1. CITF A. Allocca, M. Mantovani

2. Outline CITF schematic Resonance conditions Effect of the misalignment on the error signals Comparison with Virgo+ Effect of a change in the PRM RoC 2

3. Outline CITF schematic Resonance conditions Effect of the misalignment on the error signals Comparison with Virgo+ Effect of a change in the PRM RoC 3

4. CITF schematic 4

5. Compensation plates Pick-off Plate Real mirror thicknesses, as from https://workarea.ego- gw.it/ego2/virgo/advanced- virgo/osd/pages/list-of-installed-optics Distances as from Virgo note: VIR-0267B-15. (Referring to the Center of Mass position) CITF schematic 5

6. Lengths to control to keep the CITF at its working point CITF DoF 6 From M. Prijatelj and B. Swinkels, VIR-0274A-15 Driving matrix

7. Outline CITF schematic Resonance conditions Effect of the misalignment on the error signals Comparison with Virgo+ Effect of a change in the PRM RoC 7

8. Sideband power detected by the B4 photodiode (intra-cavity power) Upper and lower sidebands resonate at slightly different positions: it may give error signals asymmetric with respect to zero. 8 “Real” CITF ~ 1,6 nm ~ 3 nm ~0,15 nm l PRC = 11,9525 m Schnupp = 0,23096 m Is it correct? Is it a lot? Is it negligible? 1,8 kHz for the 6 MHz 15 kHz for the 56 MHz 35 kHz for the 131 MHz

9. Outline CITF schematic Resonance conditions Effect of the misalignment on the error signals Comparison with Virgo+ Effect of a change in the PRM RoC 9

10. Error signal shapes in presence of misalignments Only PRM misaligned from 0 to 3 µrad  Not exhaustive, but gives an idea about the level of criticality The change of many parameters as a function of the misalignment is checked: Working point Demodulation phase Quality parameter to get an information about the “controllability” 10

11. E rror signals vs misalignment Phase optimized for PRCL for misalignment = 0 11 B2 photodiode 6 MHz

12. E rror signals vs misalignment Phase optimized for PRCL for misalignment = 0 12 B2 photodiode 56 MHz

13. E rror signals vs misalignment Phase optimized for PRCL for misalignment = 0 13 B2 photodiode 131 MHz

14. E rror signals vs misalignment Phase optimized for MICH for misalignment = 0 14 B2 photodiode 6 MHz

15. E rror signals vs misalignment Phase optimized for MICH for misalignment = 0 15 B2 photodiode 56 MHz

16. E rror signals vs misalignment Phase optimized for MICH for misalignment = 0 16 B2 photodiode 131 MHz

17. Demodulation phase vs misalignment 17 B2 photodiode Optimized for PRCLOptimized for MICH

18. Working point vs misalignment – optimized for PRCL 18 B2 photodiode Optimized for PRCLOptimized for MICH

19. Optical Gain vs misalignment – optimized for PRCL 19 B2 photodiode

20. Optical Gain vs misalignment – optimized for PRCL 20 B2 photodiode …… … 6 MHz

21. Optical Gain vs misalignment – optimized for PRCL 21 B2 photodiode 56 MHz …

22. Optical Gain vs misalignment – optimized for PRCL 22 B2 photodiode 131 MHz

23. Optical Gain vs misalignment – optimized for MICH 23 B2 photodiode

24. 24 Optical Gain vs misalignment B2 photodiode Optimized for PRCLOptimized for MICH

25. The “quality parameter” 25 Mathematical details in: M. Mantovani et al, “Evaluating mirror alignment systems using the optical sensing matrix”, 2008 J. Phys.: Conf. Ser. 122 012026 2 Degrees of Freedom  need 2 signals to control them

26. 26 6 MHzPRCL opt PRCLPRCL opt MICH 6 MHzMICH opt PRCLMICH opt MICH Optimize the signal (for each modulation frequency) for each DoF and compute the Optical Gain (low frequency limit of the transfer function DoF  Signal) Then we build as many 2x2 Optical Matrices as many combinations we have For ex.: optimize the demodulation phase of the 6MHz signal for PRCL For that demodulation phase I have:. The Optical Gain of PRCL optimized for PRCL. The Optical Gain of MICH optimized for PRCL (which hopefully is very low) 6 MHzPRCL opt PRCLPRCL opt MICH 56 MHzMICH opt PRCLMICH opt MICH 6 MHzPRCL opt PRCLPRCL opt MICH 131 MHzMICH opt PRCLMICH opt MICH 56 MHzPRCL opt PRCLPRCL opt MICH 6 MHzMICH opt PRCLMICH opt MICH 56 MHzPRCL opt PRCLPRCL opt MICH 56 MHzMICH opt PRCLMICH opt MICH 56 MHzPRCL opt PRCLPRCL opt MICH 131 MHzMICH opt PRCLMICH opt MICH 131 MHzPRCL opt PRCLPRCL opt MICH 6 MHzMICH opt PRCLMICH opt MICH 131 MHzPRCL opt PRCLPRCL opt MICH 56 MHzMICH opt PRCLMICH opt MICH 131 MHzPRCL opt PRCLPRCL opt MICH 131 MHzMICH opt PRCLMICH opt MICH

27. 27 Optimized for MICH Optimized for PRCL 6 MHz56 MHz131 MHz 6 MHzααα 56 MHzααα 131 MHzααα

28. 28 B2 photodiode Optical parameter vs misalignment The Optical parameter is dominated by MICH OG

29. Outline CITF schematic Resonance conditions Effect of the misalignment on the error signals Comparison with Virgo+ Effect of a change in the PRM RoC 29

30. Optical Gain for PRCL in V+ 30 6 MHz The OG was reduced by ~80% at 1,5 mrad for V+ It is reduced by 80% at 0,15 mrad for AdV V+ CITF

31. Outline CITF schematic Resonance conditions Effect of the misalignment on the error signals Comparison with Virgo+ Effect of a change in the PRM RoC 31

32. AdV PRC stability 32 Cold PRM RoC Nominal PRM RoC Virgo+ PRC Gouy phase

33. 33 V+ - like configuration Gouy phase = 0,009 rad  PR RoC = 1425 m Gets worse???

34. V+ - like configuration 34 Gouy phase = 0,009 rad  PR RoC = 1425 m Mismatch modes! 6 MHz 56 MHz

35. Conclusions The 131 MHz is crucial for the lock acquisition More investigations are needed to understand how the change of the PR RoC can influence the error signal shape 35