fringe where the total RMS differential residual motion at the test mass mirror must not exceed m. Such accurate positioning of the mirrors requires very sensitive control signals. Past research showed that using small permanent magnets deliver excess noise [75, 76]. An alternative to magnetic coils, is the use of electrostatic actuators, first developed by MIT [77]. The technology has been further developed by other gravitational wave groups [78, 79, 80] and is implemented into GEO600. The actuator and sensor are referenced to the control mass stage not the ground. Position sensing of the mirror is done by capacitance sensing using electrodes attached to the control mass stage. The UWA group has looked into other methods of achieving control at the test mass stage level in an attempt to avoid the use of many wires that run the entire isolator chain to send and receive signals. This will improve the attenuation of vibrational noise being transmitted down the chain through the wires and also avoids the tedious task of installing the wires at those lower stages. The elimination of electrical wires down to the test mass stage can be solved by telemetry [81, 82], which offers wireless methods to communicate with the control hardware. The use of electrostatic actuators as opposed to mini magnetic coils does not demand much power thus telemetry in this case may be possible and advantageous in attenuating more noise Pre-isolation Control The control setup diagrams for the LaCoste and the inverse pendulum are shown in the Figures D.3 and D.5. The actuator assembly for these two stages consists of a Maxwell pair of coils and a magnet in order to provide an almost position-independent force (Figures 4.20 and 4.21). The coils are made by winding 0.25 mm thick poly-imide coated copper wires 1600 times and then held

137 AIGO Seismic Vibration Isolator 117 Fig. 4.20: Two coil actuators attached to the support frame at the base of the pre-isolator. The left is the vertical actuator used for the control of the LaCoste linkage, and the right is one of four used to actuate the wobbly table. together by vacuum torr seal. These coils are attached to the isolator support stand (ground connected) where each acts on a magnet that is attached on the moving isolator part. The positioning of the actuators (and sensors) for the inverse pendulum is shown in Figure D.4. For the LaCoste stage, two magnetic/coil actuators are used for vertical control for faster responses (in combination with the slow response from the coil springs) and are placed on opposite sides of the cube frame. Each actuator only applies forces in one dimension in-line with the coil axis. All sensing of the pre-isolator stages are done by shadow sensors (their functions as described in Section 2.2 where the testing of the Roberts linkage was discussed). The control scheme of the Roberts linkage was discussed earlier in Chapter 2. The results of improving the center of percussion of the Roberts linkage is presented later in this Chapter in Section 4.5. The digital control at AIGO is used for position sensing and alignment of isolation stages. DSP (digital signal processing) boards together with the sensing and actuating hardware described above, form the local control loops. The software Labview developed jointly by the author is used to communicate with the DSP and forms the user interface where the control loop gains and set point values can

138 118 Chapter 4. Fig. 4.21: The shadow sensor and actuator for the LaCoste linkage. be changed. A PID controller is used for each pre-isolation control stage. Specifications of the DSP hardware used are listed in Appendix D in Section D.2.2. A daughter board is plugged onto the DSP for ADC and DAC conversions to the control boards. The analogue signals pass through an anti-aliasing filter before being digitised and continue into the DSP. The control boards are manufactured to provide the power requirements and the necessary input and output channels to drive the sensors and actuators and communicate with the DSP. The rack which houses the power supplies and boards are seen in Figure LaCoste linkage stage control The LaCoste linkage stage uses 11 diagonally placed coil springs on each of the four sides of the pre-isolator frame, making 44 coil springs in total to support the weight of the isolation stages. For the heating of the coil springs, an electrical circuit comprising of these springs is created. The electrical connection between the springs is achieved by installing short flat steel strips which are bolted on together with the spring ends 7. Each spring end is hooked onto a bolt head in which the bolt is attached onto a common strip of G10 material 8. This part is 7 These connectors can be seen as the blue strips in Figure 4.16 at the ends of each of the LaCoste springs. 8 G10 is a hardened glass reinforced epoxy material of high mechanical strength and is a good insulator.

139 AIGO Seismic Vibration Isolator 119 Fig. 4.22: The control shelf consisting of power supplies and control boards required to control the pre-isolator. rigidly attached onto the frames of the inverse pendulum or the LaCoste linkage as seen in the figures. As mentioned previously, the LaCoste linkage stage uses two types of actuation: the heating of the coil springs, and through the use of magnetic/coil actuators. The actuation done through heating the springs has a rather slow response and is well suited to slow diurnal drifts that we see in our measurements. Only a small integral gain is applied to the PID control loop that uses the heating of the coil springs. Similar to the Roberts linkage, an initial current is supplied into the coil springs to allow for upward and downward control (as mentioned in Section 4.3.3). This initial current is configured in the PID control loop which

140 120 Chapter 4. assures the LaCoste stage is at the specified set point. For faster responses, the magnetic/coil actuators are used. Small differential (damping) and integral gains are applied to this control loop using this form of actuation. The control is done by splitting the error signal coming from the digitised shadow sensor signals and put through a low pass digital filter to the coil spring heater, and a high pass digital filter to the coil actuators. A cut-off frequency of about 5 mhz ( 3 minutes) is used to split the lower and higher frequency signals to the coil springs and to the actuators. Tests show that the LaCoste stage has a very low Q-factor ( 2 from Figure D.2.3), hence only a very small differential gain is used to damp the resonant mode (of frequency about 60 mhz). This low Q-factor value is mainly due to the 44 very lossy coil springs which support the LaCoste linkage. An electrical resistance of approximately 4.5 ohms is recorded in each set of 11 coil springs which includes the electrical wiring going to and coming from the power supply that provides the heating current. The diagonal springs are connected in series thus a zig-zag configuration of the current flow in the springs is used. However, each of the four sets are connected in parallel resulting in a total electrical resistance of about 1.5 ohms. An external voltage controlled current source is used to supply the heating requirements in the PID control loop. Preliminary results in controlling the LaCoste linkage to account for slow diurnal thermal drifts using the control methods described above, show that using only derivative and integral gains in the PID controller are sufficient in controlling a system with a long time constant. The LaCoste stage was able to be positioned over several days within 10 4 m of the set point. Further experimentation is planned to optimise this value and testing will be conducted on the isolator once completely assembled at the AIGO site. Inverse pendulum stage control The results presented in the rest of this section were obtained from performance testing the isolator without the suspension of the 3D isolation stack, ie. the mechanical structure only consisted of the inverse pendulum ( wobbly table ), the LaCoste linkage and the Roberts linkage. Weights were placed on the inverse pendulum frame to account for the missing mass that would usually be suspended off the Roberts linkage. The Roberts linkage stage was locked at all times with

141 AIGO Seismic Vibration Isolator 121 the inverse pendulum frame to prevent movement and to avoid its resonant peak appearing in the transfer function measured at the inverse pendulum stage. To performance test the inverse pendulum, ideally we would need to suspend the entire isolator at the stand, then shake test at this support stage. However, this is an extremely difficult exercise that requires large support rigs and actuating equipment to do it (VIRGO has mounted their inverse pendulum on special roller skates to allow for 2D motion [30], as well as TAMA mounted their SAS on oil bearings [33]). The reason for this form of actuation is to have an input large enough so that at higher frequencies, the output signal level will not be saturated by equipment noise. As can be seen in the following graphs, we were able to obtain results up to about 100 Hz using the conventional spectral analyser with seismic noise as the input (test was done in the laboratory at UWA). The control loop block diagram is shown in Figure A PID controller is used in the feedback loop where integral and differential gains were used. Proportional gain feedback seemed to be unnecessary in the position and damping control as can be seen later in the resulting transfer functions. The open loop transfer function was measured without having to measure the closed loop transfer function [83]. This was done by injecting a signal n at the position shown 9 and reading the signals immediately before and after the place of injection (signals r and m). This is shown in the following algebraic expressions. Consider ABC as the open loop transfer functions where A, B and C are the transfer functions of the control elements shown in the Figure. Thus: r n = ABC 1 + ABC, and m n = ABC, hence r = ABC (4.1) m Figure 4.24 shows the resulting open loop transfer function. The unity gain frequency is 145 mhz with a phase margin of approximately 90 degrees (Figure 4.25). There is room for further increase in the open loop gain but the amount of damping is already sufficient as seen Figures 4.26 and It is also 9 The position of injection can in principle be anywhere in the chain.

142 122 Chapter 4. Fig. 4.23: The block diagram of the control loop for the inverse pendulum. known that since the shadow sensor is measuring with reference to the suspension support frame and not by inertial motion, increasing the gain would result in an increase of seismic noise being injected back into the system. The splitting of the main resonant peak at about 50 mhz is due to the coupling of the other horizontal axis which has almost the same resonant frequency. The center of percussion effect can be observed in the notch in the transfer function at 2-3 Hz, followed by the rise in the isolation floor. Tuning to improve this isolation floor was not done at the time of writing. Attaching weights close to the leg support ends will improve the isolation at higher frequencies by the redistribution of the leg mass and making the point of center of percussion (the point of no motion) coincide with those positions. Models created based on the inverted pendulum of the SAS system (of the TAMA and LIGO project) looked at placing counter weights below the flex leg joint and showed promising results [36]. Graphs showing the effectiveness of the damping control of the inverse pendulum at resonance can be seen in Figures 4.26 and At the resonant mode frequency of 50 mhz, damping has reduced the peak from 10 3 m/ Hz down to about m/ Hz with more than one magnitude decrease in the RMS residual motion. Coupling of the rotational mode can be seen in the slight bump in the transfer function at about 450 mhz. Internal resonances can be seen starting at about 4 Hz to about 10.5 Hz. The strong appearance of these peaks is due to the other stages in the pre-isolator that were clamped locked to the first isolation stage so their vibrations due to their internal resonances have strongly coupled to the inverse pendulum frame. We know that the coil springs in the LaCoste

143 AIGO Seismic Vibration Isolator 123 Fig. 4.24: The magnitude of the open loop gain with derivative gain ([84]). Fig. 4.25: The phase of the open loop gain ([84]).

144 124 Chapter 4. Fig. 4.26: The spectral density plot of the inverse pendulum with and without damping ([84]). Fig. 4.27: RMS residual motion of the inverted pendulum with damping on and off ([84]).

145 AIGO Seismic Vibration Isolator 125 linkage stage have internal frequencies of about 17 Hz, thus it is reasonable to suspect that the peaks appearing closest to that frequency may be caused by these elements. Fig. 4.28: The theoretical horizontal residual motion of the full isolation system of AIGO using the measured pre-isolation performance ([84]). A theoretical residual motion spectrum was obtained using the horizontal residual motion shown in Figure 4.26 then multiplying this with a theoretical transfer function of the remaining isolation stages, which includes the Roberts linkage and three stages of isolation. The model used has the Roberts linkage with a resonant frequency of 50 mhz, and each of the three pendulum stages of 0.6 Hz. The resulting plot shown in Figure 4.28 shows what the fully assembled and tuned vibration isolator of AIGO can achieve by integrating its theoretical model with some real data of the first stage and seismic noise. The plot indicates that the completed and tuned suspension system has a residual motion of about m/ Hz at 10 Hz in the horizontal direction. The seismic noise level would improve had the experiment been done at the AIGO site rather then in the relatively noisy laboratory of UWA.

146 126 Chapter Suspension System of AIGO Paper AIGO High Performance Compact Vibration Isolation System E. J. Chin, J. C. Dumas, C. Zhao, L. Ju, D. G. Blair School of Physics, The University of Western Australia, Nedlands, WA 6009, Australia We present a completed prototype of the AIGO seismic vibration isolation system. The design has been developed to satisfy the isolation requirements for the next generation of interferometric gravitational wave detectors. The system relies on passive isolation and includes multiple Ultra Low Frequency (ULF) stages to achieve minimal low frequency residual motion. Two complete isolators are being installed at the high power test facility located in Gingin, Western Australia. The performance of individual mechanical stages is continually being tested and improved. Currently it is expected that residual motion close to 1 nm at 0.2 Hz will be achieved Introduction A high performance vibration isolation system is being developed for advanced gravitational wave detectors at the AIGO High Optical Power Interferometer Facility in Gingin, Western Australia. The system is distinguished by a relatively compact height, three stages of pre-isolation, an all passive design and the use of several novel isolation techniques. In addition to high performance isolation within the detection bandwidth, it is critical to the interferometer operation that the isolator provides minimal residual motion at low frequencies in order to facilitate cavity locking and to minimise noise input through actuation forces. Because pendulum systems inherently have large Q-factors, it is necessary to damp the normal modes of the suspension system. Current isolator designs developed for GEO [67], LIGO [23], TAMA [68, 43] and VIRGO [30, 31] have approached this problem with a variety of techniques, using passive and active damping designs. The isolator reported here relies on a novel passive damping technique, and a double horizontal pre-isolation design to achieve nanometre residual motion at low frequencies.

147 AIGO Seismic Vibration Isolator 127 This system consists of a three dimensional pre-isolator [12, 51]; (from Figure 4.5.2) (a) the inverse pendulum, (b) the LaCoste linkage, and (c) the Roberts linkage [35, 85]. After the pre-isolation stages an isolation stack is suspended which consists of three low frequency three-dimensional isolator stages [37, 86]. In this paper we review the AIGO isolation design and report on isolation performance measurements and tuning. Individual stage measurements have shown near ideal performance. Measurements on multistage systems always quickly reach sensitivity limit due to sensor noise and reference frame noise. Thus the ultimate noise performance is not easily verified, but the critical issue of normal mode performance and residual motion can be determined. These aspects are presented here. The design of the isolator and concepts behind these techniques are reviewed in section The experimental results and tuning progress are presented in section Finally we report in section on the status of the development of the isolation system at the AIGO site in Gingin, Western Australia Isolation Techniques The AIGO mechanical vibration isolator consists of multiple stages as shown in Figure 4.29 which uses several different techniques to attenuate seismic noise. Anti-Spring geometries are implemented into various stages to reduce fundamental mode frequencies [86, 49]. The pre-isolator consists of several stages, the inverse pendulum, the LaCoste linkage and the Roberts linkage, each with their resonant frequencies below 0.1 Hz. The inverse pendulum pre-isolation stage or sometimes called the wobbly table is effectively a table top supported at each corner by inverse pendulums. Vertical pre-isolation is provided by the LaCoste linkage [12] which is a combination of inverse pendulums and coil springs supporting the load. The Roberts linkage is a relatively simple design as illustrated in Figure A cube frame is suspended by 4 wires which are hung off the vertical pre-isolation stage. The load is suspended at about the same height that the Roberts linkage wires are attached from, resulting in a very low fundamental resonant frequency [35, 37].

148 128 Chapter 4. Inverse pendulum Roberts Linkage a d c b e LaCoste stage Euler stage Self-Damped pendulums Control mass Test mass Fig. 4.29: Isolation stages of the AIGO suspension chain. The pre-isolation stages include a, b and c. The isolation stack is defined as the three identical stages of self-damped pendulums with Euler stages; a) Inverse pendulum pre-isolator [12] b) LaCoste Linkage [12] c) Roberts Linkage [85] d) Euler springs [86] e) Selfdamped pendulums [37]

149 AIGO Seismic Vibration Isolator 129 Fig. 4.30: Roberts Linkage diagram [85]. A low frequency isolation stack is suspended from the Roberts Linkage consisting of three almost identical stages. A 40 kg mass load is suspended from each stage in a self-damped pendulum arrangement as illustrated in Figure The self-damping concept consists of viscously coupling different degrees of freedom of the pendulum mass and is discussed in the paper by Dumas [37]. The Euler spring vertical stage shown in Figure 4.32 is used to further attenuate the vertical component of seismic noise. Euler spring stages can be tuned with anti-spring geometries to achieve good low frequency performance within a very compact design as reported by Chin [86]. Each of the stages comprise of the combination of a self damped pendulum and an Euler spring vertical stage in an arrangement as illustrated in Figure Local control will be implemented at the pre-isolation stages. The combination of coil and magnet provides the actuation for the positioning and damping for both the wobbly table and the LaCoste stages. Additional heating of the coil springs at the LaCoste stage provides a means of compensating for slow temperature drifts in the vertical direction as well as correcting for creep in the isolation chain. Position control is also done at the Roberts linkage stage by heating of the individual wires (Section 2.13). In Figure 4.30a, the links AC and BD represent the suspension wires that would be heated.

150 130 Chapter 4. Double wire suspended on a pivot, free to swing. 40kg Rocker mass, high moment of inertia. Viscous damping Pivot Fig. 4.31: Self-Damping diagram [37]. Flexure Rotational arm Euler Springs Clamps Load Fig. 4.32: Euler Spring vertical stage diagram [86]. The test mass is housed in a control cage suspended from the isolation system by a single fibre suspension. Local actuation and sensing is done electrostatically via a capacitance plate mounted on the control cage [80] Experimental and theoretical results The assembly of a full scale prototype vibration isolator was completed at the university of Western Australia. The transfer functions of the inverse pendulum in the pre-isolator was measured in both the horizontal and vertical planes. These results are presented in the paper by Lee [84] along with the implementation of the Proportional-Integral-Differential (PID) control. The performance of the Roberts linkage was also recently tested and tuned. This was done by sensing the motion

151 AIGO Seismic Vibration Isolator 131 Al web rigidly clamped to the suspension tube Rocker mass Copper plates attached to Al web, rigid with respect to suspension tube Magnets attached to rocker mass Euler springs Rotational arm rests on Euler springs and is suspension point for next stage Bottom of springs is clamped to suspension tube Fig. 4.33: The combined 3D isolator stage [37]. output from point at which the 3D stack is suspended from the Roberts linkage. The shaking was done by actuating upon the inverse pendulum. The tuning of the roberts linkage is a meticulous process best explained by a theoretical model as presented in [85] (Chapter 2) showing the effect of varying the suspension point height (point P increases in height where C and D remain fixed see Figure 4.30). Not only is the normal mode frequency affected but also the high frequency isolation floor. Figure 4.34 shows the transfer function results of increasing the suspension point P. Moving this point influences the center of percussion of the Roberts linkage structure which determines the isolation floor (the concept is described in [85]). The third curve shows a vast improvement in both the normal mode frequencies and the roll off above 2.3 Hz. Increasing the mass of the structure decreases the resonant mode frequency. Also, by placing the additional mass close to the suspension point, the radius of gyration decreases thereby improving the performance. It is shown that there is a 20 db improvement at 7 Hz compared with the untuned curve (see Figure 4.34 (a) vs. (b) and (c)). However at 10 Hz we see a peak appearing as we progressively improved the isolation floor level. Further investigations are being done in an effort to find the real source of the peak 10. The low frequency isolation stack has also 10 The peak appearing at about 10 Hz in Figure 4.34 seems to be shifting towards the left as well as reducing in absolute db value with the normal mode peaks with each modification step

152 132 Chapter 4. been extensively tuned and tested, with results reported elsewhere [37, 86]. We have obtained satisfying results in which experimental curves compared well with theory. 0 (a) (b) (c) db Frequency (Hz) Fig. 4.34: Robert Linkage Frequency Response under different tuning conditions: a) Load suspended at point P b) Load suspended 12 cm higher c) Load suspended 12 cm higher and with a 5 kg tuning mass. The horizontal transfer function of the complete 3D isolation system has been simulated and is shown in Figure The RMS residual motion is also shown in Figure From these we expect an RMS residual motion of 1nm at 0.2Hz. This level of attenuation improves the ease in which to acquire cavity locking [15]. It is also expected that at 2Hz, the suspension system would have 120 db of attenuation level and an RMS motion of m [37]. which suggests that the contributing source is somewhere along the chain. The dip in the curve left of this peak is also characteristic of an up-conversion of isolation stages suspended below the Roberts linkage stage. The author suspects this peak is due to the mini pendulums that are present in the 3D stack which are defined by the distance between the gimbal supporting the mass plate and the start of the next Euler stage where the suspension wires hang to support the lower stages. The peaks at about 10 Hz in the theoretical transfer function (Figure 4.35) is due to these pendulums but with much lower Q-factors.

