1. Damping and Tuning of Violin Modes in Monolithic Silica Suspensions Stefan Goßler for the GEO 600 Team

2. Motivation Example: GEO 600 monolithic silica suspensions made in December ´02 But: High Q violinmodes may interfere with the interferometer length-control servo To supress the influence of thermal noise, high Q suspensions are a key element of the advanced interferometric detectors Damping of the violinmodes without degrading the pendulum Q

3. GEO Suspensions... Cantilever Springs Stack Isolator Coilholder for Local Control at the Upper mass Fibers Upper Mass Intermediate Mass Mirror 5.6 kg 180 mm

4. ... with Feedback 3 mm Cantilever Springs Stack Isolator Mirror Upper Masses Coilholder Fibers Intermediate Mass Cantilever springs Electrostatic Actuator (10 – 100 Hz) Magnet-Coil Actuator (0 – 10 Hz)

5. Violinmodes Q ~ Resonant Enhancement Q = f res, = Decay Time for Factor 1/e Amplitude 1 Frequency [Hz] 1500 f0f0 f1f1 Example: 3 10 8 /( 500 Hz) = approx. 2,3 Days P. Willems et al.: Q = 5,2 10 8

6. How to keep the servos happy? f 0 : Q < 3*10 6 f 1 : Q < 2*10 6 Frequencies (each eight for f 0 and f 1 ) within 10% Frequencies as high as possible (650 Hz) Frequency [Hz] 1001000 Magnitude 10 -2 1 10 2

7. f0f0 Damping & Tuning... f1f1 By coating sections of the fibers with lossy material (i.e, amorphous Teflon dissolved in fluorinert in our case)...violin modes without degrading the pendulum Q:

9. Damping & Tuning... f0f0 f1f1 Damping scales stronger with coating diameter than with coating length Frequency shift scales with mass added...violin modes without degrading the pendulum Q: By coating sections of the fibers with lossy material (i.e, amorphous Teflon dissolved in fluorinert in our case)

10. Measuring Violinmode Qs Measuring Violinmode Qs 50 kg Isolation Fiber (Fused Silica) Fused Silica Fiber with GEO parameters: 280 mm Length 220 µm Diameter 1,4 kg Lock-in Ampl. Spectrum An. Laser Split-Photodiode Elektrostatic Actuator Fused Silica Plate Fused Quarz Block (400 g) Fused Quarz Block (with Steel Clamp) Vacuum: 10 -5 mbarQ max = 3*10 7,

11. Measuring Violinmode Qs Measuring Violinmode Qs 1,4 kg Elektrostatic Actuator Vacuum: 10 -5 mbarQ max = 3*10 7,

12. Measuring Violinmode Qs Measuring Violinmode Qs 50 kg Isolation Fiber (Fused Silica) Fused Silica Fiber with GEO parameters: 280 mm Length 220 µm Diameter 1,4 kg Lock-in Ampl. Spectrum An. Laser Split-Photodiode Elektrostatic Actuator Fused Silica Plate Fused Quarz Block (400 g) Fused Quarz Block (with Steel Clamp) Vacuum: 10 -5 mbarQ max = 3*10 7,

13. Reference Fiber A fiber with: Length: 284 mm Diameter: 210 – 240 µm f 0 = 664 Hz Q 0 = 2 10 6 Coating length: 26 mm @ 1/2 of the fiber length Fiber diam.: 240 µm After coating: 300-325 µm f0f0 Bounce mode: 14.9 Hz Q 1 = 5 10 5 Coating length: 31 mm @ 1/4 of the fiber length Fiber diam.: 210 µm After coating: 340-370 µm f 1 = 1313 Hz f1f1 f 0 : 743 Hz f 1 : 1451 Hz

14. Selective Tuning... f 0 [Hz] f 1 [Hz]... of the violin modes: 741 1415 660 1306 Uncoated After Initial coating 691 1325 After 1 st corrective coating 678 1316 After 2 nd corrective coating 665 1316 724 1490 676 1380 662 1353 f 0 [Hz] f 1 [Hz] Target: 664 Hz 1313 Hz

15. Fiber Preparation for GEO 20 of 30 coated Fibers within: Before coating 3,5% f 0 = 663 Hz 0,48% Before coating 4,2% f 1 = 1314 Hz 0,86% But: Welding and suspending increases the spread by not yet known amount Target: 664 Hz 1313 Hz

16. Tuning after welding (in situ)

17. After welding: f 0 = 669,5 Hz f 1 = 1344 Hz After corrective coating: f 0 = 654 Hz f 1 = 1324 Hz Two of eight fibers were treated with a corrective coating after welding Example:

18. Results: Frequencies & Qs Amplitude [a.u.] Frequenz [Hz] 620640660 630 650670 f 0 = 645,5 Hz 3,86% Q 0 = 6 10 5 – 2,8 10 6 Q 1 = 5,4 10 5 –1 10 6 f 1 = 1287 Hz 4,86% Target: Q < 2 10 6. Target: Q < 3 10 6.

19. Conclusion It is possible to tune the violin mode frequencies (downwards) almost independently to the desired values with great accuracy In December ´02 we successfully suspended two GEO mirrors with damped and tuned violin modes (And the beam splitter only with slightly damped violin modes) It is possible to bring the Qs to the desired levels, BUT it is NOT possible to measure them prior to final installation