KAGRA Frequency Stabilization Servo Modeling Report Yuta Michimura February 18, 2015 1 Introduction This report is to summarize the results of KAGRA frequency stabilization servo (FSS) modeling. The modeling was done by using MATLAB Simulink based Noise Budget made by Chris Wipf [1]. The main script and the model for KAGRA FSS modeling are as follows: https://granite.phys.s.u-tokyo.ac.jp/svn/lcgt/trunk/kagranoisebudget/ FSS/run FSS NB.m https://granite.phys.s.u-tokyo.ac.jp/svn/lcgt/trunk/kagranoisebudget/ FSS/KAGRA FSS.mdl You will also need findnbsvnroot.m, myzpk.m, plotdobe.m, and plotspectrum.m in the same directroy to run the script. 2 Model 2.1 Simulink model The KAGRA FSS Simulink model is shown in Fig. 1. We had to use some tricks to simulate out-of-loop stability and feedback signal with Simulink Noise Budget blocks, and (see yellow and cyan areas). 1
Laser Source NPRO NbNoiseSource KAGRA FSS Model run run_fss_nb.m PMC Wideband EOM CavLPF('PMC') PMC LPF EOMFB Act('EOM') EOM Actuation EOMFBMeters PZTFB Act('PZT') PZT Actuation PZTFBMeters TempFB Act('Temp') Temperature Actuation TempFBMeters feedback signal (for saturation check) Filt('TempDg') Temp Loop Digital Filter SW(4) Switch4 Out4 In4 SW(3) In3 Switch3 Out3 SW(2) In2 Switch2 Out2 SW(1) Switch1 In1 Out1 openloop transfer function for FRC FRCOOL FRCOOLMeters out-of-loop stability after FRC servo TTFSS 2e-3 Filt('EOM') Gain3 EOM Loop Filter 1e-3 Filt('PZT') Gain2 PZT Loop Filter 4e-3 Filt('Temp') Gain1 Temperature Loop Filter FRC CavLPF('FRC') FRC LPF FRCnoise NbNoiseSource AOM AOMFB AOMFBMeters MCeFB MCeFBMeters feedback signal (for saturation check) Act('AOM') AOM Actuation Act('MCe') MCe Actuation SW(7) IMCOOL Switch7 Out7 In7 IMCOOLMeters out-of-loop stability after IMC servo Common Mode Servo Board for IMC SW(6) -0.1 Filt('AOM') Switch6 Gain5 AOM Loop Filter In6 Out6 Filt('MCeDg') SW(5) 1e-7 Filt('MCe') MCe Loop Digital Filter Switch5 Gain4 MCe Loop Filter In5 Out5 openloop transfer function for IMC SW(10) CARMOOL Switch10 10 Out10 10 In10 CARMOOLMeters out-of-loop stability after CARM servo Common Mode Servo Board for CARM SW(9) 3e7 Filt('AO') Switch9 Gain7 Additive Offset Loop Filter In9 Out9 SW(8) -1e-7 Filt('MCe2') Switch8 In8 Out8 openloop transfer function for CARM Gain6 MCe Loop Filter 2 CARM CavLPF('CARM') CARM LPF CARMnoise NbNoiseSource IMC CavLPF('IMC') IMC LPF IMCnoise NbNoiseSource CavHPF('IMC') IMC HPF CavLPF('IMC') IMC LPF2 4 3 2 1 3 2 1 4 9 8 9 8 7 6 5 6 5 7 Figure 1: KAGRA FSS Simulink model. When the CARM loop is enabled, the MCe loop in the IMC loop is disabled. 2
2.2 KAGRA cavity parameters The round-trip lengths L and finesses F of KAGRA cavities are summarized in the table below. These parameters are used to calculate the cavity pole f cp = c 2LF (1) Table 1: KAGRA cavity parameters. The round-trip length for FRC is multiplied by the refractive index of the fiber (n = 1.46). Cavity Round-trip length L Finesse F Cavity pole f c PMC 0.4 m 200 190 khz FRC 1.46 5.8 m 451 39 khz IMC 2 26.65 m 500 5.6 khz Arms 2 3000 m 1530 16 Hz 2.3 Actuators The frequency actuators we use for the FSS are summarized in the table below. Table 2: The frequency actuators for KAGRA. Note that they are rough estimates yet!! MCe actuation efficiency was measured to be 25 µm/v by K. Arai [2]. Name Detail Actuation efficiency Range Laser temperature NPRO 3 GHz/V 30 GHz Laser PZT NPRO 1 MHz/V 100 MHz 5 if Wideband EOM Newport 4004 1.5 10 Hz/V 0.6 MHz 1 Hz AOM Crystal Technology 5.3 MHz/V 40 MHz 3110-197 (with driver 1110AF- AEFO-1.5) MCe Double pendulum 280 MHz/V at DC? (on mirror) ETM 7-stage pendulum?? 2.4 Filters The filters are shown in the figures below. Note that the gain scales are arbitrary. 3