153 AIGO Seismic Vibration Isolator db Frequency (Hz) Fig. 4.35: Transfer function theoretical curve RMS Res. Motion (m) Frequency (Hz) Fig. 4.36: RMS residual motion theoretical curve.

154 134 Chapter Isolator Progress in AIGO Efforts are made to install two full vibration isolator systems at the test facility of AIGO. The isolators are assembled in a clean room environment in the central laboratory in Gingin. Each mechanical part is UHV cleaned under stringent conditions. The first system is nearing completion. Immediately following this the assembly of the second will commence to eventually form a 80 meter long East arm cavity. Performance testing of the full isolators is planned later in the year after the completion of the cavity. This will be done in UHV conditions where the cavity can be laser locked. The error signal of the locked cavity will be used to test the performance of the control system and to obtain transfer functions of the vibration isolators Acknowledgments We would like to acknowledge the Australian Research Council for their support of this work. This project is part of the research program of the Australian Consortium for Interferometric Gravitational Astronomy.

155 AIGO Seismic Vibration Isolator Postscript Status of the AIGO Vibration Isolators Fig. 4.37: Picture of the vibration isolator assembled at the AIGO site. At the time of writing this thesis, one complete vibration isolation system is installed and is partially tuned under clean room conditions in the AIGO main laboratory. This isolator is positioned at the input of the Fabry-Perot cavity in the east arm of the interferometer designed to suspend the input test mass (ITM). The entire assembly is housed under a clean tent (Figures 4.1(b) and 4.37). The

156 136 Chapter 4. isolator stand which forms the platform of the entire isolator is sitting on leg bellows which are softly connected to the bottom section of the vacuum tank (Figure 4.38(a)). In the laboratory of AIGO, independent concrete foundations are inserted at the positions where each vibration isolation system is situated. This is to minimise the vibrations in the concrete flooring caused by human activities in the main area coupling into the vibration isolation system. The leg bellows seen in Figure4.38(b) serve as a decoupler of the vibrations coming from the vacuum tank which stand on the main concrete floor. The leg bellows sit on the independent concrete floor and bridge the vacuum envelope in the tank. The isolator stand sits on the leg bellows and thus the transmission of noise vibration from the main concrete floor through the vacuum tank is minimised. Each isolation stage is tuned but not to optimal performance. At the preisolation stages, both the inverse pendulum and Roberts linkage have a resonant frequency of 60 mhz while the vertical LaCoste stage is currently at 0.14 Hz. The three main pendulums in the 3D stack have lengths of 640 mm ( 0.6 Hz) with the final pendulum which suspends the dummy test mass of length 240 mm ( 1 Hz). Each of the vertical Euler stages is temporarily tuned to have a resonant frequency of about 1.5 Hz. The final transfer function will of course reflect the interactions between the stages and the expected resonant peaks will be shifted. Further tuning will be done once the entire system is closer to completion. This includes the full installation of the control system as well as the suspension of the control mass and test mass mirror. Almost all the necessary wiring for the control system is installed on the first isolation system in the main laboratory. The tasks of making connectors, attaching mounting points and support platforms for the copper wires are completed, and a series of tests are being performed for connectivity. The break out pallet which all the wires are connected to before running to their various locations on the vibration isolator is installed and ready for connection with the hardware outside the vacuum tank. Feed-throughs on the vacuum tanks have been installed. The necessary hardware is installed for the control of the pre-isolator for the completed passive isolation system located in the main laboratory at AIGO. The

157 AIGO Seismic Vibration Isolator 137 Fig. 4.38: The bottom section of the isolator stand; a) the tank rigidly connects with the blue concrete while the leg bellows that support the isolator stand sit on the yellow concrete section and is softly connected with the vacuum tank itself; b) close up view of the leg bellow at the bottom of the tank.

158 138 Chapter 4. controls to the test mass stage has yet to be finished, mainly concerning the wiring components. Currently the PID control of the individual pre-isolation stages are being optimised. This is done through a series of tests which mainly involve the adjustments of the PID gain values in both open loop control and short term closed loop control schemes. Global control to lock a cavity in the east arm has yet to be implemented. In global control, the feedback error signals are based on signals coming from multiple parts of the interferometer. In our case, the feedback signals are coming from another vibration isolator. The signals being fed back into actuators help the cavity maintain resonance (the global signals used in this context relates to cavity length). It is intended that optical fibres will be used in the final AIGO interferometer to link the end stations for faster processing speeds and a more robust setup (currently using serial cables). In the east end station of the facility, situated 80 m from the central laboratory where the end test mass (ETM) will be suspended, the integration of the two main subassemblies as described in Section 4.3 has recently begun. Each vertical Euler stages is tuned to about 1 Hz and together with the Roberts linkage stage will soon be lifted and lowered into the second subassembly. The first assembly will be suspended off the LaCoste stage in the second subassembly which consists of the support stand and the inverse pendulum. The entire room is in a clean environment with an additional clean tent placed over the isolator. Unfortunately, the end station does not have washing facilities to clean the individual parts thus each part needs to be washed, carefully wrapped and transported from the main central laboratory for assembly. Wiring installation on the second vibration isolator is not complete. The wiring to the test mass stage along the 3D isolation stack (which includes the jellyfish layout between the individual pendulums) is installed. It is important that wiring at these isolation stages is done prior to their assembly to ease the installation process. This is mainly because the wiring involves rigid attachments of the wire connectors to the central tube as well as soldering the wires to the individual pins (which must be done outside the clean room to avoid contamination). The breakout pallet on the isolator stand as well as the connectors

159 AIGO Seismic Vibration Isolator 139 and wires running along the isolator support stand is installed, ready for further wiring connections to the upper stages. Apart from the work done on the vibration isolators and control systems, other elements that are in preparation to obtain cavity lock are the vacuum system and the optical equipment required to power and align the laser beam down the arm. The setup of the optics and laser is already sufficiently established due to previous testings and experimentations conducted in the AIGO laboratory. The laser frequency was locked in the 80 m south arm cavity to the TEM00 mode in May For the vacuum system, the construction of the required pipes and flanges and all the necessary parts for the tank to attach to the vacuum pumps is completed. Electronic gate valves that are used to control the evacuation of the air inside the tanks have been installed and tested. Both vacuum tanks that house the two vibration isolators in the east arm of AIGO have also been leak checked.

160 140 Chapter 4.

161 Chapter 5 Discussion and Conclusion 5.1 Summary The implementation of ultra-low frequency pre-isolators into vibration isolation systems has demonstrated that the residual motion of the suspended test mass is significantly reduced. The relatively new concept of the Roberts linkage is used as one of the horizontal pre-isolation stages in the AIGO vibration isolator. We have built a complete vibration isolation system in the laboratory at UWA which includes for the first time the Roberts linkage as part of the whole isolation chain. Modelling was done to gain an understanding of the performance of the Roberts linkage, particularly the change in its properties by the adjustment of various structural parameters. The model has shown it is possible by various methods to change the resonant frequency and the isolation floor, by the adjustment of parameters such as the center of mass position, the radius of gyration (which is related to mass distribution of the Roberts linkage) and the suspension height of the 3D isolation stack. Theoretical graphs were obtained and highlight some valuable properties of the isolation stage. The change in the suspension point height at which the lower stages hang from on the upper frame of the Roberts linkage influenced both the resonant frequency and the isolation floor, hence a compromise has to be made. Similar effects could be seen by the addition of small tuning masses as part of the Roberts linkage frame (at one particular height). The change in the distribution of these tuning masses while the height was kept constant changed the radius of gyration (since the moment of inertia of the structure would change). By shifting these masses it was found that the 141

162 Chapter 5 Discussion and Conclusion 5.1 Summary The implementation of ultra-low frequency pre-isolators into vibration isolation systems has demonstrated that the residual motion of the suspended test mass is significantly reduced. The relatively new concept of the Roberts linkage is used as one of the horizontal pre-isolation stages in the AIGO vibration isolator. We have built a complete vibration isolation system in the laboratory at UWA which includes for the first time the Roberts linkage as part of the whole isolation chain. Modelling was done to gain an understanding of the performance of the Roberts linkage, particularly the change in its properties by the adjustment of various structural parameters. The model has shown it is possible by various methods to change the resonant frequency and the isolation floor, by the adjustment of parameters such as the center of mass position, the radius of gyration (which is related to mass distribution of the Roberts linkage) and the suspension height of the 3D isolation stack. Theoretical graphs were obtained and highlight some valuable properties of the isolation stage. The change in the suspension point height at which the lower stages hang from on the upper frame of the Roberts linkage influenced both the resonant frequency and the isolation floor, hence a compromise has to be made. Similar effects could be seen by the addition of small tuning masses as part of the Roberts linkage frame (at one particular height). The change in the distribution of these tuning masses while the height was kept constant changed the radius of gyration (since the moment of inertia of the structure would change). By shifting these masses it was found that the 141

163 142 Chapter 5. center of percussion could be tuned while having very little effect on the resonant frequency of the Roberts linkage stage. By inserting real parameters of the Roberts linkage into the model, we were able to determine approximately the state which the isolation stage is at and we were able to take the appropriate steps to improve the performance. It was shown that the model agreed well qualitatively but varied a bit quantitatively because of imperfections in the real system. The lifting of the suspension height of the lower stages on the upper frame of the Roberts linkage stage that is part of the vibration isolation system in the laboratory at UWA, showed an improvement in the isolation floor of 20 db at 7 Hz. The AIGO group uses Euler springs for its main form of vertical isolation. Study has shown advantages in using this type of spring mechanism compared to other forms. The main advantage is the reduction in spring mass when supporting similar loads which increases the frequency of the internal modes, improving the gravitational wave frequency detection band. Research was done to further reduce the resonant frequency by incorporating geometric anti-springs into the Euler stage. The design involved lifting the mass plate wire suspension point height with respect to the upper Euler spring attachment points on the rotational arms. An inverse pendulum was effectively created and together with the stiffness of the Euler springs, suspension wire and the flexures acting as the pivots for the rotational arms, produced the desired low resonant frequencies. Non-linearities in the force-displacement curves of the Euler spring stage were seen in the results. This meant that the resonant frequency would change depending on the amount of compression the Euler springs underwent. It is undesirable to have this effect because it would decrease the predictability in the performance of the isolation stages. One issue was the amount of creep that was observed during the tests and it was shown that maraging steel gave better results compared to other spring materials. Different spring clamping conditions were tested as suggested by the theoretical model created by Winterflood [57], that the variation of the angles at which the springs launched could decrease the curvatures in the force-displacement graphs. Experimental results confirmed those obtained from the model where it showed the decrease in the curvatures of the Euler stage.

164 Discussion and Conclusion 143 With all the above techniques, a low resonant frequency of one Euler stage of 0.3 Hz was achieved. The author was involved in coordinating the task of manufacturing the first two vibration isolators to be installed and tuned at the AIGO site. This included the assurance of vacuum grade clean parts entering into the AIGO laboratory and the scheduling of tasks to maintain constant productivity. Cleaning procedures are summarised in this thesis, as are the important steps in tuning and balancing a full vibration isolator. Once completely built, the isolators must be ready to be part of the Fabry-Perot cavity which is to be built in the east arm of the facility for further experimental testing. Of concern to the author is that the measure of the overall performance of the complete vibration isolation system has not yet been obtained experimentally. Theoretical transfer function of the full vibration isolator predicted an isolation of 300 db at 10 Hz. At the time of writing, one isolator has been built and tuned at the ITM end of the east arm. The second isolation system at the ETM end is still in the process of assembly. Control of the pre-isolation stages was implemented and tested on the fully built vibration isolator to individually damp and position control the three isolation stages. Shadow sensors were used as the sensing devices while magnetic/coil actuators were used as the main form of actuation for the control of the first horizontal inverse pendulum stage. The LaCoste stage was designed to accommodate two types of actuation; the magnetic/coil actuator (for damping and faster responses), and the coil spring heating (for slow temperature drifts). In the Roberts linkage case, control was also achieved using the property of material expansion driven by electrical currents. At this isolation stage, control was done by individually heating four suspension wires. Digital PID systems were designed and coded and showed adequate results in controlling each of the pre-isolation stages. This control system has been installed in the vibration isolation system up at the AIGO facility at the ITM end and is currently being optimised.

165 144 Chapter Future Work Results that see further improvements of the isolation performance of the Roberts linkage should be obtained from further testings. This experiment was stopped due to lack of time. The vibration isolator assembled at AIGO should be an ideal platform for further experimentation with the system being in a more controlled environment. Preliminary results showed promise in the mathematical code that models the Roberts linkage. Its accuracy can be improved by inserting or adjusting variables to account for the imperfections and uncertainties in the real system (such as due to the stiffness of suspension wires). From the research reported in this thesis, the center of percussion is an important parameter when it comes to the amount of vibrational noise that can be attenuated at frequencies above resonance. Center of percussion effects can be seen in all stages of the isolator chain and the author suspects that for future performance enhancements, center of percussion tuning may play a crucial role in ensuring good isolation performance at higher frequencies. The author suggested and described methods of tuning several individual stages in this thesis. Further studies should be undertaken to assess the amount of seismic noise vibration that is being transmitted through the electrical wires, particularly the electrical wires installed into the central tubes that provide the signals going to and from the test mass stage. A measure of how effective the jellyfish arrangement is between the pendulum stages in the 3D stack should be done and tests should be done to ascertain if there are any better wire arrangements to improve noise transmission between stages. The amount of vibrational noise coupling to isolation stages becomes more important as we go further down the isolation chain. Although we have successfully controlled the pre-isolation stages to the specified set points and the damping of each stage to a sufficient level, optimisation and tweaking of the gains of the PID control loops for each of the stages are recommended. The results obtained were based on the isolation system situated in the rather noisy laboratory at UWA. Further tests on the robustness of the control system in a controlled environment in the AIGO facility will be beneficial for both local and global control.

166 Discussion and Conclusion Conclusion The facility at the AIGO site in Gingin is a test bed for high optical power experiments. The short term goal of the group is to have one Fabry-Perot cavity constructed in the east arm of the main laboratory. This involves the completion of two vibration isolation systems at the AIGO site and will allow recording of more sensitive isolator performance measurements. The completion of the cavity will also provide opportunities for experiments to be conducted on the operation of high powered lasers for next generation interferometric gravitational wave detectors. This includes experiments involving thermal noise, thermal lensing effects, parametric instability and optical spring effects, laser stability and noise, advanced local and global control systems, vibration isolation performance and high vacuum systems. In the course of this research the author has learnt the importance of seismic noise attenuation in test mass mirrors for interferometric gravitational wave detectors. More importantly, the author has gained knowledge and understanding of traditional and modern techniques used to design such systems in the field of gravitational wave research. These techniques have been studied and modeled and have been applied. The results gained during this research project will assist in the development of the high performance vibration isolation systems that are being built for a five kilometer baseline Australian gravitational wave observatory.

167 146 Chapter 5.

168 Bibliography [1] A. Einstein. Ann. der Phys., 49:769, [2] R.A Hulse and J.H. Taylor. Discovery of a pulsar in a binary system. Astrophys. J., 196:L51, [3] J.M Weisberg and J.H. Taylor. Observations of post-newtonian timing effects in binary pulsar psr Phys. Rev. Lett., 52:1248, [4] J. Webber. Detection and generation of gravitational waves. Phys. Rev., 117: , [5] V. Fafone. Resonant-mass detectors: status and perspectives. Class. Quantum Grav., 21:S377 S383, [6] A. Abramovici et al. Ligo: the laser interferometer gravitational-wave observatory. Science, 256:325, [7] D. Sigg. Commissioning of ligo detectors. Class. Quantum Grav., 21:S409 S415, [8] F. Acernese et al. Status of virgo. Class. Quantum Grav., 21:S385 S394, [9] B. Willke et al. Status of geo 600. Class. Quantum Grav., 21:S417 S423, [10] R. Takahashi et al. Status of tama 300. Class. Quatum Grav., 21:S403 S408, [11] Network Analysis of Gravitational Waves. [online] Gingin Workshop, Western Australia,

169 148 Chapter 5. [12] J. Winterflood. High Performance Vibration Isolation for Gravitational Wave Detection. PhD thesis, The University of Western Australia, [13] D. Coward, J. Turner, and D.G. Blair. Characterizing seismic noise in the 2-20 hz band at a gravitational wave observatory. Rev. Sci. Instrum., 76:44501, [14] Kuroda K. and LCGT Collaboration. Progress in gravitational wave detection: Interferometers. Nucl. Phys. B, 110:202, [15] L. Ju, D.G. Blair, and C. Zhao. Detection of gravitational waves. Rep. Prog. Phys., 63: , [16] H. B. Callen and T. A. Welton. Irreversibility and generalised noise. Phys. Rev., 83:34 40, [17] B.H. Lee, L. Ju, and D. G. Blair. Orthogonal ribbons for suspending test masses in interferometric gravitational wave detectors. Phys. Lett. A, 339: , [18] B. Lee, L. Ju, and D. G. Blair. Thin walled nb tubes for suspending test masses in interferometric gravitational wave detectors. Phys. Lett. A, 350:319, [19] S. Rowan, J. Hough, and D.R.M Crooks. Thermal noise and material issues for gravitational wave detectors. Phys. Lett. A, 347:25 32, [20] A. Heptonstall, G. Cagnoli, J. Hough, and S. Rowan. Characterisation of mechanical loss in synthetic fused silica ribbons. Phys. Lett. A, 354: , [21] S. Gras, D. G. Blair, and L. Ju. Thermal noise dependence on equatorial losses in the mirrors of an interferometric gravitational wave detector. Phys. Lett. A, 333:1 7, [22] V.B. Braginsky, Y.I. Vorontsov, and K. Thorne. Quantum nondemolition measurements. Science, 209:547, 1980.

170 Discussion and Conclusion 149 [23] R. Abbott et al. Seismic isolation for advanced ligo. Class. Quan. Grav., 19: , [24] N.A. Robertson et al. Seismic isolation and suspension systems for advanced ligo. Proc. of SPIE, 5500:81 91, [25] F. Cavalier et al. The global control of virgo experiment. Nucl. Instrum. Methods Phys. Res. A, 550: , [26] F. Acernese et al. First locking of the virgo central area interferometer with suspension hierarchcal control. Astro. Phys., volume=. [27] R. Abbott et al. Seismic isolation enhancements for initial and advanced ligo. Class. Quantum Grav., 21:S915, [28] C. Hardham et al. Quiet hydraulic actuators for the laser interferometer interferometric gravitational-wave observatory (ligo). Proc. of Cont. and Prec. Sys., ASPE Topical Meeting, [29] S. Braccini et al. Design and operation of an interferometer developed to test the suspension of the virgo gravitational wave antenna. Phys. Lett. A, 173: , [30] G. Losurdo et al. An inverted pendulum pre-isolator stage for the virgo suspension system. Rev. Sci. Instrum., 70: , [31] G. Ballardin et al. Measurement of the virgo superattenuator performance for seismic noise suppression. Rev. Sci. Instrum., 72: , [32] J. Giaime, P. Saha, D. Shoemaker, and L. Sievers. A passive vibration isolation stack for ligo: Design, modelling, and testing. Rev. Sci. Instrum., 67: , [33] S. Marka et al. Anatomy of the tama sas seismic attenuation system. Class. Quantum Grav., 19: , [34] L. Ju and D.G. Blair. Low resonant frequency cantilever spring vibration isolator for gravitational wave detectors. Rev. Sci. Instrum., 65: , 1994.

