Real Time Measurements of Single Bunch Phase and Length in the HERA Proton Storage Ring and the Observation of Multi-Bunch Oscillations

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1 Real Time Measurements of Single Bunch Phase and Length in HERA and Obseration of Multi-Bunch Oscillations Real Time Measurements of Single Bunch Phase and Length in the HERA Proton Storage Ring and the Obseration of Multi-Bunch Oscillations Elmar Vogel Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany DESY Report No. DESY-HERA--, Abstract After the luminosity upgrade of the electron proton collider HERA, the proton bunch length will become releant for the achieable luminosity. This is due to the enhancement of the effectie cross section at the interaction region when the beta function and the bunch length hae comparable magnitude, hour-glass-effect []. For a reduction of the bunch length, a better understanding of the longitudinal beam dynamics is essential. We deeloped a diagnostic system which permits real time measurements of bunch phase and length for all bunches during one turn. One can also obsere multi-bunch oscillations during acceleration which are correlated with an increase of the bunch length. Moreoer the system proides the signals needed for feed-forward and a multi-bunch feedback. In this paper the technical setup is described and first measurements are shown. TRODUCTION The HERA proton storage ring has possible bunch positions 9 ns apart, of which are occupied. The accelerator is shown in figure. To inject proton bunches into HERA, three PETRA fillings of proton bunches must be transferred. The rise time of the injection kickers requires a gap of 5 bunch positions ( ns) between the successie trains of bunches. Afterthethirdbunchtrainthereisagapof5bunch positions needed for the dump kicker at 9 GeV. At the injection energy of GeV the buckets are proided by a 5 MHz system. During ramping to 9 GeV a MHz system takes oer. The reasons for this double are the bucket matching during injection from PETRA [3, ], and the longitudinal compression of the bunches by the steeper potential of the MHz system at high energy. Typical FWHM bunch lengths after injection are. ns, during ramping the lengths are reduced to. ns by the The rise time of the injection kickers is ns. To build up the magnetic field of the dump kicker ns are needed []. Here we quote bunch length in the time domain. Since β = c.9997 at HERA, the spatial lengths are gien by multiplication with c. Hall WEST (HERA-B) resistie gap monitor LAC III (5 MeV) HERA (9 GeV) 5 MHz MHz 3.3 MHz -.3 MHz 5 MHz Hall NORTH (H) PETRA II ( GeV) DESY III (. GeV) Hall SH (ZEUS) Hall EAST (HERMES) Figure : The proton accelerator complex at DESY with the arious -Systems and the positions occupied by bunches. The gaps between the three bunch trains are needed for the build up of the fields in the injection and the dump kicker magnets. compression of the MHz System. Under the assumption of emittance conseration one would expect a bunch length of l 9 GeV.7 l GeV i.e.. ns. This means that there are processes during the ramp which increase the longitudinal emittance. To understand this undesirable phenomenon it is necessary to study the longitudinal beam dynamics together with the technical properties of the storage ring in more detail. EXISTG NGITUDAL BEAM DIAGNOSTICS. Resistie Gap Monitor Two identical resistie gap monitors [5], installed in the HERA proton storage ring, are the basis of all longitudinal beam diagnostics. The monitors delier time signals of the

2 Real Time Measurements of Single Bunch Phase and Length in HERA and Obseration of Multi-Bunch Oscillations bunches, with a time resolution of approximately ps. In figure the working principle of a resistie gap monitor [] is shown. gap j beam j output no. n Z load, n Z load, n impedance conerter network j j j,, Z 5 5 ferrite Figure : Working principle of a resistie gap monitor, and the equialent network for calculation of the impedance as seen by the beam. A beam with current j beam induces in a smooth cylindrical acuum chamber for = c the wall current j wall = j beam. The acuum chamber is separated by a small cylindrical gap, so that the wall current has to flow through an intermediate impedance conerter network K. Atthe output no. n the network supplies the oltage signal load, n to a load resistor Re (Z load, n ). This signal is related by the monitor sensitiity factor S n to the beam current j beam : outputs load, n = S n j beam () When passing the monitor the beam loses the power P monitor = jbeam Re (Z monitor) and the network supplies the power P load, n = load, n / Re (Z