1. Parametric Instabilities and Control Li Ju ( 鞠莉）, Chunnnong Zhao, David Blair Jiayi Qin, Qi Fang, Carl Blair, Jian Liu University of Western Australia Slawek Gras, S. Danilishin Xu Chen, S. Susmithan

3. Outline  What is parametric instability  Observations  Control strategies

4. Three Mode Parametric Interactions mm 00  1 =  0 -  m mm 00  1 =  0 +  m Stokes process: A photon of frequency  0 is scattered into a lower frequency photon  1, and emit a phonon of frequency  m  Parametric instability Anti-Stokes process: The scattering crates a higher frequency photon  1, absorption the phonon  m  Cooling of the acoustic mode

5. Cavity Optical Modes

6. Example of Test Mass Acoustic Modes

7. Parametric interaction in an optical cavity High power fundamental mode  o Cavity high order transverse mode  1 scattered from acoustic mode Thermally excited acoustic mode  m amplified by radiation pressure feedback Positive feedback interaction If optical mode and acoustic mode shape match and certain frequency condition was meet, optical mode energy could pump into acoustic mode  Acoustic mode ring up exponentially, destroying cavity locking

8. Experimental Investigations  Predicted by Braginsky et al 2000  Extensively investigated, especially UWA group  Detailed 3D analysis  Full model of the potential instability modes for advanced detector  Demonstrated 3 mode interactions (below instability threshold) in 80m suspended cavity  Demonstrate parametric instability in table top cavity  Proposed control strategies  Till recently, people were still doubt that it will happen in the real detector

9. Parametric instability Observed at LIGO First observed 4 th,Dec. 2014, with 2oW input power Another example with 25W, April 2015 aLIGO LLO logbook

10. Phys. Rev. Lett. (2015)

11. Parametric Gain Sensitive to Radius of Curvature 8P in Q 0 Q 1 Q m  B L 2  0  m 1+(  /  1 ) 2 R =  Parametric gain

12. Thermal tuning of RoC CO2 laser heating Ring heater

13. Example of CO2 Heating Tuned Parametric Interaction Excitation of Test Mass Modes 80m sapphire test mass cavity at Gingin CO 2 Laser heating power (W)

14. 3MI acoustic modes observed at Gingin

15. Self Thermal Lensing with Different Cavity Power 80m Fused silica test mass cavity

16. Problem Solved?  We could use thermal tuning to change RoC to destroy the frequency matching condition  However……………

17. Modeling of Parametric Instability in Advance Detector High Power Cavities Number of unstable modes in a 4km cavity with ~1MW circulating power Radius of Curvature of the end mirrors of the cavity Mine field!

19. Proposed methods of PI control  Thermal tuning  Acoustic damper  Electrostatic damper  Active feedback  Modulation  Change mirror shape (cavity mode structure)

20. Acoustic Mode Dampers  Damper to absorb the energy of the “dangerous” test mass modes (broadband)  MIT investigation  tested PZT damper Q  S. Gras (UWA graduate) modelling  Effective damping of the Q of many modes (Not all)  But thermal noise exceed Advanced LIGO noise budget  Needs more careful investigation of damper attachment S. Gras, et al, LIGO document LIGO-G1001023-v1

21. Electrostatic damper  Advanced LIGO electrostatic actuator could be used to damp the Q of the acoustic modes  no issue of thermal noise degrading  Difficulties  For multiple mechanical modes excitation, each mode needs a control loop  Identify the mechanical modes J. Miller, et al, Phys. Lett. A, 375, 788-794 (2011)

22. Active feedback scheme ETM ITM BS Second arm High order mode sensing with multi- segment PD Laser 22 ETM “wasted” transmission to be re-injected into the cavity Deformable mirror generates suitable high order mode patterns AOM create right frequency shift Mode decomposition & identification All external operation but will be complicated if multiple modes are involved.

23. PI suppression due to modulation of R 23   change with RoC  Modulate RoC with time (using thermal)  PI gain modulated  If the modulation is faster enough before acoustic mode amplitude building up, then PI is suppressed.

24. Effect of modulating R 24 a –- modulation depth  /  1  1--linewidth of optical mode

25. Experimental observation at Gingin 80m 25 Equivalent R=1.45 0.15Hz modulation

26. Another phenomena….  Table top experiment with very small mass (don’t need high power to achieve parametric instability)  effective mass: 40 ng  P in threshold: 5.7  W  Resonant f : 400kHz ̴ few MHz  mechanical Q: 10 5 SiN x membrane 50nm thick 1x1 mm 2

27. Parametric instability occurs as expected, but

28. Implication for Advanced Detector As long as it did not destroy cavity locking at the first place

29. 3 mode interaction as a tool for monitoring the state of test mass

30. Example of R change with RoC

31. R change with RoC Example (zoom in) Suppressed below 1 ~ R change 1 order of magnitude in 20cm

32. Sensitivity to wavefront distortion d r = 5cm, RoC = 2km  d=3×10 -10  RoC 2r Assume effective radius of spot r Wavefront error = d

33. 3MI Monitoring  Can the extremely high sensitivity to local and global wavefront distortions observed in single cavities be useful in aLIGO?  Can the observations of the gains of hundreds of 3MI signals be inverted to create useful tools for monitoring or controlling the global state of aLIGO?  Can 3MI observations at low power be used to predict PI at high power?

34. Estimates from Modelling of PR IFO Sensitivity  RoC/RoC  RoC Wavefront error  % of ROC range covered by  R/R > 10% ~ 1ppm2mm 6×10 -7 ~15% ~5ppm10mm 3×10 -6 ~95% Assumed gain change for detection:  R/R >10% (resolution of mean thermal peak amplitude.) ROC Coverage with high sensitivity modes

35. How many modes could we monitor in aLIGO  Modes with |R| > 10 -3 : ~ 1800 per test mass (17%)  Modes with |R| > 10 -2 : ~ 700 per test mass (10 -3 at 20W input power)  Negative gain modes are equally useful for monitoring.  To learn how to use 4 x 700 = 2800 modes is a daunting task.  Physical insights can make it easier

36. What Can we Measure?  RoC variations  Varying Guoy phase shift for HOMs at the ITM depending on transverse mode resonance/anti-resonance conditions  Sensitivity to other parameters:  Spot and transverse mode positions (sensitivity to overlap, proportional to frequency  Mirror imperfections (eg hotspots)  Thermal diffusive changes in mirror shape – coping with thermal memory  Measure test mass mean temperatures  1/f (df/dT) ~ 1.5 x 10 -4 /K. Expect  f ~ mHz: ~1mK temperature resolution  Measure thermal diffusion effects due to thermal inhomogeneity (df/dT)  Observation of multiple mode frequencies could be used for crude thermal mapping (different modes have different  f).

37. Solving the inverse problem  Low order optical modes probe low order test mass deformations  Gain differences between symmetric orthogonal pairs (eg TEM 01 and TEM10) sensitive to low order test mass deformation.  High order optical + test mass modes more sensitive to transverse mode shape and mode position

38. Conclusion  Parametric instability observed in advanced detector  Effective methods needs to be developed fast for advanced detector reaching the designed power level on schedule  All the proposed methods need careful evaluation  Needs combined methods  Use 3-mode interaction for test mass thermal state monitoring