171 150 Chapter 5. [35] F. Garoi, J. Winterflood, L. Ju, J. Jacob, and D.G. Blair. Passive isolation using a roberts linkage. Rev. Sci. Instrum., 74:3487, [36] A. Takamori. Low Frequency Seismic Isolation for Gravitational Wave Detectors. PhD thesis, [37] J.C. Dumas, K.T. Lee, J. Winterflood, L. Ju, D.G. Blair, and J. Jacob. Testing of a multi-stage low frequency isolator using euler spring and selfdamped pendulums. Class. Quantum Grav., 21:S965, [38] M. Pinoli, D.G. Blair, and L. Ju. Test on a low frequency inverted pendulum system. Meas. Sci. Technol., 4: , [39] J. Winterflood et al. Position control system for suspended masses for laser interferometer gravitational wave detectors. Rev. Sci Instrum., 66:2763, [40] L. Ju. Vibration Isolation and Test Mass Suspension Systems for Gravitational Wave Detection. PhD thesis, The University of Western Australia, [41] M.V. Plissi, C.I. Torrie, M. Barton, N.A. Robertson, A. Grant, C.A. Cantley, K.A. Strain, P.A. Willems, J.H. Romie, K.D. Skeldon, M.M. Perreur-Lloyd, R.A. Jones, and J. Hough. An investigation of eddy-current damping of multi-stage pendulum suspension for use in interferometric gravitaional wave detectors. Rev. Sci. Instrum., 75:4516, [42] G. Cagnoli et al. Eddy current damping of high q pendulums in gravitational wave detection experiments. Rev. Sci. Instrum., 69: , [43] R. Takahashi et al. Vacuum-compatible vibration isolation stack for an interferometric gravitational wave detector tama300. Rev. Sci. Instrum., 73: , [44] K. Tsubono. Application of material damping for gravitational wave detectors. Journal of Alloys and Compounds., 355: , 2003.

172 Discussion and Conclusion 151 [45] N. Kanda, M.A. Barton, and K. Kuroda. Transfer function of a crossed wire pendulum isolation system. Rev. Sci. Instrum., 65:3780, [46] M.A. Barton, T. Uchiyama, K. Kuroda, and N. Kanda. Two-dimensional x pendulum vibration isolation table. Rev. Sci. Instrum., 70:2150, [47] J. Liu et al. Vibration isolation performance of an ultra-low frequency folded pendulum resonator. Phys. Lett. A, 228: , [48] J. Winterflood, G. Losurdo, and D.G. Blair. Initial results from a long-period conical pendulum vibration isolator with application for gravitational wave detection. Phys. Lett. A, 263:9 14, [49] J. Winterflood, Z.B. Zhou, and D.B. Blair. Reducing low-frequency residual motion in vibration isolation to the nanometer level. AIP Conf. Proc., 523:325, [50] J. Liu, J. Winterflood, and D.G. Blair. Transfer function of an ultralow frequency vibration isolator system. Rev. Sci. Instrum., 66:3216, [51] L. Ju et al. Aciga s high optical power test facility. Class. Quantum Grav., 21:S887, [52] D. Coward, D.G. Blair, R. Burman, and C. Zhao. Vehicle-induced seismic effects at a gravitational wave observatory. Rev. Sci. Instrum., 74:4846, [53] F. Garoi, L. Ju, C. Zhao, and D.G. Blair. Radiation pressure actuation of test masses. Class. Quantum Grav., 21:S875, [54] P. Barriga, A. Woolley, C. Zhao, and D.G. Blair. Application of new preisolation techniques to mode cleaner design. Class. Quantum Grav., 21:S951, [55] LIGO Systems Engineering. Ligo hanford observatory contamination control plan. internal LIGO report LIGO-M A. [56] J. Winterflood, D.B. Blair, and B. Slagmolen. High performance vibration isolation using springs in euler column buckling mode. Phys. Lett. A, 300:122, 2002.

173 152 Chapter 5. [57] J. Winterflood, T.A. Barber, and D.G. Blair. Mathematical analysis of an euler spring vibration isolator. Phys. Lett. A, 300: , [58] J. Winterflood and D.G. Blair. A long period vertical vibration isolator for gravitational wave detection. Phys. Lett. A, 243:1 6, [59] A. Bertolini, G. Cella, R. DeSalvo, and V. Sannibale. Seismic noise filters, vertical resonance frequency reduction with geometric anti-springs: a feasible study. Nucl. Instrum. Methods Phys. Res. A, 435: , [60] G. Cella, R. DeSalvo, V. Sannibale, H. Tariq, N. Viboud, and A. Takamori. Seismic attenuation performance of the first prototype of a geometric antispring filter. Nucl. Instrum. Methods Phys. Res. A, 487: , [61] G. Cella, V. Sannibale, R. DeSalvo, S. Marka, and A. Takamori. Monolithic geometric anti-spring blades. Nucl. Instrum. Methods Phys. Res. A, 540: , [62] L. Ju, D.G. Blair, and J. Winterflood. Long-termed length stability and search for excess noise in multi-stage cantilever spring vibration isolators. Phys. Lett. A, 266: , [63] M. Beccaria et al. The creep problem in the virgo suspensions: a possible solution using maraging steel. Methods Phys. Res. A, 404: , [64] R. DeSalvo et al. Study of quality factor and hysteresis associated with the state-of-ther-art passive seismic isolation system for gravitational wave detectors. Nucl. Instrum. Methods Phys. Res. A, 538: , [65] S. Braccini et al. Monitoring the acoustic emission of the blades of the mirror suspension for a gravitational wave interferometer. Phys. Lett. A, 301: , [66] D.G. Blair, F.J. van Kann, and A.L. Fairhall. Behavior of a vibration isolator suitable for use in cryogenic or vacuum environments. Meas. Sci. Technol., 2: , 1991.

174 Discussion and Conclusion 153 [67] M.V. Plissi, C.I. Torrie, M.E. Husman, N.A. Robertson, K.A. Strain, H. Ward, and H. Luck. Geo 600 triple pendulum suspension system seismic isolation and control. Rev. Sci. Instrum., 71:2539, [68] R. Takahashi et al. Improvement of the vibration isolation system for tama300. Class. Quantum Grav., 19: , [69] T. Barber, J. Winterflood, and D.G. Blair. High performance vibration isolation for gravitational wave detection. submitted to Rev. Sci. Instrum. [70] E.J. Chin, K.T. Lee, J. Winterflood, J. Jacob, L. Ju, and D.G. Blair. Techniques for reducing the resonant frequency of euler spring vibration isolators. Class. Quantum Grav., 21: , [71] W.D. Weinstein. Flexure-pivot bearings. Machine Design, 37:150, [72] J.S. Jacob et al. Australia s role in gravitational wave detection. Pubs. Astro. Soc. Aus, 20: , [73] B.J.J. Slagmolen, T. Slade, and C. Mow-Lowry. Aigo vacuum part cleaning process. internal ACIGA report vers 1.2, [74] LIGO Systems Engineering. Ligo compatibility, cleaning methods and qualification procedures. internal LIGO report LIGO-E B, [75] L.E. Holloway et al. A coil system for virgo providing a uniform magnetic field gradient. Phys. Lett. A, 171: , [76] A. Abramovici et al. Improved sensitivity in a gravitational wave interferometer and implications for ligo. Phys. Lett. A, 218: , [77] P.S. Linsay and D.H. Shoemaker. Low-noise rf capacitance bridge transducer. Rec. Sci. Instrum., 53: , [78] S. Grasso et al. Electrostatic systems for fine control of mirror orientation in interferometric gw antennas. Phys. Lett. A, 244: , 1998.

175 154 Chapter 5. [79] V.P. Mitrofanov, N.A. Styazhkina, and K.V. Tokmokov. Damping of the test mass oscillations caused by multistrip electrostatic actuator. Phys. Lett. A, 278:25 29, [80] B.H. Lee, L. Ju, C. Zhao, and D.G. Blair. Implementation of electrostatic actuators for suspended test mass control. Class. Quantum Grav., 21:S977 S983, [81] X. Wang, C. Zhao, P. Kapitola, J. Jacob, L. Ju, and D.G. Blair. Noncontacting actuation by radiation powered telemetry system. Class. Quantum Grav., 21:S1023 S1030, [82] Y. Zhao, C. Zhao, L. Ju, M. Small, and D. G. Blair. Telemetry system driven by radiation power for use in gravitational wave detectors. Rev. Sci. Instrum., 76: , [83] E. Black, S. Kawamura, L. Matone, and S Rao. Tni mode cleaner/laser frequency stabilization system. internal LIGO technical note LIGO-T R, [84] C.Y. Lee, C. Zhao, E.J. Chin, J. Jacob, D. Li, and D.G. Blair. Control of preisolators for gravitational wave detection. Class. Quantum Grav., 21:1015, [85] J.C. Dumas, E.J. Chin, C. Zhao, J. Winterflood, L. Ju, and D.G. Blair. Modelling and tuning of a very low frequency roberts linkage vibration isolator. submitted to Rev. Sci. Instrum. [86] E.J. Chin, K.T. Lee, J. Winterflood, L. Ju, and D.G. Blair. Low frequency vertical geometric anti-spring vibration isolators. Phys. Lett. A, 336:97, [87] R. DeSalvo et al. Performances of an ultralow frequency vertical pre-isolator for the virgo seismic attenuation chains. Nucl. Instrum. Methods A, 420: , [88] G. Losurdo et al. Inertial control of the mirror suspensions of the virgo interferometer for gravitational wave detection. Rev. Sci. Instrum., 72: , 2001.

176 Discussion and Conclusion 155 [89] J. Winterflood, Z.B. Zhou, L. Ju, and D.G. Blair. Tilt suppression for ultralow residual motion vibration isolation in gravitational wave detection. Phys. Lett. A, 277: , 2000.

177 156 Chapter 5.

178 Appendix A Roberts Linkage ANSYS Modelling A.1 Preface The work done in modelling the Roberts Linkage was completed in two parts: analytically with the use of the mathematical package Mathematica, and numerically using ANSYS. The purpose of using ANSYS was to provide a means of checking and for guidance in developing the analytical model. The analytical findings and results are presented previously in Section 2.3. Here, the concepts of the ANSYS model are described. The code used to generate the model is presented later in Section A

179 158 Appendix A. A.2 Harmonic Analysis Model of the Roberts Linkage Nodal elements in two-dimensions are used in finite element analysis (FEA) whereby each of the nodes are linked accordingly with the designed Roberts linkage physical parameters. The structure is modeled as a triangle as opposed to a rectangle as it is simpler and the actual shape is not critical. This is because the nodal points are modeled as lumped masses with assigned inertial values (AN- SYS function - MASS21 ), and are connected together with weightless and almost infinitely stiff links (ANSYS function - COMBIN14 ). A schematic is shown in Figure A.1. The nodes shown in the figure include: 1) the input nodes for the harmonic analysis, which are also the suspension points of the Roberts linkage (nodes 1 and 2, which are also rigidly connected), 2) the suspension points at the base of the Roberts linkage (nodes 3 and 4), 3) the Roberts linkage center of mass which also includes its moment of inertia determined by the radius of gyration (node 5), 4) the point where additional masses can be placed on the Roberts linkage structure (node 6), 5) the point on the Roberts linkage structure which suspends the isolation chain (node 7), and 6) the concentrated payload mass which the Roberts linkage suspends below (node 9). The corresponding values for each of the parameters stated can be varied and is seen in the code included in the next section (in SI units). The dimensions of the structure and the values of the masses are replicated to the physical model to simulate the real system as closely as possible. The main parameters that are changed to observe their effects on the performance of the system include the length of the Roberts linkage suspension links, the height and the values of the additional masses that are placed above the Roberts linkage, the height of the suspension point of the isolation chain, and the radius of gyration of the Roberts linkage itself. Gravity is applied to the whole system. Once the values are set, a harmonic analysis is done. The position of the input and output probes are located at the designated nodes to obtain the transfer

180 Roberts Linkage ANSYS Modelling 159 Fig. A.1: The schematic of the Roberts linkage model in ANSYS showing the nodal points and linkages. function of the Roberts linkage. The input probe is located at either node 1 or 2 and the output probe is located anywhere along the center line of the Roberts linkage (node 8). This node allows the user to clearly see the center of percussion effects of the Roberts linkage. The number of data points and the frequency span are easily changed by the user to obtain the desired range of the transfer function. Figure A.2 illustrates an example of a harmonic analysis plot which shows the resonant frequency of the Roberts linkage using a set of given parameters. The motion of the model can also be viewed using the animation package in ANSYS. Figure A.3 illustrates a series of slides which show the progressive movement of the Roberts linkage structure with respect to its input nodes 1 and 2.

181 160 Appendix A. Fig. A.2: An example of a harmonic analysis plot of the Roberts linkage model.

182 Roberts Linkage ANSYS Modelling 161 Fig. A.3: Animation of the Roberts linkage in ANSYS (sequence from A to D).

183 162 Appendix A. A.3 Roberts Linkage ANSYS code This section includes the code used to generate the current model of the Roberts linkage that is used with the ANSYS software package. /COM, Planar Roberts Linkage /CLEAR, NOSTART /COM,!**************** Define parameters ****************!***************** CONTROL PARAMETERS ***************** W = X = Hw = Hcom = Mrl = Izz = 4.06 Rg = (Izz/Mrl)**0.5 Hprobe = Hsus = Mtuning = 5 Lsus = 1.75 Mload = 0 k = Nfreq = 100 Fmin = 0 Fmax = 20 AMP = 0.1!Width!Horizontal Distance to suspension point!height of 4 RL suspension wires!height of COM!RL mass!rotary Inertia of the frame!radius of gyration!height of Probe Point!Height of load suspension point (FROM RL)!Tuning mass on RL!Length of suspended stage!mass of suspended load!stiffness rigid link!number of substeps!minimum frequency!maxiumum Frequency!Forcing amplitude /PREP7!Enter the preprocessor prep7

184 Roberts Linkage ANSYS Modelling 163 /TITLE, harmonic analysis of Roberts Linkage!********************* Define Element type *********************!command ET, ITYPE, Ename, KOP1, KOP2, KOP3, KOP4, KOP5,!KOP6, INOPR ET,1,COMBIN14,,,2!Spring element (kopt2 defines xy plane!spring in 2D) ET,2,MASS21,0,0,3!Point mass type element!real Constant definitions R, NSET, R1, R2, R3, R4, R5, R6 R,1,k R,2,(Mrl/2) R,3,Mtuning R,4,Mload!Link STIFFNESS!RL half mass!tuning mass on RL!Load mass!***************** Node geometry Definitions ***************** N,1,-(X+W/2),Hw N,2,(X+W/2),Hw N,3,-W/2,0 N,4,W/2,0 N,5,0,(Hcom-Rg) N,6,0,(Hcom+Rg) N,7,0,Hprobe N,8,0,Hsus N,9,0,(Hsus-Lsus)!RL wires Sus point!rl wires Sus point!bottom corner of RL!bottom corner of RL!half mass down!half mass up!probe!load suspension point!******************** Element definitions ******************** TYPE,1!Sets element type pointer to MPC184 REAL,1!Material number 1

185 164 Appendix A. E,1,3 E,2,4!Wires!Wires E,3,4 E,3,5 E,4,5 E,3,6 E,4,6!Bottom link of RL!Half mass down!half mass down!half mass up!half mass up E,3,7 E,4,7!Probe!Probe E,3,8 E,4,8 E,8,9!Load sus point!load sus point!load wire TYPE,2 REAL,2 E,5!RL half mass Element E,6!RL half mass Element TYPE,2 REAL,3 E,8!Tuning Mass on RL TYPE,2 REAL,4 E,9!Suspended Load mass

186 Roberts Linkage ANSYS Modelling 165 /COM Elements successfully defined WPSTYL,,0.1,-1,1,,0,1 /DSCALE,1,1 FINISH!Set up workplane grid display!finish with Prep7!************** STATIC PRESTRESSED ANALYSIS ************** /COM Static Analysis to simulate the pretension spring state /SOLU ANTYPE, STATIC D,1,UY,0,0!Constrain in y direction D,2,UY,0,0!Constrain in y direction D,1,UX,0,0! D,2,UX,0,0! ACEL,0,9.81,0!Gravity PSTRES,ON EMATWRITE,YES SOLVE FINISH!***************** HARMONIC ANALYSIS ***************** /SOLU ANTYPE,HARMIC!Harmonic response analysis HROPT,FULL PSTRES,ON HROUT,OFF!Calculate prestress effects!print results as amplitudes and phase angles

187 166 Appendix A. OUTPR,All,All NSUBST,NFreq HARFRQ,Fmin,Fmax KBC,1!Number of Intervals within freq. range!frequency range from Fmin to Fmax HZ!Step boundary condition, ie. not ramped!constraints on the system D,1,UX,AMP,0 D,2,UX,AMP,0!Harmonic forcing load!harmonic forcing load SOLVE FINISH!***************** PostProcessing ***************** /POST26 FILE,,rst!Reduced frequencies file NSOL,2,1,U,X,UX1 NSOL,3,7,U,X,UX2!Select node 1, x direction!select node 7, x direction /GMARKER,1,1,1 /GMARKER,2,1,1 /GMARKER,3,1,1!Type of marker for plotting /GThk,CURVE,1 /GROPT,LOGY,ON /GROPT,LOGX,ON /YRANGE,DEFAULT!Lines for plotting!log plot LINES,201 PRCPLX,1!Number of lines for a printed page /OUTPUT,Response1,txt!Sends to text file

188 Roberts Linkage ANSYS Modelling 167 PRVAR,2 /OUTPUT,Response2,txt PRVAR,3!Sends the data to the file!sends to text file!sends the data to the file /OUTPUT /REPLOT,FAST!Resets the output to the default location PLVAR,3 FINISH!Plot

189 168 Appendix A.

190 Appendix B Ring down curve and Q-factor 169

191 170 Appendix B. This section presents the ring down curve and the calculation of the Q factor presented in Section The author would like to acknowledge the assistance of Kah Tho Lee who helped in obtaining the ring down curve shown. Fig. B.1: The ring down curve of the Euler vertical stage at the resonant frequency of 0.62 Hz. The following formula was used which was derived from first principles. Q = tπf ln( x 0 x n ) (B.1) where t is the time span, f the resonant frequency, x 0 the initial amplitude and x n the final amplitude. The following values were used to derive the Q factor of the ring down. t = 37.5secs f = 0.62 Hz x 0 = x n = (B.2) A Q factor value of 34.5 is thus obtained.