load, n) at the output n. Hence the sensitiity is r S n = Re (Z load, n )Re(Z monitor ) P load, n. () P monitor In figure 3 the assembly of the monitor is shown. Eight 5 Ω outputs are arranged around the gap. A coaxial structure enclosing the acuum chamber is loaded at the end with ferrites, to suppress reflections oer a wide range of frequencies. The load of the ferrites amounts to 5 Ω. This gap 5 P load, 5 P load,5 Figure 3: Resistie gap monitor 5 ferrite beam results in the equialent network shown in figure, and the impedance, seen by the beam, is Z monitor =5Ω. At one output the power of P load = P monitor is supplied, therefore the sensitiity factor is r S n = 5 Ω 5 Ω =5Ω. (3) The signals at the indiidual outputs depend on the horizontal and ertical beam position. This dependence can be eliminated by combining four outputs crosswise with resistie power combiners [7]. Resistie power combination results in a power loss of 5% in each combiner, i.e. the combination of four outputs yields the same power as a single output. Therefore the sensitiity is again 5 Ω.. Narrow Band Phase Measurements Seeral narrow-band diagnostic methods to measure the beam phase are implemented in HERA. The principle is shown in figure. reference signal beam phase αχ phase det. output system bandpass bunched beam caities 9 ns broadband monitor Figure : Principle of narrow-band beam phase measurements. The bunched beam passes one of the resistie gap monitors and induces narrow output signals. These signals excite oscillations in a band pass filter whose central frequency is identical to the reference, hence the phase between these oscillations and the reference, measured with a phase detector, is equal to the beam phase. High accuracy in the phase measurement is obtained by aeraging oer many bunches, achieed either by a narrow band width of the band pass filter or by using low pass filters at the output. These systems are inadequate for the obseration of multi-bunch oscillations, in particular the signal anishes for out-of-phase synchrotron oscillations. Two control loops are installed to damp synchrotron oscillations in HERA [, 9, ]. Both loops hae phase detection units as described..3 Longitudinal Bunch Shape Measurements Sampling of the longitudinal bunch shape supplies information about single bunches [5]. The signal from a resistie gap monitor is transferred ia a 35 m long 5/ Flexwell cable to a Tektronix (TEK) 9 ns c

3 Real Time Measurements of Single Bunch Phase and Length in HERA and Obseration of Multi-Bunch Oscillations 3 SCD5 oscilloscope, with an analog bandwidth of.5 GHz and a digital resolution of.5 GHz. In figure 5 different bunch shapes, recorded with this deice are presented. limiter: 9 phase 9 shift: Vlim for V( V V ( Ζ Τ Vlim for V( χ ΤV V( else ( i ( lim lim sampled signal (arbitrary units) sampled signal bucket no. at GeV bucket no. at 99 GeV sampled signal sampled signal bucket no. at 97 GeV bucket no. at 9 GeV mixer: two way power splitter: two way 9 power splitter: IF I 9 Q IF Γ ( Ζ ( ( I Q ( Ζ ( ( Ζ ( i ( Ζ ϑ ( Table : Mode of action of components used in phase detectors and I/Q demodulators. Figure 5: Different longitudinal bunch shapes, taken by sampling the signal of a broadband resistie gap monitor with a TEK SCD5 oscilloscope. The setup is ery useful for the obseration of selected bunches, but the SCD5 has an effectie dead time of about 5 ms. In practice one gets a bunch shape eery second. This acquisition rate is too low to obsere synchrotron oscillations with a typical frequency of 5 Hz. The accuracy of the bunch phase measurement is directly connected to the jitter of the trigger signal proided to the oscilloscope. Since the jitter of the HERA timing is about ±5 ps the maximum phase error is ±3. with respect to a MHz bucket. This is too inaccurate. The dead time problem can be soled by using a fast frame oscilloscope, which is triggered on the same bunch eery th reolution, see e.g. [3]. This technique is also often used for phase space tomography [,, 3]. There is no easy way to implement the simultaneous obseration of all bunches in HERA. Considering all this, the setup of a new diagnostic tool to measure all bunch phases and length synchronous was indispensable. 3 REALTIMEMEASUREMENTSOF SGLE BUNCH PHASE AND LENGTH The resistie gap monitor is located behind the injection point near the Hall West where the proton beam is transferred from PETRA to HERA. A future feed-forward system for beam-loading compensation at injection would use this monitor. 