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Rick Savage, Malik Rakhmanov, Keita Kawabe, and Joe Betswieser

Summary of recent measurements of g factor changes induced by thermal loading in the  H1 interferometer. Rick Savage, Malik Rakhmanov, Keita Kawabe, and Joe Betswieser. Measurement Technique.

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Rick Savage, Malik Rakhmanov, Keita Kawabe, and Joe Betswieser

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  1. Summary of recent measurements ofg factor changes induced by thermal loading in the  H1 interferometer. Rick Savage, Malik Rakhmanov, Keita Kawabe,and Joe Betswieser

  2. Measurement Technique • Dynamic resonance of light in Fabry-Perot cavities (Rakhmanov, Savage, Reitze, Tanner 2002 Phys. Lett. A, 305 239). • Laser frequency to PDH signal transfer function, Hw(s), has cusps at multiples of FSR and features at freqs. related to the phase modulation sidebands.

  3. Misaligned cavity • Features appear at frequencies related to higher-order transverse modes. • Transverse mode spacing:ftm = f01- f00 = (ffsr/p) acos (g1g2)1/2 • g1,2 = 1 - L/R1,2 • Infer mirror curvature changes from transverse mode spacing freq. changes. • This technique proposed by F. Bondu, Aug. 2002.Rakhmanov, Debieu, Bondu, Savage, Class. Quantum Grav.21 (2004) S487-S492.

  4. H1 data – Sept. 23, 2003 • Lock a single arm • Mis-align input beam (MMT3) in yaw • Drive VCO test input (laser freq.) • Measure TF to ASPD Qmon or Imon signal • Focus on phase of feature near 63 kHz 2ffsr- ftm

  5. Data and (lsqcurvefit) fits. ITMx TCS annulus heating  decrease in ROC (increase in curvature) R = 14337 m R = 14096 m Assume metrology value for RETMx = 7260 m Metrology value for ITMx = 14240 m

  6. To investigate heating via 1 mm light … • Lock ifo. for > 2 hours w/o TCS; Plaser= 2 W • Break full lock (t = 0) and quickly lock a single arm. • Misalign input beam (MMT3) in yaw • Measure temporal evolution of Hw(s) • H1 Xarm dataFeb. 18, 2005 • Simple exponential fit to estimate initial curvature

  7. Inferred curvature changes:ITMx = 293 m ITMy = 177 m Ratio:DRITMX/ DRITMY = 293m/177m = 1.7 Yarm measurement Feb. 19, 2005

  8. Xarm Comparison with model – Phil Willems

  9. Comparison • Note: unlike TCS heating measurements, where only ITM was heated, 1064 nm light resonating in arm cavity heats both ITM and ETM. • Time constants – simple exponential fittITMX = 7.7 min; tITMY = 7.2 min (noisy data) • Change in radius of curvatureDRITMX/ DRITMY = 293m/177m = 1.7 • g factor change greater in xarm by factor of 1.7 • ETM absorptions differ? • ITM absorptions differ? • If ITM bulk/surface absorption ratios differ, then absorption ratio could be larger (or smaller) • Joe Betzwieser’s POY and POX time-depentent spot size measurements

  10. Calibration using TCS results • TCS calibrationXarm: 220m / 37mW = 5.9 m/mWYarm: 190m / 45mW = 4.2 m/mW • Surface (not bulk) absorption • 1064 nm heatingXarm: 293m / 5.9 m/mW = 49mWYarm: 177m / 4.2 m/mW = 42 mWAssumes all heating on surface and no absorption in ETMs • Surface-equivalent, ITM-onlyabsorption calibration 14.5 km D ~ 220 m 14.28 km 13.9 km D ~ 190 m 13.71 km

  11. “Cold” values from 1064 nm meas.ITMX: 14.226 km difference ~ 50 mITMY: 13.615 km difference ~ 100m Systematic errors? Alignment drifts – sampling different areas of TM surfaces More complex, time-dependent behavior of surface distortions? Phil Willems studying with time-dependent model of surface distortions g factor measurements and reduced data available inLIGO-T050030-00-W 14.5 km D ~ 220 m 14.28 km 13.9 km D ~ 190 m 13.71 km Issues – “cold” curvature differences

  12. P. Willems’ time-dependentHello-Vinet model - Xarm

  13. Yarm comparison

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