192 Appendix C Review Paper for the Astronomical Society of Australia C.1 Preface This paper was written for the Astronomical Society of Australia and reports on the importance and status of the ACIGA gravitational wave observatory in Gingin. It was published in 2003 whereby the entire section on the vibration isolator was written by the author. The references of this paper are listed at the end of this section and are not included in the bibliography section of the thesis. 171

193 172 Appendix C. C.2 ACIGA Review Paper Australia s Role in Gravitational Wave Detection J. S. Jacob 1, P. Barriga 1, D. G. Blair 1, A. Brooks 3, R. Burman 1, R. Burston 4, L. Chan 1, X. T. Chan 1, E. J. Chin 1, J. Chow 2, D. Coward 1, B. Cusack 2, G. de Vine 2, J. Degallaix 1, J. C. Dumas 1, A. Faulkner 1, F. Garoi 1, S. Gras 1, M. Gray 2, M. Hamilton 3, M. Herne 1, C. Hollitt 3, D. Hosken 3, E. Howell 1, L. Ju 1, T. Kelly 3, B. Lee 1, C. Y. Lee 5, K. T. Lee 1, A. Lun 4, D. McClelland 2, K. McKenzie 2, C. Mow- Lowry 3, D. Mudge 3, J. Munch 3, D. Paget 1, S. Schediwy 1, S. Scott 2, A. Searle 2, B. Sheard 2, B. Slagmolen 2, P. Veitch 3, J. Winterflood 1, A. Woolley 1, Z. Yan 1, C. Zhao 5 1 School of Physics, University of Western Australia, Perth; 2 Department of Physics, Faculty of Science, Australian National University, Canberra; 3 Department of Physics, University of Adelaide, Adelaide; 4 Department of Mathematics, Monash University, Melbourne; 5 School of Computer and Information Science, Edith Cowan University, Perth An enormous effort is underway worldwide to attempt to detect gravitational waves. If successful, this will open a new frontier in Astronomy. An essential portion of this effort is being carried out in Australia by the Australian Consortium for Interferometric Gravitational Astronomy (ACIGA), with research teams working at Australia National University, University of Western Australia and University of Adelaide involving scientists and students representing many more institutions and nations. ACIGA is developing ultra-stable high-power continuous-wave lasers for the next generation interferometric gravity wave detectors; researching the problems associated with high optical power in resonant cavities; opening frontiers in advanced interferometry configurations, quantum optics and signal extraction; and is the world s leader in high-performance vibration isolation and suspension design. ACIGA has also been active in theoretical research and modelling of potential astronomical GW sources, and in developing data analysis detection algorithms. ACIGA has opened a research facility north of Perth, Western Australia which will be the culmination of these efforts. This paper briefly reviews ACIGA s research activities and the prospects for Gravitational Wave Astronomy in the southern hemisphere.

194 Review Paper for the Astronomical Society of Australia 173 C.2.1 Introduction Gravitational Waves (GWs) are ripples in space-time which carry energy and angular momentum at the speed of light. Predicted by the General Theory of Relativity, there has been to date only indirect evidence for their existence, through the observation of energy loss from binary pulsars (Weisberg and Taylor, 1984). Numerous experiments have confirmed the underlying theory of General Relativity to a high degree of precision. Yet, the direct observation of GWs is still necessary for the wave solutions of Einstein s field equations to be fully investigated. More importantly, however, the ability to directly detect GWs will also create a new kind of Astronomy. Researchers in Australia are deeply involved in the pursuit of this discovery. Throughout the 80 s and 90 s, scientists at the University of Western Australia (UWA) were leaders in the field of Resonant Bar GW detectors. Now, work that will have a direct and vital impact on the world s second generation of GW interferometer detectors is underway across Australia. Ultrastable, high-power continuous-wave lasers are being developed at the University of Adelaide (UA). Advanced interferometer design, signal extraction, data analysis, and quantum optics projects are underway at the Australian National University (ANU). UWA is now a world s leader in high-performance vibration isolation and suspension design, as well as conducting research in the areas of thermal noise, thermal lensing effects, optical spring and radiation pressure effects, and astronomical sources of GWs. These various projects come together as the Australian Consortium for Interferometric Gravitational Astronomy (ACIGA) which is collaborating with the U.S. LIGO project to develop key technologies for the Advanced LIGO program. ACIGA has build a research facility 80 km north of Perth, named the Australian International Gravitational Observatory (AIGO). Gravity Waves: A New Spectrum for Astronomical Observation Since antiquity, our only source of information about the stars has been through their electromagnetic radiation. Developments in technology have allowed us to expand our window on the universe from strictly visible radiation to infrared, microwave, radio, ultra-violet, x-ray and gamma-ray radiation. Gravitational

195 174 Appendix C. wave astronomy offers an entirely new spectrum of radiation through which to explore the universe. Just as Maxwell s equations predict oscillating electric and magnetic fields which, once initiated, self-propagate at the speed of light, Einstein s General Theory of Relativity predicts the propagation of waves of gravitational and gravitomagnetic fields at the speed of light. Similar to the way electromagnetic waves are created by the acceleration of charges, GWs are created by the acceleration of mass. Since there is only one kind of gravitational charge (compared to two kinds of electric charges: positive and negative), and since conservation of momentum disallows unopposed acceleration, periodic mass dipoles are not possible. However, periodic mass quadrupole moments are possible in the form of a rotating non-spherically-symmetric mass, such as a twirling dumbbell. Gravitational wave luminosity is proportional to the square of the third time derivative of the mass quadrupole moment and to the constant G/c 5, where G is the universal gravitational constant and c is the speed of light. This is an extraordinarily small number. The significance of GWs to Astronomy is impossible to predict. Because GWs are created by bulk motions of matter, and because normal matter is almost totally transparent to GW radiation, they may allow us to listen in on regions and processes that are otherwise hidden from view, such as the inner regions of a supernova core collapse. Whereas electromagnetic telescopes are our eyes on the universe, GW detectors constitute ears which will allow us to hear for the first time the sounds produced by the universe. This paper s purpose is to review Australian research efforts in support of the international search for gravitational waves. The remainder of this introduction will present Australia s historical involvement in GW research, and will outline the current and future techniques being developed for GW astronomy. The following section will present more detailed information about likely astronomical GW sources, which is also the subject of much study in this country. The third section will discuss very long baseline laser interferometry in some detail, widely regarded as technically the best chance for GW detection within the next 10 years. Following this, an in-depth review of Australia s role in key scientific areas

196 Review Paper for the Astronomical Society of Australia 175 relating to GW research is presented. Finally, the Australian International Gravitational Observatory will be introduced with its current state of development, its near-term role in international GW research and high power laser interferometry development, and its long-term prospects as the premier southern hemisphere GW antenna. Predicting and Searching for Gravity Waves Since 1915 One simple principle underlies the design of all gravitational wave detectors. GWs are waves of gravity gradient, or in other words tidal forces, which create tidal deformations analogous to those exerted by the static tidal force of the moon on the earth. The signal is manifested as an oscillatory strain h = L/L, which can be detected through a simple linear strain measurement or through a differential measurement of strain between two orthogonal directions. The transduction of the GW strain may occur through the coupling of the signal into the acoustic phonon field within a large mass, or through the coupling into an electromagnetic photon field between freely suspended masses. Ideally, the size of the acoustic detector should be of order half an acoustic (phonon) wavelength of the expected signal frequency, while for an electromagnetic detector the scale should be half the electromagnetic (photon) wavelength of the expected signal frequency. For GWs in the audio frequency band originating from processes associated with stellar mass black holes and neutron stars, the above designs dictate the use of acoustic resonators of a few meters scale, and of electromagnetic detectors of a few hundred kilometers scale. For lower frequency signals associated with non-relativistic binary stars and supermassive black holes the scale increases by about four orders of magnitude. Resonant Bar Detectors Both acoustic and electromagnetic detection were defined in the early years of gravity wave research, though acoustic detectors were the first to be developed (Weber, 1960). A resonant bar detector consists of a large, vibration-isolated suspended mass for which the fundamental resonant frequency is the same as the GW frequency of interest. A GW of that frequency will excite vibrations in

197 176 Appendix C. the bar which can be detected. Weber s bar was made of aluminium due to it s high phonon velocity and low acoustic losses. Since then, many variations and improvements to resonant bar technology have been made. In Perth, technology development for the first acoustic detector began in The 1.5 tonne cryogenic niobium bar detector, Niobe, was developed during the 1980 s at UWA (Linthorne et al., 1990). In 1993 Niobe was shown to have the lowest noise temperature of any detector to date (Blair et al 1995). From 1993 to 1997 the antenna was operated almost continuously in search of gravitational waves, and in 1997 again set the record low noise temperature (Tobar et al 1999). In 2000 Niobe was operated again with an improved amplifier, demonstrating yet another new record low noise temperature (Coward et al 2002a). However, in 1999 Australian Research Council (ARC) funding for Niobe was discontinued, making long-term continuous operation impossible. Since then, all gravitational wave research at UWA has concentrated on technology development for advanced laser interferometer gravitational wave detectors. Interferometry as a more Promising Detection Technique The sensitivity of an acoustic detector is fundamentally limited by its size, which is in turn limited by the speed of sound within the bar material and the requirement that the fundamental resonant frequency of the bar match a desired detection frequency. These considerations have so far limited bars to just a few meters in length for detecting signals of frequency up to about 1 khz. If the detection method were to use photons instead of phonons, the scale of the detector having the same upper frequency limit could be increased by a factor of Given that GWs are strain waves, this would increase the detector displacement by the same factor. A detector of this scale (150 km) would be analogous to a half-wave electromagnetic dipole antenna. In practice, earth-based detectors are limited to a few kilometers in length due to economics as well as the curvature of the earth. In any case, the advantages of measuring differential strain using light instead of sound are numerous. A Michelson interferometer is capable of sensing differential changes in optical path lengths of much less than a wavelength of light over the entire length

198 Review Paper for the Astronomical Society of Australia 177 of each arm. When the two arms of the interferometer form a 90 angle, the arm lengths are affected by a GW in anti-phase due to GW s quadrupole polarization, naturally doubling the single-baseline sensitivity. An interferometer measures the relative strain of its two arms by comparing the optical path lengths between a beamsplitter and mirrors which terminate each arm, referred to as test masses. The sensitivity of interferometry is sufficient to reduce the necessary size of detectors to only a few kilometers, making them much easier to construct on the surface of the earth. Instruments such as these, though complex and largely still under development, offer the best opportunity for detecting GWs in the 100 to 1000 Hz range. Space-based interferometers would have fewer size restrictions. Without the seismic noise constraints of earth-based detectors, they could provide detection of GWs in the 10 1 to 10 5 Hz range. The LISA project (Laser Interferometer Space Antenna), a joint proposal of NASA and ESA, intends to do just that. There are four major earth-based interferometric detection efforts underway outside Australia. The Laser Interferometer Gravitational wave Observatory (LIGO) project in the US is a joint project of CalTech, MIT and the National Science Foundation and operates two 4 km baseline interferometers at sites in Hanford, Washington and Livingston, Louisiana. GEO is a joint German-British 600 m baseline interferometer near Hannover, Germany. VIRGO is a joint French- Italian project near Pisa, Italy with a 3-km arm length. TAMA in Japan is a 300-m interferometer. These first generation facilities serve two purposes. The first is to determine the upper limits on the strength of GW emissions, and with luck, to detect rare high-strength signals. The second is to push the development of the necessary technologies for achieving a sensitivity that will guarantee routine GW detection. Detection of GWs with this first group of instruments is likely only in the event of a galactic supernova or a relatively nearby binary coalescing event occurring while two or more detectors are operational in coincidence. While it is likely that there will be confirmed GW detection in the near future, technology must improve before GW detection will become a regular part of astronomical inquiry.

199 178 Appendix C. To that end, LIGO has already made plans for the next-generation interferometers, called Advanced LIGO. An essential part of the Advanced LIGO program is the ability to operate with high optical power in the interferometer. This requires extremely clean high power lasers that can produce about 100 watts of optical power at a single wavelength and in a single spatial mode (TEM 00 ). Since the optical power is built up in resonance to levels on the order of megawatts, advanced optics are required that can cope with such high incident optical power. Very low absorption substrates and coatings, and very high reflectivity mirrors are needed, as well as a way of handling the thermal lensing effect - the change in focal length caused by local heating through absorption of light in the optics. The Australian Consortium for Interferometric Gravitational Astronomy (ACIGA) plays two vital roles in GW research. The first is to collaborate with LIGO in the development of high optical power technologies. The Australian International Gravitational Observatory (AIGO) site at Gingin, Western Australia (80 km north of Perth) will initially serve as a research and testing facility for high power optics and thermal lensing, with several experiments now planned on an 80 m baseline suspended optical cavity. Its second role is to develop the AIGO site into the first southern hemisphere GW observatory, completing the global network of GW detectors. Such a network is essential for coincidence checking of GW signals and for determining the likely origins of GW signals. C.2.2 Astronomical Sources of GW s This section provides a brief overview of several potentially observable types of gravitational wave sources based on current and planned interferometric detectors. It is not intended to be an exhaustive list but rather to highlight the rich diversity of possible sources. A more comprehensive and rigourous treatment of GW sources can be found in Cutler and Thorne s (2002) review. Astrophysical sources of GWs can be broadly categorized as being either continuous or burst sources. Continuous sources are ones yielding slowly evolving emission, with characteristic evolution time that is very long compared with the observation time. By choosing 1 year as a practical observation time, sources that could be considered continuous include compact binary systems in the gradual

200 Review Paper for the Astronomical Society of Australia 179 in-spiral phase (due to GW radiation reaction) prior to the last few minutes of their evolution. The final seconds before coalescence will produce the strongest GWs, in a type of burst signal often termed a chirp because of the rapidly increasing amplitude and frequency as the compact objects coalesce. The most intensely studied theoretical sources of this type involve black holes (BHs) and neutron stars (NSs). Wide-band detectors can potentially detect the GW chirp signals from NS/NS coalescing binaries out to 300 Mpc, NS/BH binaries (M BH < 10M ) out to 650 Mpc and BH/BH ones out to redshift z = 0.4 (Cutler & Thorne 2002). Rates for these events are calculated by extrapolating the local density of massive stars, based on observational data from our Galaxy, out to cosmological distances (Kalogera et al. 2001; Belczynski & Kalogera 2001). Radio astronomy provides observational constraints on the number of NS/NS binaries using the observed numbers of binary pulsar systems, and recent estimates of event rates for GW detectors range from yr 1. For the case of NS/BH mergers, there are no observations of pulsar-bh systems, so detectability rates rely on population synthesis techniques to simulate the evolution of a population of progenitor binary systems. Kalogera et al (2001) find NS/BH event rates of yr 1. For BH/BH mergers, similar methods yield rates of yr 1 but Cutler and Thorne (2002) point out that such calculations ignore the role of globular clusters in the formation of BH/BH binaries and that the lower limit may consequently be an order of magnitude higher. Rapidly spinning pulsar NSs are potential continuous GW sources. When a neutron star reaches maximum stability in its final state, it possesses a crystallised solid crust. Because of spin the crust will have assumed an oblate axisymmetric shape due to centrifugal forces, with an axis that follows the spin axis. If its angular momentum deviates from this preferred axis, the NS will wobble as it spins. Such a NS will emit GWs at twice its rotational frequency. Pulsars with spin frequencies above 100 Hz are possible detectable sources of GWs. Sources with characteristic evolution times that are very short compared with the observation time can be considered as burst sources. A typical burst source example is a core-collapse supernova (SN), for which the evolution time could be of

201 180 Appendix C. order milliseconds. Because the core-collapse process involves relativistic compact mass motion, GW emission should be an intrinsic feature of these events. But modelling stellar core collapse is an extremely difficult and complex task. Early attempts to predict GW emission were semi-quantitative, predicting a broadband emission lasting for a time of order milliseconds; see Eardley (1983) for an early review. Because of recent advances in super-computing and computational techniques, we are just beginning to gain insight into the details of how GW emission might occur. Stellar collapse certainly exhibits all of the necessary conditions for strong GW generation: large mass flow in a compact region (hundreds to thousands of kilometers) at relativistic speeds. However, these conditions are not sufficient to guarantee strong emission. In particular, the degree of asymmetry in collapse is not well understood. If stellar cores are rapidly rotating, instabilities can develop that are certain to drive strong GW emission. The new-born NS may be dynamically unstable, resulting in a bar-mode instability. Recent simulations suggest that a fast-spinning newborn NS may develop into a bar-shaped object with a radius that is large compared to the final NS radius (Shibata et al. 2000). A bar-mode instability is one of the more promising mechanisms by which a significant fraction of the collapsing system s energy can be emitted in GWs. Bar-mode instabilities occur in objects whose rotational kinetic energy exceeds some fraction of their potential energy. Simulations show that general relativity enhances the instability to bar formation (Saijo et al. 2001) and that the bar will be long-lived. GWs from this source will contain information on the evolution of the bar mode and reveal the dynamics of the process through the frequency evolution of the GWs. Only rough estimates exist for the detectability of these sources, but it is plausible that they could be detected out to the Virgo cluster (15-20 Mpc) at a rate of several per year. Unfortunately, SN rates are too low in our Galaxy for us to expect to observe a Galactic SN during a period of even tens of years observation time (e.g. Dragicevich, Blair & Burman 1999). But if some or all of the processes discussed above are common to a large fraction of core-collapse events, then we could pos-

202 Review Paper for the Astronomical Society of Australia 181 sibly observe several events per year, assuming sensitivities of the planned second generation detectors. Gamma-ray bursts (GRBs) have been observed for decades but their true nature is just beginning to come to light. They are associated with host galaxies that are not particularly luminous; the galaxies appear blue (Hogg & Fruchter 1999) and the location of the optical transient is never very distant from the galaxy center, in agreement with the idea that long GRBs (those lasting > 2 s) are associated with massive and short-lived progenitors (for a recent review see Djorgovski et al. 2001). The central engine could be a fast-spinning BH surrounded by a very dense (neutron-dense) torus. In this case the available energy sources, apart from gravitational radiation, are in the form of neutrinos, accretion of the torus material onto the BH, and rotation of both the torus and the hole. M. van Putten (2001) has developed a model in which the accretion disk of the magnetised newborn BH becomes highly compressed, resulting in an accreting torus. The torus might develop large non-axisymmetries or lumpiness, in the process emitting GWs. He has shown that about 10% of the BH s spin energy could be radiated away in GWs. Estimates for the amplitude of this source yield a GW energy emission equivalent to 0.3 M, radiating in a frequency range around 1 khz. Coincidence analysis between EM emissions and GW signals could provide a powerful probe for investigating these enigmatic phenomena further. Several current theories of early Universe Cosmology, including inflationary and Grand Unified Theories, predict strong GW emission from the epoch of graviton decoupling. Detection of a GW background from the early Universe would have a profound impact on early Universe cosmology and on high-energy physics, opening up a new window to explore very early times in the evolution of the Universe, and correspondingly high energies that will never be accessible by other means. Relic GWs carry unique information from the primordial plasma, providing a snapshot of the state of the Universe at that epoch: cosmological GWs could probe deep into the very early Universe. The GW background from the primordial Universe is a stochastic background, random in amplitude with an energy density spread across a large bandwidth.

203 182 Appendix C. There is another type of GW stochastic background one comprised of the cumulative emissions from astrophysical sources throughout the Universe (eg. Ferrari, Matarrese & Schneider 1999a,b). This background is very interesting, because it may be continuous across certain frequency bands but comprised of discrete events within other bands. The background from massive binary systems may form the continuous component, with burst sources such as SNs and GRBs producing a GW background that can be described as popcorn noise. Most of the sources, as observed in our frame, will be at cosmological distances with highly redshifted emissions. Coward et al (2002b), part of the Australian consortium, have produced graphical and audio Monte-Carlo simulations using some computed SNe generated GW waveforms as a basis. C.2.3 Principles of Laser-Interferometric GW Detection Numerous types of interferometers (e.g. Michelson, Fabry-Perot and Sagnac), and many variations on these (e.g. power-recycling, signal recycling, dual-recycling, resonant recycling, open-area Sagnac, zero-area Sagnac, delay line, resonant sideband extraction, all-reflective, and so forth) have been proposed and investigated as potential GW detectors. As can be expected, each variation offers an advantage in the form of suppressed sensitivity to certain sources of noise, and each comes with disadvantages that ultimately mean greater sensitivity to other sources of noise. The configuration selection process becomes an exercise in determining which type of noise source can be adequately dealt with externally, and to which noise sources the interferometer must have the greatest immunity. When all noise sources, such as seismic noise, laser noise, suspension and optics thermal noise, and partial-vacuum scattering have been dealt with, most major interferometer configurations come out about equal in signal sensitivity and are limited by the same pair of complimentary noise sources: photon shot noise and radiation pressure noise. In this realm, various tricks can be employed which pit one against the other, but to reduce both at the same time runs up against the Standard Quantum Limit (SQL), the theoretical sensitivity limit imposed by the Heisenberg Uncertainty Principle.