3. Bunch Phase The bunch phase is the phase deiation between the bunch center and the bucket minimum. We hae to determine this phase for eery bunch in a long train. This is possible with a band-pass filter which has a decay time well below the 9 ns separation between two bunches. An I/Q demodulator is used to obtain the phase in the full range from to. The I/Q demodulator requires two analog-to-digital conerters (ADCs), but the resulting data structure is an adantage for a digital control system, since successie data points correspond to the real and imaginary part of the angular pointer of the signal, and matrix multiplication can be used for the ealuations. To understand the functioning and adantages of an I/Q demodulator, I first describe the principle of a phase detector. In electrical engineering it is conentional to present a oltage ( by an angular pointer ( ( = Im[ (] = V (sin[ω t + ϕ (], () where V ( is the amplitude and ϕ ( the phase of the signal. Table shows the action of the components, included in phase detectors and I/Q demodulators, in terms of angular pointers. The components of a phase detector are a limiter, a low pass filter, a controllable phase shifter and a frequency mixer see figure. The output signal of the phase detector should depend only on the phase shift between the and the local oscillator input. For this reason the amplitude of the signal is first limited to a constant alue. Higher harmonics generated by the limiter are damped by a low

4 Real Time Measurements of Single Bunch Phase and Length in HERA and Obseration of Multi-Bunch Oscillations limiter low pass I phase shifter mixer 9 control of phase shifter IF two way power splitter IF mixer mixer two way I 9 9 power splitter Q Figure : Principle of a phase detector. IF Q pass filter. The resulting signal is mixed with the signal in a frequency mixer. Before doing this, the phase of the signal is shifted by a controllable phase shifter by 9. We get the output signal ( = V V lim sin [(ω ω ) t+ +(ϕ ϕ ()]. (5) The frequency is set equal to the frequency ω = ω and for small phase deiations ϕ ϕ ( the sine function is linearized: ( V V lim [ϕ ϕ (] () Phase measurements with a phase detector suffer from seeral sources of errors. In practice the phase ϕ ϕ ( consists of a constant and a time arying part, which one is interested in. First the constant part is subtracted by tuning the phase shifter. Large phase deiations lead to errors because of the replacement of the sine by its argument. A limiter also contains capacitie components which lead to a phase shift of the output signal, dependent on the input amplitude. Finally one has to measure V V lim for the calibration. Phase measurements with an I/Q demodulator aoid these problems. An I/Q demodulator consists of two frequency mixers, a two way power splitter, and a two way 9 power splitter, see figure 7. The demodulator outputs are Q ( = I ( = V V ( sin[(ω ω )t+ +(ϕ ϕ ()] (7) V V ( cos[(ω ω )t+ +(ϕ ϕ ()]. () In the special case ω = ω one speaks of downconersion to the base band. We get full information about the amplitude V ( and phase ϕ ( of the signal ( at the demodulator outputs. The beam monitor signal of a single bunch excites an oscillation in a broadband 5 MHz band pass filter, which Figure 7: Principle of an I/Q demodulator. is analyzed with an I/Q demodulator by down-conersion to the base band, using the frequency as local oscillator. Before sampling the I and Q signals with two ADC channels they are smoothed with low pass filters. The correct sampling time is gien by the condition that the expression p ( I () +( Q () assumes its maximum. In this case we get the 5 MHz Fourier component of the bunch signal by A 5, meas = max q( I () +( Q () q ( I,max ) +( Q,max ) (9) A 5 = C 5 A 5, meas () and the phase 3 by φ =arctan Q,max I,max + φ offset. () where C 5 is the oerall gain in the circuit and φ offset the phase offset between and inputs. The following contradictory conditions must be fulfilled by the band pass filter:. The remaining oscillation in the filter must be small when the next pulse arries. This means, the decay time of the signal in the filter has to be sufficiently small e.g. the bandwidth has to be large.. After the I/Q demodulator and the low pass filters a certain period of time is necessary for sampling at the signal maximum. For slowly arying signals the analog digital conersion is less sensitie to jitter in the ADC timing signals. For this reason larger decay times of the signal in the filter are desirable which imply a small bandwidth of the filter. 3 In longitudinal beam dynamics the bunch phase is usually denoted by φ. We measure the phase φ = φ φ s with respect to the bucket minimum, which is equal to the phase of the synchronous particle φ s.

