Violin Modes S 2 Line Noise Investigation S

Violin Modes S 2 Line Noise Investigation S. Klimenko, F. Raab, M. Diaz, N. Zotov (thanks to Gaby and Andri for discussions) LIGO-G 030130 -00 -Z presented by S. Klimenko l Outline Ø Tracking of violin modes in S 2 Ø Work in progress Ø Conclusion

VM Monitoring l Narrow lines are monitored with the Line. Monitor Ø Integration time – 1 min Ø we assume that the harmonic’s amplitudes do not change much during the integration time T (line width << 1/T) l The Line. Monitor estimates an, f and fn Ø Violin frequencies are known, measure amplitude and phase. Ø Line parameters are constantly measured and stored in trend files Ø Two harmonics for each mode are monitored. Some first harmonics and most of the second harmonics are not visible for 1 min integration time

Violin Amplitude l A – pendulum vibration amplitude l l a – mirror motion amplitude (<<A) V – amplitude measured by Line. Monitor in ADC counts, converted to a using calibration n – wire-mirror coupling: l Thermal noise: l Ø quality factor l Wire/Mirror motion: m M

H 2 violin modes for S 1 run l Thermal noise from measured Q’s of H 2 violin modes Ø Fred: e-log 9/8/02 Ø The raw data (red circles) is compared to the estimated thermal noise (blue curve) 343. 754 39, 000 343. 814 143, 000 ETMX 344. 051 70, 000 ETMX 344. 110 143, 000 349. 201 116, 000 349. 245 90, 000 349. 282 90, 000 349. 659 175, 000

Calibrated Amplitude l l R 0 – response function C 0 – sensing function H 0 – open loop gain (0. 376 @ 344 Hz) g, a – t-calibration

Average square amplitude l l P(a) – Raylegh distribution P(a 2) – exponential Ø slope s gives <a 2>

Amplitude distribution

exponential

external excitation l non-exponential tail Ø can be excluded from the fit Ø Line. Mon outlier triggers could be used as veto for the analysis. l shifted Rayleigh distribution Ø slope is not affected by shift

L 1 Violin thermal noise very preliminary frequency , Hz 343. 06 343. 48 displacement noise, mf 14. 5 15. 8 343. 65 344. 42 346. 65 346. 94 12. 9 19. 9 16. 6 18. 1 stat. error ~ 1% expected noise for simple mechanical model: 15. 0 -15. 5 mf (depends on M and w)

Conclusion & Plans l Thermal excitation of the violin resonances is observed Ø measured noise: 13 -20 mf Ø expected noise: 15. 0 -15. 5 mf Ø more accurate mechanical model should be used for better agreement between measured and calculated noise. Ø the noise measurement could be affected by servo. l Plans Ø do analysis of H 1 and H 2 modes (Sergey) Ø calculate thermal noise from measured Q-factors and compare with the Line. Monitor results (Fred)