204 Review Paper for the Astronomical Society of Australia 183 Reduction of Noise Sources Photon shot noise increases with signal frequency and can be reduced by using more photons (higher optical power). Radiation pressure noise is highest in the lower frequency range and increases with optical power. Thus, there is an optimal amount of optical power that depends on the required detection frequency. Also, the narrower the detection band, the better the optimisation can be made, until the SQL is reached. Most current interferometer designs aim for a reasonably broad detection band of 100Hz to 1kHz, since this increases the likelihood of observing a GW event. At present, sensitivity is almost universally shot-noise limited; hence the push for higher optical power lasers and optics in future detectors. Sensitivities close to the SQL are thought to be sufficient to ensure routine GW detection. This assumes that other noise sources have been adequately dealt with. Seismic Noise. By far the most predominant noise source affecting any earthbased GW detector is seismic noise. This is the continuous, broad-spectrum, multiple degree-of-freedom motion of the surface of the earth caused by natural processes such as ocean waves, wind, animal movements, tidal forces, diurnal local heating, or tectonic activity, as well as by human activity such as road traffic, plant machinery, or foot traffic. Typical seismic amplitudes are given by x s αf 2 mhz 1 2 where α 10 6 to This is at least eight to ten orders of magnitude larger than the expected test mass motions due to GWs. Interferometers are affected in two ways by seismic noise. Firstly, seismic noise can overwhelm by at least one million times any GW signals by disturbing the motions of the test masses at the frequencies of interest. Secondly, seismic vibrations can prevent an interferometer from locking onto a single interference fringe and can prevent optical cavities from attaining resonance, thus barring the interferometer from operating at all. Reducing seismic noise in the detection band is a straightforward process of suspending test masses from successive stages of mechanical vibration attenuators in series. This must be done for each degree of freedom. For horizontal motion, the simplest arrangement is a series of pendulums and masses. For vertical motion, spring-mass combinations are used. Each stage is designed to have a

205 184 Appendix C. resonant frequency well below the detection band. One drawback to this approach is the likelihood that the numerous internal modes in the pendulum suspension wires and vertical isolation springs could resonate at specific frequencies within the detection band. There are two approaches to solving that problem. One is to identify and digitally remove these resonant peaks from the data during the data processing stage. The other, favoured by ACIGA, is to attend to the mechanical design of all isolator components to minimise the number of internal modes falling within the detection band. This has only become possible through a number of pioneering advances, including most significantly a vertical isolation spring with internal frequencies on order 1000 times higher than its fundamental spring-mass frequency (Winterflood, 2002). More will be said of this in section C.2.5. Ensuring that the overall residual motions of the test mass are low enough to operate the interferometer is a more difficult problem. Each isolation stage has its own resonance which actually amplifies seismic noise at that frequency. Additionally, low-frequency seismic motions are not attenuated at all by the multiplestage isolators mentioned above. Two revolutionary approaches to this are used by ACIGA. One is to construct pendulum isolation stages which can internally dissipate energy from their own periodic motion. Called self-damping pendulums, this technique significantly reduces the amplitude of pendulum resonant modes, thereby reducing the residual test mass motion. The other approach, used in conjunction with self-damping, is to suspend the isolators from a very low-frequency pre-isolator. The resonance of the pre-isolator (typically to 0.1 Hz) is easily controlled through active damping, effectively eliminating residual motion of the test mass at low frequencies. The pre-isolator also attenuates seismic motion that would otherwise excite both fundamental and higher order resonances in subsequent isolation stages. Figure C.1 shows the effect of adding low-frequency pre-isolation to one axis of motion. Five ordinary isolation stages alone (dotted line with five peaks) are adequate for removing seismic noise from the detection band (i.e. above 100 Hz), but the isolator resonant peaks without pre-isolation result in unacceptably large residual motions of the test mass. The solid line shows the pre-isolation

206 Review Paper for the Astronomical Society of Australia 185 Fig. C.1: Effect on relative amplitudes of adding a very low frequency pre-isolation stage. Vertical units are ratio of output to input, in db. Two five degree-of-freedom systems are numerically modeled here to illustrate the effect of drastically reducing (by about one power of 10) the resonant frequency of one of the degrees of freedom, representing a pre-isolation stage. approach with one very low-frequency peak and four ordinary isolation stages. With pre-isolation, the isolator peaks are reduced to levels which the interferometer feedback controls can overcome, allowing the device to be locked onto a single interference fringe. Also, care is taken to avoid any kind of moving, sliding or pivoting joint or bearing in the mechanical design. Only elastic flexures are used. The reason for this is that the discontinuity between static and sliding friction in moving hinges create impulses that excite resonances throughout the isolation and suspension structure. The broad-spectrum nature of such impulses means that resonances of any frequency are excited, including those which contaminate the detection band. Laser Noise. Frequency fluctuations, intensity noise, and multiple TEM modes all emulate the signal produced by a GW in the interferometer output. There-

207 186 Appendix C. fore, each of these must be dealt with in the design and selection of the input laser. High power lasers are not all that rare today; however, producing continuous wave, highly monochromatic, low noise, single-mode (TEM 00 ) laser light of significant power still requires considerable effort. Frequency stabilisation techniques are well developed for low-power lasers, and must now be adapted for use with higher power. Further immunity to frequency and phase noise in the interferometer is obtained through modulation and sideband extraction techniques. Phase noise due to multiple spatial modes is largely eliminated through the use of input and output mode cleaners - optical cavities in which only the particular desired mode is resonant. ACIGA is playing a key role in developing and demonstrating these laser techniques at high optical power. Thermal noise. This noise source is divided into two separate phenomena: thermal noise of the test mass and thermal noise of the suspension. In either case, Brownian motion of the molecules comprising part of the interferometer can directly couple into the interferometer phase measurement and reduce the signal to noise ratio. The most straightforward approach to thermal noise is operating the entire interferometer at cryogenic temperatures (something proposed for detectors on the 10 to 20 year horizon). However, this is not currently feasible due to the expense and complexity. A more basic approach therefore is taken, which in the long run will also enhance the effectiveness of the cryogenic approach. Thermal noise has been studied within materials that have very high internal Q-factors, meaning materials that have very low internal friction or material losses; in other words, minimal phonon scattering behaviour. It has been found that the thermal energy in such materials can be essentially sequestered within the internal resonance modes. The result is that with the exception of a few very narrow frequency bands which can easily be isolated at either the detection or data processing stages, the material is vibrationally very quiet. Materials with high Q values are therefore highly desirable as test mass mirror substrates. Fused silica and grown sapphire are two such substrate materials that are being studied for use in GW interferometers. The purity of the materials, the

208 Review Paper for the Astronomical Society of Australia 187 way they are grown, annealed, and polished, and the selection of coating materials all have an influence on the Q-factor and overall level of thermal noise, and are therefore subjects of intense study. Suspension thermal noise is physically identical to test mass thermal noise, but is treated in a slightly different way. Rather than material selection being the essential solution, more attention is paid to the mechanical design of the suspension and its components. Again, the preferred approach is to sequester thermal energy into narrow, high-q resonances. Even more desirable are high Q resonances which have frequencies that lie outside the detection band. More will be said of this in section C.2.4. Vacuum system. Partial scattering of the laser light between test masses creates phase disturbances indistinguishable from the GW signal. It is therefore essential to operate the interferometer in as complete a vacuum as possible. LIGO attempts to operate in a vacuum of about 10-9 Torr. The difficulty and expense of achieving this in 8 kilometers of 1 meter diameter pipe can be easily appreciated. Fortunately, AIGO s objectives can be accomplished at vacuum levels of just 10 7 Torr. Cleanliness, especially with regard to hydrocarbon contaminants, is also an important issue within the vacuum envelope. Hydrocarbon molecules are easily forced into the surfaces of optics by radiation pressure. This causes reflectivity and other properties of the optics to degrade rapidly, and can cause extreme local heating of a substrate, possibly resulting in failure of the material. For these reasons, care is taken to eliminate all sources of hydrocarbons in the vacuum vessels and pumps, as well as on the suspension and isolation hardware, and even within the laboratory building. Signal Extraction Principles in Interferometry A simple Michelson interferometer detector is shown schematically in Figure C.2. The interferometer consists of three free masses -one beamsplitter, and two test masses at right angles to form the end mirrors. These masses are vibration isolated and suspended so that at frequencies well above isolator resonances they can move freely as inertial test masses. When a gravitational wave passes it cre-

209 188 Appendix C. Fig. C.2: The basic Michelson configuration. The output of a laser is split into two arms which recombine at a photodetector in either constructive or destructive interference. Differences in the lengths of the arms of less than one wavelength of light are detectable as variations in intensity at the photodetector. ates relative phase shifts between the two beams. These are read out as intensity variations in the interferometer output, giving information about the incoming gravitational wave. For simplicity, consider the case of an incident gravitational wave perpendicular to the plane of the interferometer with a polarisation direction parallel to the interferometer arms. The passing wave will make one arm of the interferometer optically shorter and the other longer in half of the wave period, and reverse the contraction-elongation process in the other half-period. The relative change of optical lengths of the two arms L = L2 L1 can be described as a phase shift, ϕ = 2πL λ (C.1) This results in a change in the interference pattern at the output of the beamsplitter. The relative difference in optical path L is proportional to the arm length L = h L. Generally, an interferometer is sensitive to a linear combination of the two polarisation fields, and gravitation wave strain, h, in the above equation is h = F + h + + F h (C.2) where F + and F are coefficients depending on the direction to the source and the orientation of the interferometer. Because the gravitational signal is extremely

210 Review Paper for the Astronomical Society of Australia 189 small, it is very difficult to monitor the small time-varying changes in the interference pattern due to the passing gravitational wave. In practice, the phase difference arising from the optical arm length variations is obtained by the socalled nulling method. The idea is to always keep the light returning from the two arms 180 out of phase so that its output is always a dark fringe. This is done by feeding the error signal back to the end mirrors via positional actuators to create a compensating phase shift such that the interferometer output remains locked on a dark fringe. The control signals applied to the end mirrors contain the information of the gravitational wave disturbance. In this way the effect of power fluctuations in the laser beam can be minimised, the circulating optical power in the two arms is maximised, and the shot noise level is minimised. Various modulation-demodulation techniques have been proposed and extensively studied for extracting the signal and locking the interferometer at a dark fringe. Schemes known as external modulation (Strain and Meers 1991, Drever 1982, Man et al 1990, and Gray et al 1996) and frontal modulation (Takahashi et al 1994, Regehr, Raab & Whitcomb 1995, Flaminio & Heitmann 1996, and Ando, Kawabe & Tsubono 1997) have been particularly investigated because their modulators are outside the interferometer. Thus, as opposed to internal modulation, these schemes avoid introducing losses or wavefront distortion within the interferometer (Billing et al 1979). Although quantum-noise-limited sensitivity has been achieved with internal modulation at low laser power level (Shoemaker et al 1991, Stevenson et al 1993 and 1995), no large-scale laser interferometer detectors will use this configuration because it introduces losses and wavefront distortion. Instead, frontal modulation has been chosen and implemented in LIGO (Landry 2002), VIRGO (Bondu et al 2000), GEO (Freise et al 2002) and TAMA (Ando et al 2001) projects due to its simplicity and robustness, Analysis of Interferometer Data Every GW detector possesses a threshold below which a decision on whether or not a GW event occurred cannot be made. This threshold is determined by the detector noise and a probabilistic argument that either rejects or accepts that a GW signal is present tin the data. A signal-to-noise ratio (S/N) is used to

211 190 Appendix C. determine if a signal is present in a noise background, and can be optimised if prior knowledge of the signal is available. Matched filtering is a technique that relies on knowing the general form of the signal a priori, and optimises the S/N by applying a replica (template) of the signal to a data set where the signal might be present. This template optimally enhances the S/N if it matches the signal in both phase and amplitude. Matched filter templates for likely sources are being developed based on current theoretical models for GW emission. Close compact binaries are one source type where the signal has been modeled in a post-newtonian formalism that has allowed templates to be constructed. But the computational cost of matched filtering becomes enormous for a blind search if one has no knowledge of the source direction, masses of the binary objects, and initial phase and orientation angles of the binary orbit. This is a major computational problem that is being tackled by many groups in an effort to reduce the computational cost of close binary searches. One methodology using a network of detectors to improve the detection confidence, but this is even more computationally expensive than a single detector search. The number of templates required is greatly reduced if one is searching for known sources, such as galactic pulsars. Observations of cosmic neutrino and astrophysical EM events may provide a means of performing coincidence tests between conventional astronomical observations and GW detectors. For the case of random or stochastic backgrounds, such as the proposed primordial cosmological background, the method of cross correlation is the optimal signal processing strategy. Each detector is assumed to be independent in detector noise, so that by combing the signal from several detectors the signal grows linearly while the noise grows as the square root of observation time, thus improving the S/N. This is because the noise is uncorrelated but the signal will be correlated if the detectors are separated by less than one reduced wavelength and the detectors are optimally aligned. This method has been implemented using the two LIGO detectors in 2002 and has provided the first upper limit on a cosmological background of GWs. Cross-correlation may also be implemented to detect the presence of a GW background from astrophysical sources throughout the Universe (see section C.2.2).

212 Review Paper for the Astronomical Society of Australia 191 C.2.4 ACIGA Research Activities ACIGA has undertaken research in the four main interferometer subsystems : Advanced configurations; lasers and optics; isolation, suspension and thermal noise; and data analysis. Here we will briefly summarise our major achievements in these areas. Signal recycling. Figure C.3(a) shows the proposed optical layout of a second generation laser interferometer gravitational wave detector. It differs from first generation interferometers (such as LIGO and VIRGO) by the presence of the signal recycling mirror. A passing gravity wave induces phase modulation sidebands on the carrier light circulating inside the arm cavities. At the main beamsplitter the carrier light is directed toward the power recycling mirror, where it is resonantly reflected back into the interferometer, to build up the stored power. This is termed power recycling (Drever 1983). On the other hand the signal sidebands are ejected at the main beamsplitter toward the signal mirror, where they are resonantly reflected back into the interferometer to enhance the signal. This effect is known as either signal recycling (SR) (Meers 1988) or resonant sideband extraction (RSE)(Mizuno et al. 1993) depending on the resonant condition of the signal sidebands in the cavity formed by the signal mirror and the reflecting element in the interferometer arms, see Figure C.3(b). From here on we will refer to the general class as signal recycling, SR. The influence on the signal occurs only over a frequency range determined by the effective band width of the signal recycling cavity, hence signal recycling modifies the frequency response of the interferometer. One of the major problems to be solved to be able to implement signal recycling schemes is how to obtain signals to control the various optical cavity and Michelson degrees of freedom to maintain resonance and to extract the gravity wave signal. After examining various modulation schemes for interferometer control (Stevenson et al. 1993, Gray et. al 1996), we proposed a control scheme for a simple SR interferometer and experimentally verified the predicted frequency response. Following this, we demonstrated resonant sideband extraction on a Sagnac interferometer (Gray 1998). This work revealed the important result that

213 192 Appendix C. (a) Power Recycling mirror Arm cavities (b) Carrier High Finesse Cavity Sidebands Laser Signal RecyclingÕ Mirror Coupled Cavity Signal Recycling/Resonant Sideband Extraction in a Michelson tunable mirror = tunable finesse Fig. C.3: (a) Optical layout of a second generation laser interferometer showing power and signal recycling. (b) Principle of signal recycling: the carrier light builds up in the arm cavities and is not affected by the signal mirror. Build up of signal sidebands depends on resonant condition in the signal cavity. the Sagnac arrangement is highly sensitive to beam splitter imbalance when arm cavities are present. More recently, we invented and demonstrated a control signal for RSE on a Michelson interferometer (Shaddock et al. 1998), the interferometer arrangement favoured for Advanced LIGO, which allows dynamic tuning of the peak response frequency. Our scheme, which uses a phase modulated carrier plus a subcarrier, now forms the basis of the control scheme which is likely to be adopted by LIGO. The success of our RSE work leads to interferometers with tuneable peak response frequency. However, tuning the bandwidth requires the SR mirror to have a variable reflectivity. Changing the resonance condition of either a cavity or a Michelson interferometer varies the amplitude of the reflected field in both cases. This suggests either optical element could be used as a variable reflectivity mirror. Our analysis shows that the Michelson has the advantage that only the magnitude of the reflected field is changed, not its phase (in contrast to a cavity). This has advantages when designing an orthogonal control scheme (de Vine et al 2002a) leading us to demonstrate the first tuneable bandwidth signal recycled interfer-

214 Review Paper for the Astronomical Society of Australia 193 ometer (de Vine et al 2002b). Work on the development of a suspended VRM is in progress. Quantum optics. In 1980, Caves realised that the sensitivity of an interferometer could be improved by using squeezed states. Classical light is best represented by a coherent state: a state which the noise is the same in all quadratures and is set by the Heisenberg Uncertainty Principle (HUP). Squeezed states of light are states in which the noise in one quadrature has been reduced below the HUP level at the expense of an increase in the noise in the conjugate quadrature. Squeezed states are made using non linear optical processes such as second harmonic generation and Optical Parametric Oscillation. The world record for the generation of a squeezed cw vacuum state is held by Lam et al (1999) in which they measured 7 db squeezing (inferring that up to 10dB was generated). If shot noise is the factor limiting the sensitivity, squeezing the phase quadrature of the vacuum input to the interferometer as demonstrated in Figure C.4 would improve the sensitivity. This allows the SQL to be reached, at a lower optimum power level, but not surpassed. On the other hand, if the interferometer is limited by radiation pressure noise, light squeezed in the amplitude quadrature must be used to improve the sensitivity (again at best to the SQL). We reported improvement in S/N ratio of a power recycled interferometer (as depicted in Figure C.4a) by injecting a squeezed vacuum state (McKenzie et al 2002). Results are summarised in Figure C.5. Using a benchtop scale Michelson interferometer, with a shot noise limited signal generated by modulating the piezo at 5.46 MHz, we injected a 3 db squeezed state via the empty beam splitter port of both a simple Michelson and a power recycled (recycling gain of 10) Michelson interferometer. As shown in Figure C.5 the results show that squeezing and power recycling are not only compatible but the effectiveness of the squeezed state is actually enhanced. The major source of loss of the squeezed state was in the optics used to inject the squeezed beam and extract the signal. This experiment was a vanguard experiment pointing the way for the use of non classical light in interferometers. Whilst it was restricted to shot noise suppression due to the nature of the experiment, future laser interferometers will be limited by quantum noise (shot noise and radiation pressure noise) over most of

215 194 Appendix C. (a) (b) Fig. C.4: (a) A power recycled Michelson interferometer showing where a squeezed vacuum state is injected to modify quantum noise. (b) The lines represent the magnitude of the electric field phasors emerging from each of the interferometer to be interfered on the beam splitter. The phase difference represents the signal. On the left the vacuum state is a coherent state. On the right, a squeezed vacuum state is injected, showing the improvement in S/N achieved by using squeezing (or alternatively that a smaller signal could be measured).