5 Real Time Measurements of Single Bunch Phase and Length in HERA and Obseration of Multi-Bunch Oscillations 5 signal from resistie gap monitor 5 MHz bandpass filter with about 3 MHz bandwidth 5 MHz reference signal ( enl,max Ζ f 3 db BW first order filter enl, max e f signal after bandpass filter ( low pass filter ( MHz ADC 5 MHz I/Q demodulator ADC ADC Q ( I,max ( Q,max Q ( analysis of band pass filter oscillation Figure : Measurement principle of the phase and amplitude of the 5 MHz Fourier component of a single bunch signal: The signal from the resistie gap monitor excites an oscillation in a band pass filter, which decays before the next bunch passes the monitor. The I/Q demodulator determines the in-phase (I) and out-of-phase (Q) components of the bunch induced oscillation, referred to the 5 MHz reference frequency. center frequency: design type: bandwidth ( db): input frequency: pass band ripple: impedance: insertion loss: dynamic range: operating temperature: connectors: 5. MHz series connection of two Butterworth filters of first order, importand is a constant cycle duration 5 MHz DC to. GHz < ±. db 5 Ω at in- and output < db < dbm to > dbm - Cto5 C SMA Table : Properties of 5 MHz band pass filter. 3. For useful phase information the filter should not ring and the cycle duration should be constant. To hae no ringing effects in a filter, the progression of the phase oer the frequency has to be a monotone and smooth function. Simulations based on measured bunch shapes showed that two Butterworth filters of first order in series fulfill these criteria. The filter specification is gien in table. The filter was custom designed from a company according to these specifications. Ζ Ζ f e sin t ϑt enl, max two first order filters in series Figure 9: Response of an ideal 5 MHz band pass filter and a series connection of two band pass filters, each of first order, to an impulse excitation. In figure, some technical details hae been omitted: amplifiers for increasing signal leels and attenuators to suppress signal reflections. An example of the bunch phase measurement is shown in figure. Here bunches are measured without noticeable synchrotron oscillation and the measured phase alues during a.5 s long period are plotted in a histogram, subtracting the indiidual time-aeraged phase of each bunch. A Gaussian distribution is obsered with a FWHM of.9, with respect to the 5 MHz radio frequency. This number is an upper limit for the resolution of the detection system, since the phase noise of the bunched proton beam itself is included in the data. 3. Bunch Length Two typical bunch shapes at GeV and 99 GeV, as recorded with the fast oscilloscope, are shown in figures and. An almost Gaussian shape is obsered, een during strong synchrotron oscillations at 99 GeV. Under the assumption of a Gaussian bunch shape the experimental setup described here permits a bunch length determination in real time. If we measure at least two Fourier coefficients at different frequencies we are able to calculate the bunch length: Consider the monitor signal of a Gaussian bunch shape A ( = e t σ () πσ with the bunch length l FWHM = β c ln σ. The Fourier

6 Real Time Measurements of Single Bunch Phase and Length in HERA and Obseration of Multi-Bunch Oscillations no of measurements at bunches during.5 s width of distribution: FWHM = sampled signal from SCD5 (arbitrary units) Bucket at 99. GeV FWHM =.73 ns centroid = -.9 ns Gauss fit FWHM =.9 ns centroid =.7 fs phase deiation of each bunch from its indiidual aerage during.5 s in Figure : Relatie measurement errors of single shot phase measurements. Figure : Bunch shape during bunch oscillations at 99 GeV. sampled signal from SCD5 (arbitrary units) Bucket at 39.7 GeV FWHM =.3 ns centroid = -.5 ns Gauss fit FWHM =.3 ns centroid = -.5 ns From the phase measurement described in section 3., one obtains not only the bunch phase but also the amplitude of the 5 MHz Fourier coefficient of the longitudinal bunch