Gain 10 4 10 3 10 2 10 1 100 101 102 103 104 105 106 10 5 0 13 10 12 10 11 10 10 10 9 10 8 10 7 10 6 14 FRC servo filters Phase [deg] 180 120 60 0 60 120 Temp TempDg PZT EOM 180 Figure 2: Filters for the FRC servo. Gain 102 101 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 10 12 0 13 14 IMC servo filters Phase [deg] 180 120 60 0 60 120 MCe MCeDg AOM 180 Figure 3: Filters for the IMC servo. 4
Gain 102 101 100 10 1 10 2 10 3 10 4 10 5 10 6 10 7 CARM servo filters 10 8 10 9 10 10 10 11 10 12 4 Phase [deg] 180 120 60 0 60 120 MCe2 AO 180 2.5 Noises Figure 4: Filters for the CARM servo. The frequency noises of each component are shown in the figure below. bkagra requirement CARM FRC IMC NPRO Frequency noise [Hz/rtHz] Figure 5: Frequency noises. shown here is unrealistic!! 5
3 Result 3.1 Openloop transfer functions The openloop transfer funtions are shown in the figures below. Gain FRC servo OLTFs Phase [deg] 180 120 60 0 60 120 Temp PZT EOM FRC total 180 Figure 6: Openloop transfer functions for the FRC servo. Gain IMC servo OLTFs Phase [deg] 180 120 60 0 60 120 MCe AOM IMC total 180 Figure 7: Openloop transfer functions for the IMC servo. 6
Gain CARM servo OLTFs Phase [deg] 180 120 60 0 60 120 AO MCe2 CARM total 180 Figure 8: Openloop transfer functions for the CARM servo. 3.2 Out-of-loop frequency stability The out-of-loop frequency stabilities are shown in the figures below. The stability shown here is the stability when the servos for the next stages are turned off. For out-of-loop stability after the FRC servo, the IMC and the CARM loop is off. For the IMC stability, the FRC loop is on, but the CARM loop is off. When th CARM loop is on, the MCe loop in the IMC loop is disabled. The blue line labeled shows the bkagra frequency noise requirement [3]. 7
FRCOOL NoiseBudget Figure 9: Out-of-loop frequency stability after the FRC servo. IMCOOL NoiseBudget IMC noise Figure 10: Out-of-loop frequency stability after the IMC servo. 8
CARMOOL NoiseBudget Figure 11: Out-of-loop frequency stability after the CARM servo. 3.3 Feedback signal saturation check The spectra of feedback signals are shown in the figures below. Check if they are not saturating with your eyeballs. The blue line labeled shows the actuation range in Hz for each actuator. TempFB NoiseBudget Figure 12: Spectra of feedback signals for the Temp. 9
PZTFB NoiseBudget Figure 13: Spectra of feedback signals for the PZT. EOMFB NoiseBudget IMC noise Figure 14: Spectra of feedback signals for the EOM. 10
MCeFB NoiseBudget IMC noise Figure 15: Spectra of feedback signals for the MCe. AOMFB NoiseBudget Figure 16: Spectra of feedback signals for the AOM. 11
ETMFB NoiseBudget IMC noise Figure 17: Spectra of feedback signals for the ETM. References [1] The source code is available from https://svn.ligo.caltech.edu/svn/aligonoisebudget. Some instructions are given at https://awiki.ligo-wa.caltech.edu/aligo/noisebudget. [2] Koji Arai, Shuichi Sato, Ryu Takahashi: Mode Cleaner Suspensions Transfer Functions. http://tamago.mtk.nao.ac.jp/tama/ifo/recycling1/suspension tf/ 020322 MC/tfMC020322.pdf [3] Yoichi Aso, Yuta Michimura, Kentaro Somiya: KAGRA Main Interferometer Design Document, JGW-T1200913. http://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/docdb/showdocument?docid= 913 12