216 Review Paper for the Astronomical Society of Australia 195 Fig. C.5: A signal/noise curves from Mckenzie et al. (2002). There are 4 traces: smallest peak is for the basic interferometer; squeezing is then injected; power recycling is added; finally power recycling with squeezing. their frequency band. Noise reduction below the standard quantum limit can be achieved by injecting a squeezed vacuum state in which amplitude and phase noise are correlated. Experiments are now under way using classical modulation signals to demonstrate the principal of quantum noise cancelation (Mow-Lowry 2002). Research on other third generation quantum technologies, such as quantum speed meters and quantum optical springs is also being actively pursued. High Power Laser Development at UA Laser development at the University of Adelaide conducted in support of ACIGA has two main areas of focus: developing high optical power and reducing laser noise. Though the goal of 100 W of output power seems modest compared to pulsed lasers available today, this power level is unprecedented in a continuous wave laser with the mode quality and frequency stability specified for GW detector applications. In this section the development of an ND:YAG (1064 µm) laser with virtually diffraction-limited beam quality is described.

217 196 Appendix C. Fig. C.6: Top view of the side-pumped Nd:YAG slab laser. Master laser light enters through a high-reflectivity mirror (top, right) and undergoes total internal reflection inside the slab, until exiting through an output coupler, right. This light stimulates photon emission inside the slab, that is being energised or pumped by diode laser light delivered to the slab by the 72 optical fibres (top and bottom). Building power. The basic approach used is to side-pump a slab of the laser medium while controlling temperature gradients in the slab using a combination of forced water heat exchangers and thermoelectric devices. Carefully controlling temperature gradients minimises thermal lensing effects and improves the spatial stability of the output beam. Temperature gradient control is achieved by cooling the pumped sides of the slab with water while the top and bottom face temperatures are precisely controlled using thermoelectric devices which can either heat or cool the slab as needed. The slab is pumped by light from laser diodes brought up to the slab via optical fibres (see Figure C.6). Each diode laser is wavelength-tuned to the absorption peak of the slab using individual feedback loops. Using this design and 100W of pumping power, a near-diffraction limited 20 W laser output was produced (Mudge et al 2000). A scaled-up version is now being tested to produce a target output of 100 W using 520 W of pumping power. Reducing noise. An ideal interferometer is sensitive only to the phase difference of the two arms and should reject any common-mode fluctuations in the input light. In practice however, laser frequency noise can couple into the output

218 Review Paper for the Astronomical Society of Australia 197 Fig. C.7: Method of scaling stabilised laser power through injection locking of successive master-slave lasers. The diode-pumped Nd:YAG laser requires an input light source to stimulate emission. The stability of the first master laser determines the stability of subsequent slave lasers. due to unavoidable asymmetry in the interferometer arms. Also, intensity noise can couple into the output through radiation pressure variations between the two arms. Reducing these sources of noise at the source - the input laser - is of prime importance. Frequency stabilisation is achieved using the Pound-Drever-Hall (PDH) technique described by Drever et al. (1983). Due to several practical considerations, PDH stabilisation is only readily applicable to relatively low power lasers. Research at UA has therefore centered on injection locking of high power slave lasers using a stabilised low power master laser. This method has also been extended to three stages for very high output powers, as illustrated in Figure 7. A 5W injection-locked slave laser has been demonstrated (Ottaway et al. 2000) with noise performance suitable for use in GW detector interferometers. The intention is to use it as a master laser to an even higher power slave laser. Intensity noise has been investigated as primarily the result of fluctuations in pumping laser intensity. Ottaway et al. (2000) working at UA have also demonstrated the use of intensity stabilisation through feedback on multi-emitter high-power diode lasers pumping a high-power slave laser, again with promising results for GW interferometry. Test mass research at UWA Very low loss materials are needed to minimise the internal thermal noise of test masses in GW detectors. The two leading candidate materials are fused silica and grown sapphire. All currently operating detectors use fused silica as the test

219 198 Appendix C. mass material. However, intensive research at UWA has been focused on sapphire test mass for use in advanced detectors. Sapphire as a test mass material has several advantages over fused silica. First, sapphire has the lowest acoustic loss of all known materials, having a loss angle φ < 10 8 compared to φ < 10 7 for fused silica. Secondly, sapphire has a higher sound velocity than fused silica, which results in higher-frequency internal modes and thus lower thermal noise. Third, sapphire has a high thermal conductivity which is an advantage in cryogenic detectors (Kuroda et al 1999, Ju et al 2002), as well as making it less sensitive to thermal lensing. However, the optical absorption of sapphire is higher than fused silica, typically 20 ppm with some small samples reaching as low as 3 ppm. It is believed that proper annealing of the sapphire will reduce the absorption level. Sapphire is intrinsically birefringent, though this can be overcome by high precision alignment of the test mass position. At UWA, the inhomogeneous birefringence was measured (Benabid et al 1999), showing that this type of birefringence is actually much smaller than the stress-induced birefringence which would also occur in isotropic materials. Intrinsic birefringence is therefore not seen as a major drawback to sapphire. Rayleigh scattering in sapphire can also introduce noise in gravitational wave detectors. Measurements showed that the scattering level is about 50 times higher than the fundamental limit predicted by thermodynamic fluctuation theory (Benabid et al 1998). This is due to the existence of micro point defects in the material. High purity sapphire samples should have lower scattering. It has also been observed that scattering is not uniform over sapphire test masses (Yan et al 2003). This is a disadvantage to sapphire which must be investigated further. One important issue for thermal noise is the test mass suspension. Although the gravitational restoring force of a pendulum is lossless, there is still some loss in the material comprising the suspension pivot. The loss angle of the pendulum can be expressed as (Saulson 1990) ϕ p = k s k g ϕ = γq (C.3) where k s is the spring constant of the suspension flexure, k g is the gravitational spring constant, γ = k s /k g is the Q enhancement factor (also called dilution

220 Review Paper for the Astronomical Society of Australia 199 Fig. C.8: The Niobium flexure suspension concept. Internal suspension wire modes are eliminated and the test mass Q-factor optimized by the absence of wires and wire bonding. The metal flexure is robust, and installation is simple. The X-shaped flexure slides into dovetail grooves in the test mass and in the supporting structure above it. factor) which is geometry dependent. ϕ is the loss angle of the suspension material and Q = 1/ϕ is the quality factor. It can be seen that choosing low loss suspension material is essential. Currently, fused silica fibres bonded to a fused silica test mass gives the lowest pendulum loss (Cagnoli et al 2000). However, bonding fused silica fibre to sapphire has the problem of localised stress due to the mismatch of thermal properties. Besides, fused silica fibre is fragile, prone to moisture damage and not compatible with cryogenic applications. At UWA, research has centered on an alternative suspension technique-the Nb flexure module suspension shown in Figure C.8. Niobium was selected as the flexure material because it has the lowest acoustic loss of any metal. It is non-brittle and has a room temperature thermal expansion coefficient compatible with sapphire. It also has excellent yield to Young s modulus ratio (which leads to high γ) and an excellent cryogenic thermal conductivity. The flexure module makes replacement quite simple in case of damage to the suspension. The short membrane flexure has the advantage of avoiding violin string modes which contaminate the GW observation frequency band. Tests resulted in a pendulum Q-factor of using a small monolithic Nb pendulum, though it is expected to achieve Q-factors of greater than 10 7 when γ is optimised (Ju et al 2001). One issue of flexure module suspension is that it requires a small groove to be cut in the sapphire test mass. This can introduce additional losses into the

221 200 Appendix C. test mass. However, tests conducted on a small sapphire test mass (Bilenko et al 2002) show that the degradation is reversible with annealing. A Q-factor of should be achievable with a 10 kg test mass. Data Analysis of the Interferometer Output The ACIGA Data Analysis program works in close collaboration with the LIGO Data Analysis program. Since 1999 ACIGA have made significant contributions to the LIGO Data Analysis System (LDAS), in particular, the Data Conditioning API (Blackburn, LIGO doc. T E). These range from the infrastructure of the Universal Data Type (UDT) and command syntax implementation, to sophisticated signal processing algorithms such as a system identification theorybased spectral line removal tool. LDAS underpins the search codes used by LIGO to produce astrophysical results from the raw interferometer output. ACIGA have worked intensively with the LDAS development group for the last three years, meeting weekly by teleconference, exchanging technical s on a daily basis, and participating in Mock Data Challenges in the US to integrate and scientifically validate software components (Finn, LIGO doc. T E). ACIGA is a partner in an international exchange of Physical Environment Monitor (PEM) data (Marka, LIGO doc. G D), along with LIGO, GEO and VIRGO. Environmental variables such as seismic motion, magnetic field and power grid voltage fluctuations, are sampled continuously and exchanged between the globally separated project sites (see Figure C.9c). The sampling is GPS synchronised to ensure sub-microsecond precision of event detection. The PEM data sets are searched for cross-correlations, and the ACIGA Data Analysis program seeks to contribute to the identification and characterisation of terrestrial noise sources that could couple into two or more globally separated gravitational wave detectors. Additionally, the exchange has provided a test-bed for the US-based Network Data Analysis System (NDAS) prototype, which collects and stores environmental data from participating sites for analysis, and allows evaluation of timing and synchronisation issues in advance of an eventual full-scale gravitational wave data exchange. NDAS has recently been upgraded, and is currently

222 Review Paper for the Astronomical Society of Australia 201 Fig. C.9: Top: Computing facilities used by the ACIGA Data Analysis program. (a) The Australian Partnership for Advanced Computing s National Facility (APAC-NF) is used for numerical simulations of global gravitational wave detector networks. (b) The ACIGA Data Analysis Cluster (ADAC) is used to run the LDAS software, and to test new components of the software such as spectral line removal tools. (c) The Mass Data Storage System (MDSS) is used for conversion and storage of large amounts of locally generated environmental data. Bottom: (a) Optimal location for a southern hemisphere GW observatory intersects Western Australia s Indian Ocean coastal plains. (b) Typical output of a line removal software tool developed at ANU. (c) Seismometers used to collect environmental data used in the PEM international cross-correlation data exchange. being used to move and analyse gravitational wave detector data as part of S2, the 2 nd LIGO Science Run, involving the 3 LIGO detectors, GEO and TAMA. The ACIGA Data Analysis program is based in the Department of Physics at The Australian National University (ANU), with strong ties to The ANU Supercomputer Facility (ANUSF) which houses the multi-terabyte Mass Data Storage System (MDSS) (see Figure C.9c) and the Australian Partnership for Advanced Computing (APAC) s National Facility (APAC-NF) (see Figure C.9a).

223 202 Appendix C. The MDSS is used to store data from LIGO interferometers and from the local (ANU) environment monitors. In the future it will store data from AIGO. The APAC-NF is used for general high-performance computing tasks, including Monte-Carlo simulations of the performance of networks of gravitational wave detectors. We have used these simulations to determine the optimal configuration for a global network of gravitational wave observatories; in particular, that Western Australia is a uniquely optimal site for an observatory to complete the existing global network (Searle et al 2002) (see Figure C.9a, bottom). The ACIGA Data Analysis Cluster (ADAC), which was recently installed in the Department of Physics at ANU (see Figure C.9b), gives ACIGA a conformant LDAS implementation to analyse LIGO data without duplication of LIGO s investment in the development of data analysis tools. The facility consists of three dual-processor servers managing a Beowulf cluster of eight high-performance nodes, gigabit Ethernet switching, and a terabyte local cache of RAID storage capacity. The cluster has already been used in the characterisation of the performance of line removal tools on actual LIGO data (Searle 2002) (see Figure C.9b). In the terms of the memorandum of understanding between ACIGA and LIGO, ACIGA has access to data taken by the LIGO interferometers during all engineering (i.e. commissioning) and science runs. Access to all of these terabyte-scale datasets is, however, impractical over the internet. We intend to purchase two LIGO-compatible tape drives for installation at ADAC and Gingin and a multi-terabyte reusable tape cache to facilitate exchange of data between ACIGA and LIGO sites. We also plan the formation of a local archive of LIGO data on the MDSS. In late 2002 we directly participated in the first science analyses of data taken from LIGO s S1 Science Run. We have worked closely with the LIGO Stochastic Background search group to develop line removal tools. Line removal was integrated into the stochastic background pipeline, and the impact of correlated spectral lines on the stochastic background search codes was assessed (Searle 2002). The analysis culminated in the setting of an upper limit on the strength of a cosmological background of gravitational radiation, the results of which are currently in preparation.

224 Review Paper for the Astronomical Society of Australia 203 Fig. C.10: Aerial photo of the AIGO site 80 km north of Perth. Two 80-m arms are visible extending from the central laboratory. The site benefits from minimal seismic interference from human activity, and unspoiled natural bushland abounding in biodiversity. Bringing it all together: AIGO The culmination of the four research areas described above is the AIGO facility near Gingin north of Perth, Western Australia. Opened in 2000 by the Hon. R. Court, Premier of Western Australia, the site consists of a 20m 20m central lab, two end-stations, workshops, meeting rooms and accommodation rooms. As of this writing, leak detection and repair of the test mass vacuum tanks and one 80-m beam pipe is nearing completion and an enclosure for the lasers and input optics has been built inside the central lab. By mid-year 2003, all the research done in ACIGA for the past several years will be brought together for the first fully-suspended high-power optical cavity experiments. The following section describes the facility in more detail, and some of the research that will be conducted there.

225 204 Appendix C. C.2.5 AIGO High Optical Power Test Facility The High Optical Power Test Facility will make use of all the major research achievements of ACIGA in order to provide a platform for a series of experiments slated for mid 2003 through The first stage requires a suspended 72 m cavity in which the substrate of the input test mass (ITM) mirror is inside the optical cavity. An input laser power of about 5 W will be used. Predictions of thermal lensing effects and substrate absorption will be checked, and tests of cavity locking systems and wavefront distortion control will be made. The second stage requires only that the ITM be reversed so that the reflective side faces the cavity. Absorption of the coating will be tested, and the input power will be increased to around 20 to 50 W. The third stage of tests sees the addition of a power recycling mirror (PRM) and a cavity power build-up of around 200 kw. Optical spring effects will be investigated using this configuration (see Figure C.11). This section describes some of the specific research problems to be addressed at AIGO/HOPTF as well as some of the specifics of the HOPTF experimental infrastructure. Thermal lensing and radiation pressure/optical spring effect are discussed. Then, details about the data acquisition system, vibration isolation system and vacuum system are presented. Thermal Lensing Increasing the optical power within the interferometer arm cavities is necessary to reduce shot noise and increase sensitivity, but doing so creates new problems. Thermal lensing and the optical spring effect are two of the problems anticipated for high optical power interferometry. Thermal lensing is the term given to induced wavefront distortions due to the absorption of significant amounts of power within the transmissive optics of the interferometer (Strain et al. 1994). The absorbed optical power (usually less than 1 W for the ITM) causes a non-uniform rise in temperature in the optics substrate. The extent of this depends mainly on the energy profile of the absorbed beam and the thermal conductivity of the substrate. The temperature variation (around 1 K) changes the optical path length inside the test mass, due in part (about 60%) to the temperature-dependence of the refractive index. Another 35% comes from

226 Review Paper for the Astronomical Society of Australia 205 Stage 1 Stage 2 Stage 3 Fig. C.11: The first three experiment stages for HOPTF. AR and HR designate anti-reflective and high-reflectivity optical coatings, respectively. In Stage 1 the substrate is situated inside the optical cavity in order to investigate thermal lensing. In Stage 2 the ITM optic is reversed. In stage 3 a power recycling cavity is added, and the input power increased.

227 206 Appendix C. simple thermal expansion of the substrate, causing a slight bulge where the beam is incident. An additional 5% of thermal lensing is attributable to a synergy of these two effects, namely an additional refractive index change as a result of induced mechanical stress, due to the fact that the thermal expansion is nonuniform (the photoelastic effect). For a laser beam of 3 kw and a transmissive sapphire test mass, the optical path length change measured across the beam diameter is typically around 25 nm. One consequence of thermal lensing is mode coupling. Due to non-sphericity of the induced thermal lens the beam spatial fundamental mode is cross-coupled into higher modes which are non-resonant within the cavity, resulting in decreased power in the cavity, added noise at the photodetector, and an offset in control feedback loops. Furthermore, a strong thermal lens can also reduce fringe contrast at the photodetector and make the resonant cavity unstable, because the radius of curvature, and therefore the focal length of the mirrors, has actually changed. One way to control thermal lensing is to reduce the thermal gradient inside the optics (Ryan et al 2002). A heating device may be added close to the material which heats the edge of the optics through radiative heat transfer. Physical contact, although more efficient for heat transfer, is not considered because it degrades the thermal noise performance of the test mass. This method is suitable for weak to moderate thermal lensing. For strong thermal lensing, a compensation plate may be used. A compensation plate is a fused silica plate (chosen for high transparency and low thermal conductivity) with a heating wire wrapped around it. The plate is placed in the cavity near the optics and compensates for thermal lensing by creating the opposite thermal gradient. The temperature of the wire is adjusted to make the spatial variation in optical path length of the compensating plate exactly opposite to that of the optics. Radiation Pressure & Optical Spring Effect It is well known that light carries momentum as well as energy. Radiation pressure can be interpreted as the transfer of momentum from photons as they interact with a surface. This effect is usually quite small. However, if the incident light

228 Review Paper for the Astronomical Society of Australia 207 power is very high, such as in the planned Advanced LIGO (Gustafson, LIGO doc. T D) gravitational wave detector and High Optical Power Test Facility (HOPTF), this effect is substantial. For instance, in the planned final stage of HOPTF, the laser power circulating in the arm cavity will be 200 kw. At this level of laser power the radiation pressure applied on the mirror is about 1.3 mn, sufficient to deflect the UWA pre-isolator by 20 m, which is 40 times the free spectral range of the cavity. Because the mirror motion will modulate the intensity inside an optical cavity, the resultant change in radiation pressure will act back on the mirrors. Thus, the light in the optical cavity acts like an optical spring. The spring constant depends on the frequency offset between the laser and the cavity resonance. The optical spring phenomenon leads to a correlation between radiation pressure fluctuations and intensity fluctuations. This arises because a radiation pressure fluctuation exerts a force which changes the cavity length, which in turn changes its resonance condition and hence the light intensity inside the cavity. At the quantum level the noise correlations can be used to suppress the total noise below the SQL (Buonanno and Chen 2001). At the classical level, the cross coupling between intensity and radiation pressure can lead to various effects which include amplification or attenuation of perturbations, instabilities, bistability and mechanical frequency tuning effects. Their effects depend on the parameters of the optical-mechanical system. In experiments to date most observations have focused either on the real or the imaginary component of the optical spring. Many optical spring phenomena have been observed. Bistability was first observed by Dorsel et al (1983). Very recently, Tucker et al (2002) examined the radiation pressure effect in a microscopically scaled tuneable Fabry-Prot cavity in which the real component of the optical spring contributed substantially to the mechanical resonant frequency. Strong frequency tuning and hysteresis were observed. Cohadon et al (1999) successfully cooled the Brownian motion of a mirror via the radiation pressure of a laser beam. In association with the UWA niobium bar gravitational wave detector Tobar (1996) investigated the electro-mechanical coupling due to the microwave radiation forces across the transducer. He developed a detailed model for the

229 208 Appendix C. phenomenon which includes both the real and imaginary components of the electromagnetic spring. The real part changes the stiffness of the cavity while the imaginary part changes its quality factor Q. Results showed detailed agreement between theory and experiment. Both frequency tuning (real component) and cold damping (imaginary component) were observed in agreement with theory, and the phenomena were utilised to substantially aid in the operation of the detector (Blair et al 1995). Chang et al (1997) examined the microwave radiation pressure induced expansion of a solid dielectric resonator. We proposed to undertake a similar comprehensive investigation of the phenomena in suspended optical cavities and to determine whether the effects can be utilised to stabilise and cold damp mechanical resonant modes. The work will lead the way towards the exciting goal of making a gravitational wave detector able to exceed the SQL based on the theory of Buonanno and Chen (2001). Data Acquisition, Transfer and Analysis The foundations of a system for data collection and transfer are well established at the HOPTF. A prototype data collection system, using National Instruments hardware and software, is installed and capable of logging 16 analog channels. This data includes 3-axes of magnetometer data, 3 axes of electromagnetic pulse data, 2-axis seismic data at two different locations, vertical seismic data from each test mass, wind speed and direction, and power grid noise data. The system will be scaled up in accordance with future requirements. Measures have been taken to ensure the time accuracy of the data collection system. An ultra-stable Rubidium atomic clock is used to regulate and synchronize the data sampling frequency of all channels to a high precision. A GPS receiver is installed on the roof of the main building, and will allow data to be time-stamped to an accuracy of less than 400 ns. The purchase of a server-grade computer is currently planned for the site. The computer will be configured to collect, process and store logged data in an automated fashion, and will be capable of running the LDAS software.