signal. The natural choice for the second frequency is MHz at HERA. To measure the MHz Fourier component a band pass filter is used whose specifications are identical to those gien in table, except for the center frequency of MHz. In figure 3 the bode diagrams of both band pass filters are shown. Bode Diagrams component is Figure : Bunch shape at GeV. A (ω) = σ π e σ ω. (3) Rearrangement of the ratio A A(ω ) yields the bunch length l FWHM = β c s r ln ω ln A. () ω A In HERA the proton elocity is c, forsimplification one can set β = c to. A A(ω ) Phase (deg) Magnitude (db) MHz 5 MHz Frequency (MHz) MHz MHz Figure 3: The Bode diagrams of the 5 MHz and MHz band pass filters. The output signal of the filter is detected by an diode, smoothed by a low pass filter, and then digitized by an

7 Real Time Measurements of Single Bunch Phase and Length in HERA and Obseration of Multi-Bunch Oscillations 7 ADC. Figure shows the setup. signal from resistie gap monitor signal after bandpass filter Mhz bandpass filter with about 3 MHz bandwidth A max MHz amplitude after low pass filter low pass filter A( ADC MHz ADC Figure : Principle of the MHz bunch Fourier component measurement. Taking into account the characteristic cure from the diode F diode (A max ) A max and the different oerall gains C 5 and C at 5 MHz and MHz, the bunch length is gien by r l FWHM =.375 ns ln A 5 (5) A A 5 A = C 5 C A 5, meas A, meas. () In practice the ratio C 5 /C is determined by comparing the results of this method with direct FWHM measurements using the TEK SCD5 oscilloscope. For long bunches the MHz Fourier coefficient is small and the signal to noise ratio becomes unfaorable. At a bunch length of. ns the measurement error of the single shot measurement is less than 5. ps, see figure 5. bunch length by analyzing the bunch shapes, recorded with the fast oscilloscope. A reasonable correlation is obsered. The spread is mainly caused by multi-bunch oscillations during acceleration from GeV to 9 GeV, where bunch length oscillations are always present. Therefore the results from the fast oscilloscope depend on the particular measurement times. The FWHM determination from the fast oscilloscope uses only the center peak and disregards the population in the head and tail of the bunch, while the real time method takes account of these particles. The disadantage of the real time method is that particles spilled oer into the neighboring MHz buckets enhance the MHz Fourier component and therefore the calculation of the bunch length (5) results in a shorter alue. bunch length in ns, measured with the fast oscilloscope bunch length in ns, measured with the real time measurement no of measurements at bunches during.5 s aerage bunch length of the bunches at 9 GeV: l FWHM =. ns width of distribution: FWHM = 5. ps aerage bunch length of the bunches at GeV: l FWHM =.5 ns width of distribution: FWHM =.5 ps length deiation of each bunch from its indiidual aerage during.5 s in ps Figure 5: Length measurements of bunches with no obserable oscillations. Figure shows the correlation of the aerage bunch length during a time interal of.5 s, measured with the method presented and the determination of the FWHM Figure : Correlation of the alues determined by the real time bunch length measurement method and the FWHM measurement with the fast oscilloscope. During the writing of this paper I found that the measurement of the bunch phase with two Fourier coefficients of the longitudinal bunch shape has also been attempted by [5]. MEASUREMENT OF MULTI-BUNCH OSCILLATIONS. Timing For detection of multi-bunch oscillations the clock and trigger signals must be proided to the ADC boards in a special way. The clock signals are rectangular signals with a frequency of. MHz, the bunch repetition frequency, deduced from the reference by counting waes with ECL gate arrays. The clock signals can be shifted under remote control in steps of 5 ps, to ensure that the ADCs sample the signal maxima.

8 Real Time Measurements of Single Bunch Phase and Length in HERA and Obseration of Multi-Bunch Oscillations Because of the low synchrotron frequency, Hz to Hz, it does not make sense to measure the bunch parameters eery turn. In this case one synchrotron oscillation cycle would fill the ADC memory of k (553) samples per channel. The ADC boards used are able to start seeral times a measurement cycle with an eligible number of samples, 5 samples for each cycle are selected. Measuring eery th reolution has turned out to be a good compromise between time and frequency resolution. A trigger signal is proided eery th reolution, by diiding the beam reolution trigger (7.3 khz) by. In this way, the phase and amplitude of an indiidual bunch are sampled with a frequency of 55 Hz, fast enough for the obseration of bunch phase oscillations ( Hz to Hz) and length oscillations ( Hz to Hz). The total recording time is.5 s. phase in based on 5 MHz bucket number. Data acquisition Ground loops on the signal path which carry high frequency signals hae been suppressed by using DC blocks. After down conersion of the signals DC blocks could not be used any more. Background noise could be remoed by using sampled alues from unoccupied bunch positions for an offset correction []. The dump gap consisting of 5 bunch positions was used for this purpose. Since the reolution frequency is 7.3 khz, we suppress eery unwanted signal modulation in the technical setup with a frequency lower than 7 khz. Errors caused by net frequency and ground loops are suppressed rather well. Seeral measurements were made with incomplete filling of the ring. To remoe unoccupied bunch positions from the data, a minimum alue of the 5 MHz Fourier component was required. 5 EXPERIMENTAL RESULTS 5. Multi Bunch Oscillations On account of the beam loading transients, the bucket minima are not equidistant. This results in a shift of the bunch phasing with respect to the reference signal from one bunch to the next. Thus the first step for data presentation is the calculation of the aerage phase of each bunch during the measurement time of.5 s. The data are shown in figure 7. A systematic ariation of the phase is seen along the three trains of bunches. During multi bunch oscillations a single bunch carries out phase oscillations with a typical amplitude of about its aerage alue. For a graphical representation only the phase deiations of each bunch from its aerage phase during the obseration time are presented using a colored pixel plot. The two axes in figure are the bucket position and time while the phase deiation from the aerage is indicated by the pixel color. The presentation of bunch lengths is done in the same way, figure 9 and. Similar graphic representations hae already been used at Fermilab. Figure 7: The aerage phase of each bunch during a measurement time of.5 s..55 time in s 9 bucket number color scale in - + Figure : Multi bunch dipole oscillation at 99 GeV. The axes are the bucket position and time. The phase deiation from the aerage bunch phase with respect to 5 MHz is gien by the pixel color. With this diagnostic tool one obseres multi bunch oscillations during eery ramp of the proton storage ring. At energies aboe 3 GeV one sees the most impressie oscillations. Usual they persist up to 9 GeV. In the stored 9 GeV beam the multi bunch oscillations decay within half an hour. After the decay the pattern shown in figure is obtained, which is characteristic of a quiet beam without measurable multi bunch oscillations remaining for the rest of the luminosity run.