230 Review Paper for the Astronomical Society of Australia 209 Even with the recent addition of a satellite broadband connection at AIGO (512 kbps), live data transfer is not yet possible between the AIGO site and ANU where the data will be analysed. A direct wireless link to the UWA campus using 2.4 GHz IEEE b compliant hardware is being investigated which could raise the connection rate to 11 Mbps. The Vibration Isolator Sensitivity (h/hz 1/2 ) seismic noise Noise Floor Curves shot noise pendulum thermal noise Internal mode thermal noise Frequency (Hz) Fig. C.12: Graph of typical noise sources of an interferometer gravitational wave detector. At low frequencies, seismic noise forms an impenetrable wall defining the detection band. The detection band noise floor is defined by thermal noise of the suspension (pendulum) and of the test mass. The high-frequency detection limit is defined by photon shot noise, essentially statistical counting error. The lower frequency limit for earth-based interferometric GW detectors is established in the first instance by seismic noise. Human activity (including transport, machinery, and even foot traffic) as well as natural processes (ocean waves, wind gusts, animal movements and tectonic activity) all produce ground vibrations that create low frequency noise on the order of ten billion times stronger than GW signals. For instance at 100 Hz, the seismic RMS amplitude has a value of

231 210 Appendix C. Transfer Function Vertical Higher order internal modes Horizontal Frequency Hz Fig. C.13: Typical simulated transfer functions of the horizontal and vertical directions of isolation. Vertical graph scale is ratio of output to input amplitudes. Note the higher order internal modes; the vertical appears at lower frequency than the horizontal. The Euler type vertical springs have been implemented into the AIGO isolation stack to eliminate these modes from the detection band. about m/ Hz, approximately ten orders of magnitude higher than the desired sensitivity. Eliminating seismic noise is therefore fundamental to achieving required detector sensitivities. Ideally, a vibration isolator would substantially eliminate seismic noise in the detection band and minimise residual motion of the suspended test mass. The mechanical vibration isolation system at AIGO is designed to produce a residual motion of the test mass mirror on the order of nanometers. Figure C.12 shows a typical sensitivity curve for an earth-based interferometer with appropriate seismic isolation. It highlights the dominance of seismic noise in the low end of the detection band, and also indicates that thermal noise in the isolator is the next strongest noise source. The complete vibration isolation system consists of pendulums, masses and springs arranged in a chain of several stages that are suspended from a pre-

232 Review Paper for the Astronomical Society of Australia 211 isolation stage. The purpose of an isolation system is to attenuate the transmission of seismic vibrations to the test mass to an acceptably low level. An isolation stack consisting of n stages improves the performance by a factor of f n at frequencies above the last resonance (the corner frequency ). The isolator is designed to have its normal mode resonant frequencies all well below the lowest detection frequency while every attempt is made to place the higher internal modes of the isolator above the detection band (see Figure C.13). Pendulums are used as horizontal passive vibration isolators because they are good attenuators of vibration at frequencies above their resonance. They can also have high internal frequency modes. But for isolation in the vertical direction, some kind of spring must be used. Energy from the vibrational motion between the suspension point and the test mass has to somehow be momentarily stored. Suspending massive loads requires the storage of more energy. For a soft spring to store it, the spring must displace a great distance, and must therefore be very large. This reduces the frequencies of the spring s internal modes and places more of them directly in the detection band. The solution to this problem is to store the vast majority of the gravitational energy in a rigid structure and the miniscule, residual amount due to small fluctuations in a very soft (low stiffness) spring. This can be accomplished using a thin, flat structure loaded in axial compression which rigidly supports a load up to its buckling limit, then collapses into a low-stiffness buckled spring via Euler buckling. First introduced by the UWA suspension group, Euler Springs have been implemented in the AIGO isolation stack. An Euler spring is a column of spring material that has been compressed beyond its Euler buckling limit. The main advantage in using these springs is that they minimise the spring mass required to support the suspended test mass. This results in having far higher internal modes leaving the detection band clear of resonance peaks. The springs also allow for the construction of more compact forms of 3D vibration isolators due to their very small size (see Figure C.14). The vibration isolation chain developed for AIGO consists of several stages and is illustrated schematically in Figure C.15. The ultra low frequency pre-

233 212 Appendix C. Fig. C.14: Euler Springs shown here can support about 100 kg with a bounce frequency of less than 1Hz. They are about 200 mm long, and have their first internal resonance at about 4kHz. The configuration shown is typical of the ACIGA vertical vibration isolation stages, with springs under compression loaded from the top by a pair of pendulum wires forming the subsequent horizontal isolation stage. isolation stage suspends the conventional isolation stages to further reduce residual motion. It uses the principle of multiple inverse pendulums supporting a platform termed the wobbly table to achieve very low resonant frequencies in the horizontal direction. A LaCoste pendulum is employed to reduce the vertical spring-rate in the pre-isolator. The low spring-rate is obtained by effectively incorporating an inverse pendulum effect caused from the torque created by the spring that acts against the mass under the force of gravity. The second section of the pre-isolation stage is essentially a 2D pendulum called the Roberts linkage. Each individual stage of the pre-isolator has a resonant frequency of no more than 100 mhz. The main vibration isolation chain consists of a cascade of four horizontal and vertical stages where the last is the mirror control mass stage. They are suspended from each other by simple wire pivots consisting of a wire loop wrapped around a pin attached to the central tube. The amplitude of vibration at the resonant frequency of each pendulum is amplified by an amount determined by its Q-factor. It is thus necessary to implement damping mechanisms into the isolation system. A frame independent

234 Review Paper for the Astronomical Society of Australia 213 Fig. C.15: A schematic diagram of the vibration isolation stack for AIGO displaying the three main sections: a pre-isolation stage, multi-stage vibration isolation chain, and the test mass. The pre-isolation consists of a 2-D inverse pendulum horizontal stage, a LaCoste vertical stage, and a Robert s Linkage 2-D horizontal stage. Suspended from the Robert s Linkage stage is the isolation chain consisting of four vertical Euler spring-mass stages interspersed with three 2-D horizontal self-damping mass-pendulum stages. This extremely compact design utilises less than 3 meters of vertical space and is confined to a 1.8 m diameter vacuum tank.

235 214 Appendix C. method termed self-damping involves the use of strong rare earth magnets and copper plates spaced closely together inducing eddy currents due to relative motion between them. The coupling of the pendulum with the inertial mass pivoting on the pendulum creates current loops in the cooper plates and allows energy to be dissipated. The final stage of the isolation stack is the test mass control stage. This includes a sapphire test mass mirror suspended from the control mass by a niobium flexure. The complete final stage will be suspended from a vertical Euler stage and will weigh about 40 kg. C.2.6 Summary ACIGA research activities include aspects of the four critical areas for GW interferometry: advanced configurations and quantum optics; isolation, suspension and thermal noise; high power lasers and stabilisation; and data analysis. Closely related to data analysis is the astrophysical research also done in ACIGA studying potential sources of GW waves and creating expected detection profiles. ACIGA s activities play a vital role in the international gravitational wave research community. The level of nationwide collaboration, the depth of support and the range of specialties drawn upon is unprecedented in Australian astrophysics. This effort has already paid dividends in placing Australia in the vanguard of GW research and attracting students and visitors from all over the world. Besides the obvious connection to the future of Astronomy, the techniques and new science developed for this project have applications in many other fields, including optical Astronomy. The benefits of this program are not limited to just scientific progress. Technology spin-offs and collaborations with Australian industry have already occurred and are expected to continue. C.2.7 Acknowledgements This work is supported by the Australian Research Council, the Department of Education, Science and Training (DEST), and by LIGO Laboratories.

236 Review Paper for the Astronomical Society of Australia 215 The authors wish to thank the LIGO ACIGA Advisory Committee: Jordan Camp, Bill Kells, David Ottoway, David Reitze, Benno Willke, and Mike Zucker. Also acknowledged is David Shoemaker for his support of this committee. The authors also wish to thank the Gravity Waves technical staff at UWA: Ken Field, Peter Hay, Mike Kemp, John Moore, Xiaomei Niu, Tim Slade, Daniel Stone, Vinnie Nguyen, and Xiaolin Wang. Leica Kelly is also thankfully acknowledged for administrative assistance at UWA.

237 216 Appendix C. References Ando M et al 2001 Stable Operation of a 300-m Laser Interferometer with sufficient Sensitivity to detect Gravitational-Wave Events within Our Galaxy Phy. Rev. Lett Ando M, Kawabe K and Tsubono K 1997 Signal separation technique for a powerrecycled interferometric gravitational wave detector Phys. Lett. A Belczynski K., Kalogera V., 2001, ApJ Lett., 550, L183 Benabid F, Notcutt M, Ju L et a 1998, Birefringence measurements of sapphire test masses for laser interferometer gravitational wave detector, Phys. Lett. A Benabid F, Notcutt M, Ju L et al. 1999, Rayleigh scattering in sapphire test mass for laser interferometric gravitational-wave detectors: I. Measurement of scattering attenuation coefficient, Optics Communications Bilenko I A, Ju L, Paget D et al. 2002, Niobium flexure suspension design for high Q sapphire test masses for future gravitational wave detectors, Meas. Sci. Technol. 13, Billing H, Maischberger K, Rdiger A, Schilling R, Schnupp L and Winkler W 1979 An argon laser interferometer for the detection of gravitational radiation J. Phys E: Sci. Instrum Blackburn J K, The Data Conditioning API s Baseline Requirements, LIGO Document T E, Blair D G, et al, 1995 Phys. Rev. Lett Blair D G, Ivanov E N, Tobar M E, Turner P J, van Kann F, and Heng I S 1995 Phys Rev Lett Bondu F, et al Virgo injection system Classical and Quantum Gravity, Buonanno A and Chen Y, 2001 Phys. Rev. D Cagnoli G, Gammaitoni L, Hough J et al., 2000 Very high measurements on a fused silica monolithic pendulum for use in enhanced gravity wave detectors, Physical Review Letters 85, Chang S, Mann A G, Luiten A N, Blair D G, 1997 Phys. Rev. Lett Cohadon P F, Heidmann A, Pinard M, 1999 Phys. Rev. Lett Coward D M, Blair D G, Clay R, Mazzitelli G, 2002a Class Quant Grav

238 Review Paper for the Astronomical Society of Australia 217 Coward D M, Burman R R, Blair D G, 2002b, MNRAS, 329, 411 Cutler C., Thorne K. S., 2002, preprint gr-qc/ de Vine G et al 2002a Class.Quant.Grav.7, de Vine G et al 2002b Opt.Lett Djorgovski S G et al., 2001, in Gamma Ray Bursts in the Afterglow Era: 2nd Workshop, eds. N. Dorsel A et al, 1983 Phys. Rev. Lett Dragicevich P M, Blair D G, Burman R R 1999, MNRAS, 302, 693 Drever R W P 1982 Interferometric detectors for gravitational radiation Gravitational Radiation, Proc. Les Houches Summer Institute ed T Piran and N Deruelle Drever R W P 1983, in Gravitational Radiation, ed N. Deruelle and T. Piran, North Holland. Drever R W P, Hall T L, Kowalski F V, Hough J, Ford G M, Munley A G and Ward H 1983 Laser phase and frequency stabilization using an optical resonator J. Appl. Phys. B Eardley D M, 1983, Gravitational Radiation, ed N. Dereulle and T. Piran, North Holland, Amsterdam, p. 257 Ferrari V, Matarrese S, Schneider R, 1999a, MNRAS, 303, 247 Ferrari V, Matarrese S., Schneider R, 1999b, MNRAS, 303, 258 Finn L S et al, LDAS Data Conditioning API: Mock Data Challenge #1, LIGO Document T E, Flaminio R and Heitmann H 1996 Longitudinal control of an interferometer for the detection of gravitational waves Phys. Lett. A Freise A et al 2002 Performance of a 1200 m long suspended Fabry-Perot cavity Classical and Quantum Gravity Gray M B 1998 Applied Optics Gray M B, Stevenson A J, Harb C C, Bachor H-A and McClelland D E 1996 External phase-modulation interferometry Appl. Opt

239 218 Appendix C. Gustafson E, Shoemaker D, Strain K A, Weiss R, LSC White paper on detector research and development, LIGO document No T D, Hogg D W, Fruchter A S, 1999, ApJ, 520, 54 Ju L, Baker M, Blair D G, 2001, High-Q niobium membrane flexure pendulum, Physics Letters A 280, Ju L, Blair D G, Bilenko I, Paget D, 2002 Low loss niobium flexure suspension systems, Class. Quantum Grav. 19, Kalogera V., Narayan R., Spergel D., Taylor J. H., 2001, ApJ, 556, 340 Kuroda K, Ohashi M, Miyoki S et al., 1999 Large-scale cryogenic gravitational wave telescope, International journal of Modern Physics D 8, Lam P K et al 1999 J.Opt.B: Quant.& Semi.Class.Opt. 1, Landry M 2002 LIGO sensing system performance Classical and Quantum Gravity, Lawrence R., Zucker M., Fritschel P., Marfuta P., and Shoemaker D., 2002, Adaptive thermal compensation of test masses in advanced LIGO, Class. Quantum Grav. 19, Linthorne N P, Veitch P J, Blair D G, Turner P J, Tobar M E and Mann A G 1990 Niobium gravitational radiation antenna with superconducting parametric transducer Physica B Man C N, Shoemaker D, Manh Pham Tu and Dewey D 1990 External modulation technique for sensitive interferometric detection of displacements Phys. Lett. A Mrka S et al, Status of Network Data Analysis Server Prototype and Environmental Data Exchange, LIGO Document G D, McKenzie K et al 2002 Phys.Rev.Lett.88, (1) (4) Meers B J 1988, Phys.Rev.D38, 2317 Mizuno J et al, 1993, Phys.Lett.A175, 273 Mow-Lowry C 2002 Honours Thesis, The Australian National University Mudge D, Ostermeyer M O, Veitch P J, Munch J, Middlemiss B, Ottaway D J, Hamilton M W, 2000 IEEE Journal of Selected Topics in Quantum Electronics 6,

240 Review Paper for the Astronomical Society of Australia 219 Ottaway D J, Veitch P J, Hollitt C, Mudge D, Hamilton M W, Munch J 2000, Applied Physics B 71, Regehr M W, Raab F J and Whitcomb S E 1995 Demonstration of a power-recycled Michelson interferometer with Fabry-Perot arms by frontal modulation Opt. Lett Saijo M, Shibata J, Baumgarte T W, Shapiro S L, 2001, ApJ, 548 Saulson P R, 1990, Thermal noise in mechanical experiments, Phys. Rev. D 42 (8) 2437 Searle A C, 2002 Line removal techniques for LIGO data, at GWDAW2002 in Kyoto, Japan, December 2002, Searle A C, Scott S M and McClelland D E, 2002 Network sensitivity to geographical configuration, in Classical and Quantum Gravity Shaddock D A et al 1998 Applied Optics Shibata M., Baumgarte T W, Shapiro S L, 2000, ApJ, 542 Shoemaker D, Fritschel P, Giaime J, Christensen N andweiss R 1991 Prototype Michelson interferometer with Fabry-Perot cavities Appl. Opt Stevenson A J, Gray M B, Bachor H A and McClelland D E 1993 Quantum noise limited interferometer phase measurements Appl. Opt Stevenson A J, Gray M B, Harb C C, Bachor H A and McClelland D E 1995 Interferometer with internal and external phase modulation Aust. J. Phys Strain K A and Meers B J 1991 Experimental demonstration of dual recycling for interferometric gravitationalwave detectors Phys. Rev. Lett Strain K.A., Danzmann K., Mizuno J., Nelson P.G., Rdiger A., Schilling R. and Winkler W., 1994, Thermal lensing in recycling interferometric gravitational wave detectors, Phys. Lett. A 194, Takahashi R, Mizuno J, Miyoki S and Kawashima N 1994 Control of a 10 m delay line laser interferometer using the pre-modulation method Phys. Lett. A Tobar M E, 1996 PhD thesis, The University of Western Australia Tobar M E, Locke C R, Heng, I S, Ivanov E N, Blair D G, rd Amaldi Conference CP

241 220 Appendix C. Tucker R S, Baney D M, Sorin W V, Flory C A, 2002 IEEE J. Select. Topics Quantum Electron van Putten M. H. P. M., 2001, Phys. Rep., 345, 1 Weber, J., 1960, Detection and generation of gravitational waves, Phys. Rev Weisberg, J. M. and Taylor J H, 1984, Observations of post-newtonian timing effects in the binary pulsar PSR , Phys. Rev. Jett., Winterflood, J., Barber T et al Using Euler Buckling Springs for Vibration Isolation. Class. Quantum Grav. 19: Yan Z, Ju L, Zhao C, Blair D G, 2003, Rayleigh scattering study of sapphire cylinder test masses, Preprint, upcoming Amaldi 5 conference.