9 Real Time Measurements of Single Bunch Phase and Length in HERA and Obseration of Multi-Bunch Oscillations bunch lenght (FWHM) in ns c time in s. 5 5 bucket number Figure 9: The aerage length of each bunch at 99 GeV during a measurement time of.5 s bucket number color scale in - + Figure : At stationary states of the storage ring one obsere always a quiet beam. Here for example at 9 GeV. time in s 9 bucket number color scale in ns aerage of bunch length (FWHM) in ns c ma.3. 9 ma ma Figure : Multi bunch quadrupole oscillation at 99 GeV. 5. Emittance Blow Up In figure the aerage length of all bunches is plotted ersus the time together with the energy. At the injection energy of GeV one obseres jumps related to the injection of the second and the third train from the pre-accelerator PETRA. On the ramp from GeV to 9 GeV the optics is changed at arious intermediate energies: 7 GeV, 5 GeV, 3 GeV and 75 GeV. The steps in the energy ramp are correlated with small jumps in the aerage bunch length and with multi bunch oscillations. In a storage ring the longitudinal emittance is theoretically consered. So the bunch lengthening is indicated better by calculating the longitudinal emittance. The longitu- energy in GeV. 3 5 time in min 3 5 time in min Figure : The change of the aerage bunch length during ramping form GeV to 9 GeV, see text. dinal emittance is gien by []

10 Real Time Measurements of Single Bunch Phase and Length in HERA and Obseration of Multi-Bunch Oscillations S FWHM = π t FWHM E FWHM (7) with [7] t FWHM = l FWHM c E FWHM = β s = φ FWHM ω () E s p U ( φfwhm ) (9) η E FWHM is the energy deiation, t FWHM the time deiation of a particle with phase deiation φ FWHM, β = c, E s the energy of the synchronous particle and η = + γ t γ the slip factor with γ t =7.7 and γ = E s E. The oltage of the double harmonic System aerage of bunch emittance (FWHM) in mevs ma.3. 9 ma ma 3 5 time in min creates a bucket potential V = V 5 sin φ + V sin φ () U ( φ) = e V 5 (sin φ π h s (φ s φ)+ 5 +cosφ s cos φ)+ + e V (sin φ π h s ( φ s φ)+ 5 +cosφ s cos φ). () φ s is the synchronous phase and φ the phase deiation. To simplify the calculation of the longitudinal emittance using (7), (), (9) and (), the synchronous phase φ s was set to zero. The time-eolution of the emittance is plotted in figure 3. One obseres a strong increase from GeV to 9 GeV. To get more insight, the time deriatie of the emittance is plotted in figure. It exhibits strong maxima at 3 GeV and 99 GeV. These are associated with multi bunch oscillations of large amplitude. A close look at figure reeals that the stepwise increase in the emittances do not occur during the optics change at fixedenergybutratherin the acceleration periods in between optic changes. Obiously an optics change at constant energy does not cause multi-bunch oscillations. Possible reasons for the excitations of oscillations during acceleration are chromaticity effects, errors in the tracking between the field in the superconducting bending magnets and the radio frequency and the effects of passie impedances caused by steps in the beam pipe, or of actie impedances like the feed-back systems. Inestigations concerning possible multi-bunch instabilities in HERA are underway. All pictures of multi bunch oscillations presented in this paper were taken at 9th March at 99 GeV where a big blow up of the longitudinal emittance took place. Figure 3: Eolution of the longitudinal emittance (FWHM) during the energy ramp from GeV to 9 GeV. time deriatie of aerage bunch emittance (FWHM) in mevs/s energy in GeV GeV 99 GeV 3 5 time in min 3 5 time in min 9.3. ma.3. 9 ma ma Figure : The time deriatie of the longitudinal emittances is a measure of the emttiance blow up. CONCLUSION In this paper the technical setup to measure the proton bunch phase and the length of each indiidual bunch during one HERA reolution has been described. The most

11 Real Time Measurements of Single Bunch Phase and Length in HERA and Obseration of Multi-Bunch Oscillations important parts of this setup are custom designed filters for measuring the 5 MHz and MHz Fourier components of the indiidual bunch shapes. A special timing of ADC boards permits the measurement of multi-bunch dipole and quadruple oscillations. As a first result the simultaneous appearance of huge multi-bunch oscillations and emittance blow up was shown. 7 ACKNOWLEDGMENTS Many people were inoled in the on-going realization of the hard- and software. I would like to thank Peter Albrecht, Ralf Apel, Josef Baran, Wolfgang Bensch, Bernd Closius, Guenter Delfs, Hans-Thomas Duhme, Peter Gasiorek, Serguei Goloborodko, Torsten Gresmuehl, Stee Herb, Gerd Hochweller, Andrej Kholodniy, Manfred Luehmann, Jorgen Lund-Nielsen, Tomasz Plawski, Willi Radloff, Rainer Saust, Victor Soloie, Andreas Sommer, Klaus-Ulrich Tode, Richard Wagner, Manfred Wendt, Hong Gong Wu and Xiang Zeng. For helpful discussions I would like to thank Alexander Gamp, Uwe Hurdelbrink, Wilhelm Kriens, Michiko Minty and Stefan Simrock. I would also like to thank Peter Schmueser for his adice during writing this paper. I would like to thank as well the Deutsches Elektronen- Synchrotron DESY for proiding all the necessary resources. REFERENCES [] M. A. Furman, The hourglass reduction factor fo asymmetric colliders, Asymmetric B-Factory collider Note No. SLAC-ABC--REV (99) [] personal communication with J. Rümmler, DESY (999) [3] W. Kriens, PETRA Bunch Rotation, in Proceedings of the Particle Accelerator Conference, Vancouer, Canada, 997, (DESY Report No. DESY-M-97-N, 997) [] G. Wiesenfeldt, Untersuchungen zur longitudinalen Strahlanpassung beim Protonentransfer on PETRA nach HERA, Diplomarbeit, Uniersity of Hamburg (995) [5] G. Lopez et al, ObserationofProtonBunchBehaiorin HERA, in Int. J. Mod. Phys. A, Proc. Suppl. A, p. 5 (993), identical with Proceedings of International Conference on High Energy Accelerators, Hamburg, Germany, 99 [] D. Bussard, Schottky Noise and Beam Transfer Function Diagnostics, in Proceedings of CERN Accelerator School - Fifth Adanced Accelerator Physics Course, Rhodes, Greece, 993 (CERN Report No. CERN-95--ol., p. 75, 995) [7] Priate communication with M. Wendt from DESY. His signal combination method is based on a idea already used at CERN. () [] A. Gamp, Sero Control of Caities under Beam Loading, in Proceedings of CERN Accelerator School - Engineering for Particle Accelerators, Oxford, United Kingdom, 99 (CERN Report No. CERN-9-3-ol., p. 39, 99) [9] W. Kriens, Neue Kontrollen für die Frequenz- und Transfersteuerung bei HERA, in DESY Accelerator Operation Seminar Grömitz, Germany, 999 (DESY Report No. DESY-HERA-99-, p. 5, 999) [] W. Kriens, Neue Kontrollen für die Frequenzsteuerung und Synchronisation bei HERAp in DESY Accelerator Operation Seminar Grömitz, Germany, (DESY Report No. DESY-M--5, ) [] [] S. Hancock, P. Knaus, M. Lindroos, Thomographic Measurements of Longitudinal Phase Space Density, in Proceedings of the European Particle Accelerator Conference, Stockholm, Sweden, 99 [3] S. Hancock, S. Koscielniak, M. Lindroos, Longitudinal Phase Space Tomography with Space Charge, CERN Report No. CERN-PS--- () [] D. A. Edwards, M. J. Syphers, An Introduction to the Physics of High Energy Accelerators (John Wiley & Sons, 993) [5] C. Boccard, T. Bogey, J. P. Papis and L. Vos, Intensity and Bunch Length Measurement for Lepton Beam in the Injection Lines of the SPS and LEP, in Proceedings of Second European Workshop on Beam Diagnostics and Instrumentation for Particle Accelerators (DIPAC 95), Lübeck- Traemünde, Germany, 995, (CERN Report No. CERN SL/95-5 (AP), 995) [] Y. Chernousko suggested this idea, DESY (999) [7] W. Pirkl, Longitudinal Beam Dynamics, in Proceedings of CERN Accelerator School - Fifth Adanced Accelerator Physics Course, Rhodes, Greece, 993 (CERN Report No. CERN-95--ol., p. 33, 995) [] W. Kriens, M. Minty, Longitudinal Schottky Monitoring for Protons in HERA, in Proceedings of the European Particle Accelerator Conference, Vienna, Austria,