242 Appendix D Local Pre-isolation Control Paper D.1 Preface This paper was published in the proceedings of the Fifth Amaldi Conference in The author is listed as third author. At the time of this work, the author had just begun to be involved with the controls of the pre-isolation stages (without the suspension of the 3D stack below). He was involved in the measuring of the open loop control gain in which he assisted in the programming of the PID control in Labveiw. An improvement in the coding was created by the author for the controls of the pre-isolator that was part of the complete vibration isolator which was assembled at a later date. The author was also involved in the measurements of the transfer functions and the computation of the residual and RMS residual motions in both horizontal and vertical directions as presented in the paper. 221

243 222 Appendix D. D.2 Pre-isolation Control Paper Control of Pre-isolators for Gravitational Wave Detection C. Y. Lee 2, C. Zhao 2, E. J. Chin 1, J. Jacob 1, D. Li 2, D. G. Blair 1 1 School of Physics, The University of Western Australia, Nedlands, WA 6009, Australia; 2 School of Computer and Information Science, Edith Cowan University, Mt Lawley, WA 6050, Australia An ultra-low frequency pre-isolator (PI) has been built by ACIGA for micro-seismic noise isolation and reduction of suspension chain resonant mode amplitudes. A multidimensional control system, based on Digital Signal Processing (DSP), has been developed for position control and normal mode damping of the PI. In this paper, we demonstrate the successful control of the suspension system. D.2.1 Introduction One major noise source of terrestrial interferometric gravitational wave detectors at low frequency is seismic noise [30]. Not only does the noise limit in-band sensitivity, but it also affects interferometer operation due to large amplitude motions below the signal band. Various high performance vibration isolation systems [23, 30, 87, 12, 33, 57, 88, 89] have been developed to reduce this noise. A multistage suspended-chain pendulum combined with cantilever spring or Euler springs [56] has been demonstrated to provide sufficient horizontal and vertical vibration isolation well above the resonant frequencies. The shortcoming of the multistage suspended-chain isolator is that it isolates all seismic noise above its resonant frequencies, but amplifies the amplitude of any excitations at the resonant frequencies and consequently generates large residual motions. This makes it difficult to lock interferometer optical cavities because large forces must be applied to the test masses to acquire lock. Furthermore, the large locking forces mean that extra actuation noise is coupled to the test masses. To avoid this problem, multistage isolators can be suspended from an ultra-low frequency pre-isolator [12]. The PI provides a large reduction of the amplitude of the normal modes of the suspended isolation chain due to its very low frequency

244 Local Pre-isolation Control Paper 223 isolation performance. This can also suppress the micro-seismic peak due to ocean waves. Consequently, the mirror residual motion is greatly reduced and the interferometer is easier to lock. The use of ultra-low resonant frequency stages with very low spring constant also makes it possible to actuate on the pre-isolator by using low power coil-magnet actuators to achieve substantial adjustment of the optical cavity length. Various prototype pre-isolators have been developed at the University of Western Australia [12, 89], VIRGO [88], and TAMA [33] for this purpose. LIGO [23] is investigating the feasibility of stiff active isolation. A full-scale 3 dimensional pre-isolator has been completed for the Gingin high optical power research facility of Australian Centre of Interferometric Gravitational Astronomy (ACIGA). This pre-isolator has two low frequency horizontal stages and a single vertical stage. The first horizontal stage is an inverse pendulum while the second is a Roberts Linkage [35]. Vertical isolation is provided by a LaCoste stage [12]. The control work presented in this paper is the first to use the combination of the LaCoste stage with double horizontal stages forming the ACIGA pre-isolator. An interferometer has to be locked to a dark interference fringe with a tolerance to reduce the shot noise and avoid saturating the dark fringe detector [87]. Because of environmental temperature changes and long-term drift, the mechanical drift of the pre-isolator is large. These drifts must be removed by servo control. Clearly, this actuation must extend down to zero hertz. The preisolator is the ideal place to correct the very low frequency residual motion due to its ultra-low resonant frequency, large dynamic range, and low spring constant. D.2.2 Experimental Setup Figure D.1 shows an image of the pre-isolator developed at ACIGA. It is a cubic structure of about 1 m linear dimensions. The two horizontal isolation stages consist of a 4-legged inverse pendulum, followed by a cube shaped Roberts linkage [12] nested within it. The LaCoste linkage [56] provides isolation in the vertical direction. This linkage is based on coil springs and flexure arms for tilt rigid vertical motion. All horizontal and vertical stages have been tuned to 30 mhz,

245 224 Appendix D. Fig. D.1: Pre-isolator designed by ACIGA. Coil mounted on PI stand Magnet mounted on the frame of inverse pendulum LED Aperture Shadow Sensor Fig. D.2: Coil-magnet actuator and shadow sensor.

246 Local Pre-isolation Control Paper 225 Fig. D.3: Experimental control setup on the inverse pendulum. but the work described here are tuned to below 60 mhz. The dynamic range for all horizontal and vertical stages is +/-5 mm. Conventional shadow sensors and coil-magnet actuators (as shown in Figure D.2) are used to control all degrees of freedom of the pre-isolator. To control the inverse pendulum four sensor-actuator pairs are mounted onto the bottom of each side of the inverse pendulum and its frame. The experimental control setup is shown in Figure D.3. All detected signals from the sensors, before digitization, are passed through anti-aliasing filters and input to the DSP. The DSP implements the PID control algorithm. The output control signal from the DAC is sent to a coil driver, and then directly to drive the coil. The control system for the horizontal consists of 4 sensor/actuator pairs mounted on the inverse pendulum as shown in Figure D.4. This is a 2 in 2 out system. Along the x-axis, the position signal is the average of the signal from shadow sensor A and C, and the actuation is applied to the coil A and C evenly. Similarly along the y-axis, the position signal is the average of the signal from the shadow sensor B and D and the actuation is applied to the coil B and D evenly. We assume that the shadow sensors and actuators are balanced. A similar method is used to control the vertical stage shown in Figure D.5. For this vertical stage, we use one sensor and two actuators. Two actuators are driven by the same control signal and mounted on opposite sides of the PI stand

247 226 Appendix D. Sensor/actuator B Sensor/actuator A Sensor/actuator C Sensor/actuator D Fig. D.4: Top view of inverse pendulum where the 4 sensor/actuator pairs are mounted on the inverse pendulum and its frame. Fig. D.5: Experimental setup on the vertical stage. shown in figure D.7. One extra output signal will be used to pass current down the springs of the vertical stage to compensate for changes in temperature over long periods of time, as shown on Figure D.5.

248 Local Pre-isolation Control Paper 227 Magnet mounted on the vertical stage Coil mounted on the side of the frame Fig. D.6: Front view of coil-magnet mounting. The DSP, ADC and DAC are off the shelf products of Sheldon Instruments Inc. which have following main features. (1) DSP: The system use SI-C33DSP-PCI boards with PCI bus, which use Texas Instruments TMS320C33 DSP processor. The processor has 150 MFLOP peak performance, 32 bit floating point precision. Sheldon Instruments provides a residential library for programming the DSP in the LabView environment. (2) ADC and DAC: SI-MOD is a daughter board plugged into the DSP board. The board has 32S/16D, 0 Hz to 100 khz additive sampling ADC channels The ADC resolution is 16 bits. The maximum input voltage level is between +/-10 Vp. Four analog outputs on the board can each update at rates up to 100 khz, with 16 bits of resolution. These bipolar outputs have a maximum +/-10 Vp range, along with a 3-pole linear phase smoothing filter. D.2.3 Experimental Results Tests of the pre-isolator were performed in air on a full-scale pre-isolator with a fixed load (not suspended) of 410 kg dummy masses. Figure D.7 shows the measured open loop gain. The unity gain frequency is at 145 mhz. The phase margin at the unit gain frequency is 90 degrees. There is margin to increase the open loop gain with a stable loop. However, if we look at the performance

249 228 Appendix D. (a) (b) Fig. D.7: The open loop gain of the horizontal control loop with derivative gain only, (a) magnitude and (b) phase. of the damping (Figure D.8), the damping has been very effective. On the other hand, because the shadow sensor detects the relative motion between the inverse pendulum and the suspension frame instead of the pendulum inertial motion, higher loop gain will result in higher seismic noise re-injection. Hence, the open loop gain is kept low as to have effective damping without significant noise reinjection. The split peaks at around 50 mhz are due to the coupling of another horizontal axis which has the similar resonant frequency. The dip at 2-3 Hz is due to the center of percussion of the inverse pendulum which we have not tuned. Figure D.8 shows the horizontal stage residual motion with damping on and off. The horizontal stage has a resonant frequency 50 mhz as shown on the graph with the damping off. When the damping is on this peak is damped effectively. There is a rotational coupling which causes a small peak at 450 mhz. Structural resonance is obvious between Hz. The horizontal RMS residual motion is shown in the right plot of Figure D.8. It shows clearly the effectiveness of the damping. The RMS residual motion is reduced from around 10 4 to 10 5 at 30 mhz. Reinjected damping noise was calculated to be at m/ Hz at 100Hz. The left plot of Figure D.9 shows the spectral density of the vertical stage residual motion. The peak represents the resonant frequency at 60 mhz. There was no need for damping because the Q-factor was as low as 2. The right plot of Figure D.9 shows the vertical RMS residual motion.

250 Local Pre-isolation Control Paper 229 Damping off Damping on Damping off Damping on (a) (b) Fig. D.8: Performance of the horizontal stage; plot (a) shows the residual motion spectral density of the inverse pendulum in x-axis measured by the shadow sensor with damping on and off; plot (b) shows the RMS residual motion with damping on and off. (a) (b) Fig. D.9: Performance of the vertical stage; the left plot shows the residual motion spectral density measured with the vertical shadow sensor; the right plot shows the vertical RMS residual motion.

251 230 Appendix D. Fig. D.10: The theoretical horizontal residual motion of the full suspension isolation chain using the experimental pre-isolator results. A theoretical performance graph of the entire suspension chain is shown in Figure D.10. This was obtained by multiplying the horizontal residual motion spectral density of the inverse pendulum (Figure D.8) with a theoretical transfer function which consists of the remaining cascade of stages suspending the test mass mirror. The theoretical stack includes the Roberts Linkage of resonant frequency (ω) 0.05 Hz, and three pendulum stages with ω = 0.6 Hz. In addition to reduce the normal mode motion of the suspended isolator chain, another purpose of using pre-isolators is to compensate the large long term drift of the interferometer length and micro-seismic noise. We demonstrated the DC control on the horizontal and vertical stages. Figure D.11a shows that the preisolator with large oscillating motion due to active shaking. Derivative gain was applied to damp it at about 20 seconds. Integrator gain was applied to control the inverse pendulum to a required position (DC position control). As can been seen, once control was taken off at 540 seconds, the inverse pendulum showed damped oscillation. Figure D.11b shows the control process of the vertical stage. Initially the vertical stage was in a free state. Then integrator gain was applied with a set position of -3.5 mm. The vertical stage moved to -3.5 mm in about 350 seconds. The set position was changed to 3.2 mm at about 580 seconds, the vertical stage

252 Local Pre-isolation Control Paper 231 Displacement (mm) Damping stage changing setpoint Integrator switch back on at different setpoint damping stage control off control off Time (sec) (a) Displacement (mm) initial state setpoint and stabilize state achieved integrator gain applied -3 setpoint and stabilize -4 state achieved Time (sec) (b) integrator gain turned off oscillating state free state Fig. D.11: (a) The control of the inverse pendulum, (b) the control of the Vertical stage moved towards this set position over a time of about 300 seconds. Once the integrator gain was turned off, the vertical stage showed damped oscillation and continuing drift. In the future we intend to replace the Sheldon controllers with advanced DSP controller developed in collaboration with VIRGO. D.2.4 Conclusion The ACIGA pre-isolators which provide two stages of horizontal pre-isolation and one stage of vertical pre-isolation have been successfully controlled using DSP controllers. All stages can be tuned to below 60 mhz. In the near future, the system will be used to control the optical cavities in high power facility at Gingin. D.2.5 Acknowledgements This work is supported by the Australian Research Council, and is part of the Australian Centre for Interferometric Gravitational Astronomy.

253 232 Appendix D.

254 Appendix E Euler Spring Vibration Isolator Paper E.1 Preface This paper was published in the Fifth Amaldi Conference in The author has published a similar paper with substantially more content that presented further theoretical and experimental work. This later paper was accepted in Physics Letters A and makes up Section 3.3 of Chapter

255 234 Appendix E. E.2 Euler Spring Paper Techniques for Reducing the Resonant Frequency of Euler Spring Vibration Isolators E. J. Chin, K. T. Lee, J. Winterflood, J. Jacob, L. Ju, D. G. Blair School of Physics, The University of Western Australia, Nedlands, WA 6009, Australia We present results on frequency reduction techniques applied to Euler spring vibration isolators. The implementation of geometric spring coefficient reduction on vertical Euler springs is shown to provide between one and two orders of magnitude reduction in the effective spring constant. The results are based on a single Euler stage that is part of the full vibration isolation system being developed at AIGO. Issues concerning the stability of the system are presented and methods of improvement are suggested and discussed. Further experimentation on a single vertical Euler stage has achieved a resonant frequency of 0.3 Hz. E.2.1 Introduction Groups around the world have developed various mechanical filtering methods to achieve high levels of vibration isolation. Low-frequency curved-cantilever springs were developed by the gravity group at the University of Western Australia and have shown good performance [34]. The super-attenuators of Virgo use sets of triangular cantilever spring blades in each stage for vertical isolation [30, 31]. Other groups developing high performance vibration isolation systems include LIGO [23], TAMA [68, 43] and GEO600 [41]. A similar isolation system to the super-attenuator of VIRGO is the Seismic Attenuation System (SAS) developed by the collaboration of LIGO and TAMA [33]. A new type of spring system using Euler springs for vertical isolation was recently introduced by the UWA gravity group and has since replaced the cantilever spring isolators [56]. Euler spring isolators will be used as part of a complete isolation system for the Australian International Gravitational Observatory (AIGO) located at Gingin, Western Australia. An Euler spring is a column of spring material that has been compressed elastically beyond its buckling load. The main

256 Euler Spring Vibration Isolator Paper 235 advantage in using this type of spring is that it stores no static energy below its working range. This minimises the spring mass required to support the suspended test mass thereby increasing the resonant frequencies of the internal modes of the spring elements. This is advantageous in that the higher the frequency of the internal modes, the broader the isolation bandwidth obtained. The spring also allows for the construction of more compact forms of three dimensional vibration isolators due to their minimal size. E.2.2 Vertical Euler Stage with Reduced Spring Coefficient Pivoting rotational lever arms are used to constrain the spring loading direction and displacement, allowing them to be stably compressed in the longitudinal direction, as shown in Figure E.1. The longitudinally compressed Euler spring can buckle sideways in either one of two directions: towards the pivot or away from the pivot. Investigations have revealed that an Euler spring buckling towards the pivot is non-linear. It has much lower effective spring coefficients and regions of instability can easily be obtained [56, 57, 69]. A higher and complimentary spring coefficient is achieved when the springs bend away from the pivot. If an equal combination of springs buckling towards and away from the pivot is used, the almost constant spring coefficient of non-rotational compression can be obtained. It is easy to use springs in pairs to achieve reasonably linear performance. Paired springs are also necessary in order to permit spring coefficient reduction over a useful operating range. We found that effective spring coefficient cancelation was very difficult in the case of non-paired springs. A spring-rate reduction technique was proposed in Reference [56], which incorporates geometric variation into the Euler stage in order to further reduce the spring coefficient. The geometry is illustrated in Figure E.1a. An inverted pendulum of height h is created in the pivot arm. The suspension point is positioned at the top of the arm as shown. The Euler springs were clamped to the lower part of the central tube, shown experimentally in Figure E.1b. The mass load was hung by wires that were attached to the suspension points of the rotational arms. Vertical triangular

257 236 Appendix E. a) b) Pivot Suspension points r h l The inverse pendulum height Euler Springs Lower spring clamps Central tube Mass load Fig. E.1:. The vertical Euler stage, a) schematic diagram, and b) practical implementation. plates with slots allow the inverse pendulum height to be varied by adjusting the position of the suspension points. Force-displacement curves were derived for a single Euler stage with varying inverse pendulum height (Figure E.2). Excellent spring-rate cancelation is observed. Corrections were required due to the effective pivoting point of the suspension wire. The bending in the wire effectively defines a new point of suspension [71] that is lower than the clamping position defined at the bottom of the wire holder. This point depends on the wire thickness and as a result the amount of inverse pendulum effect in the system is reduced. The wire stiffness contributes to two separate undesired effects: a) an addition to the stiffness of the system and b) the lowering of the suspension point. Next we show the corrected force-displacement curve using 0.5 mm wire. The plot was based on the parameters: 4 Euler springs of length (l) = 134 mm, rotational arm length (r) = 64 mm and the load of the test mass of approximately 40 kg. The force is normalised to the critical force which is the force needed to start buckling the springs. The displacement is normalised to the length of the Euler springs. It is known that the behaviour of the Euler springs is strongly dependent on the angle at which they launch from the clamps [56]. With the appropriate launch

258 Euler Spring Vibration Isolator Paper 237 Force (normalised) Force vs Displacement h = h = 40, 30, 20, 10, 0, -10, -20 (values are in millimetres) Displacement (normalised) Fig. E.2: A force-displacement plot showing the predicted behaviour of the system as the inverse pendulum height (h) is varied. angle it is theoretically possible to obtain an almost ideal force-displacement curve with a constant gradient, so that the resonant frequency is independent of spring displacement in the working range. E.2.3 Experimental Results and Discussion The Euler spring material used was AISI C1095 tool steel of 0.5 mm thick, in the form of a feeler gauge strip. A constant Euler spring length of 134 mm was used throughout experimentation so direct comparisons of results could be made. Graphs of vertical spring displacement versus load as well as the corresponding resonant frequencies were obtained. Resonant frequency reduction was observed as the inverse pendulum height was raised. Although this was expected the actual amount of reduction created by corresponding h values were much less than calculated. In addition different launch angles were experimented with by inserting very shallow angled wedges between the clamps and the springs. The results obtained with this adjustment also agreed qualitatively with theoretical predictions but disagreed in the actual values obtained. An example of the amount of discrepancy in our results is the following. At the inverse pendulum height of 21 mm, spring-rate cancellation for the system with a suspension wire thickness of 1 mm is expected. With this configuration, a frequency around 0.1 Hz should

259 238 Appendix E. be obtained. At an h value of 81 mm, a resonant frequency of only 0.67 Hz was achieved. We believe the main reasons for the significant departures from theory have to do with the poor elastic properties of the material used and the difficulty of well defining the launching angles of the flex strips at the clamped ends. As soon as the spring strip takes on a slight set in curvature due to its poor creep properties, or slightly slips differentially between the clamping jaws due to the high bending and shear forces, the effective launching angle is altered resulting in a non-constant Euler spring coefficient. Combining this with the geometric reduction technique gives a region of high spring coefficient at one displacement adjacent to a region of instability at another displacement. This makes it very difficult to maintain operation in the small section between these regions which has low resonant frequencies, and makes the theory far from accurate. The results indicate that it is important to include launching angle adjustments in the Euler spring system so that manipulating the behaviour of the springs can be easily done. The following graph (Figure E.3) shows the progressive improvement in the transfer functions: a) the original Euler stage design without the inverse pendulum (resonant frequency of 2.5 Hz) and b) the transfer function of the system with launching angle rads at h = 75 mm. The two results show an order of magnitude improvement in the effective spring coefficient. Plot c) was obtained by implementing further improvements. This included replacing the springs with a material (AISI 301) with higher yield strength and lower creep. The spring clamping was also improved. This gave a resonant frequency of 0.50 Hz. The isolation floor of -45 db above 10 Hz that is seen in transfer function c can be reduced by considering dynamic inertia effects (usually termed the center of percussion) [56]. Future work includes center of percussion tuning to reduce this isolation floor. Following these experiments a new and improved stage was designed. The Euler springs were relocated so as to be co-linear with the suspension point as shown in Figure E.4a. The spring steel was replaced with maraging steel as first

260 Euler Spring Vibration Isolator Paper 239 on tuning to reduce this isolation floor. Transfer functions 40 a 20 c b 0 db Frequency (Hz) Fig. E.3: A plot of transfer functions showing the progressive reduction in the resonant frequency of the vertical Euler stage. 20 a) Inverse pendulum db b) Transfer function 10 Rotational arm 0 Altered Euler spring configuration -20 Lower spring clamp Frequency (Hz) Fig. E.4: a) The latest design of the vertical Euler stage showing the inverse pendulum and the new Euler spring configuration, b) The resulting transfer function showing a resonant frequency of 0.3Hz. introduced by VIRGO [63]. Preliminary tests showed a significant reduction in the creep rate to more acceptable levels (less than 1 mm/day for a 40 kg load). A test mass of approximately 80 kg was used in an experiment with the latest stage design with Euler spring length and thickness of 175 mm and 0.8 mm respectively. Figure E.4b shows the resulting transfer function, with a resonant frequency of 0.3 Hz. Further improvements will include incorporating a device to