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Kazuhiro Yamamoto Faculty of Science, University of Toyama

KAGRA and future plans for suspensions and optics in KAGRA. Kazuhiro Yamamoto Faculty of Science, University of Toyama. 21 th May 2019 Gravitational Wave Advanced Detector Workshop @ Hotel Hermitage, La Biodola, Isola d’Elba, Italy. 1. 1. 1. 1. Abstract.

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Kazuhiro Yamamoto Faculty of Science, University of Toyama

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  1. KAGRA and future plans for suspensions and optics in KAGRA Kazuhiro Yamamoto Faculty of Science, University of Toyama 21th May 2019 Gravitational Wave Advanced Detector Workshop @ Hotel Hermitage, La Biodola, Isola d’Elba, Italy 1 1 1 1

  2. Abstract • Introduction thermal noise of KAGRA+ on future plan white paper. • Kazuhiro’s personal (too ambitious) comments for KAGRA+ thermal noise. • How to estimate parameter to calculate thermo-optic noise 2 2 2 2 2 2 2 2

  3. Contents • Introduction • KAGRA + • Thermo-optic noise • Summary 3 3 3 3 3 3 3 3

  4. 1.Introduction KAGRA : Sapphire mirrors suspended by sapphire fibers. Sapphire mirrors are cooled down (around 20K). Only sapphire fibers can transfer heat generated in mirror (heat absorption). This is an important point in design. 4 4 4 4 4 4 4 4 4

  5. 1.Introduction KAGRA : Sapphire mirrors suspended by sapphire fibers. Sapphire mirrors are cooled down (around 20K). Only sapphire fibers can transfer heat generated in mirror (heat absorption). This is an important point in design. Takafumi’s talk 5 5 5 5 5 5 5 5 5

  6. 2.KAGRA+ • KAGRA + • Future Planning Committee is writing white paper (Matteo’s talk on Monday afternoon). • Recommendation • Near term (5 years) : High Frequency (HF) or Frequency Depend SQueeZing (FDSQZ) • Middle term (10 years) : Heavier mirror (40 kg) • Here we discuss these plans. 6 6 6 6 6 6 6 6 6

  7. 2.KAGRA+ Heat absorption in recommended plans Frequency Depend SQueeZing (FDSQZ) or Heavier mirror (40 kg) Input power at BS is about 2times larger than that of bKAGRA (current design). High Frequency (HF) Input power at BS is about 5 times larger. 7 7 7 7 7 7 7 7 7

  8. 2.KAGRA+ Heat absorption in recommended plans Frequency Depend SQueeZing (FDSQZ) or Heavier mirror (40 kg) Power at BS is about 2 times larger than that of bKAGRA. High Frequency (HF) Power at BS is about 5 times larger. We assume that absorption of substrate per cm and coating is same as bKAGRA (current design). https://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/DocDB/ShowDocument?docid=9537 8 8 8 8 8 8 8 8 8

  9. 2.KAGRA+ We assume that absorption of substrate per cm and coating is same as bKAGRA (current design). We need thicker fibers (about 2mm in diameter). Note : 1.6 mm in diameter of bKAGRA 9 9 9 9 9 9 9 9 9

  10. 2.KAGRA+ We assume that absorption of substrate per cm and coating is same as bKAGRA (current design). We need thicker fibers (about 2mm in diameter). Note : 1.6 mm in diameter of bKAGRA https://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/DocDB/ShowDocument?docid=9537 10 10 10 10 10 10 10 10 10

  11. 2.KAGRA+ • Thicker fiber issues • Large contribution of pendulum mode • Lower violin modes • We must check these points. 11 11 11 11 11 11 11 11 11

  12. 2.KAGRA+ Except for fibers, we do NOT assume any improvement, tricks, and magical items. Almost all parameters (Q-values, heat absorption, …) are same as those of bKAGRA, current design. Mirror temperature is about 20K. Mirror thermal noise is comparable with that of bKAGRA. So, we consider suspension thermal noise. 12 12 12 12 12 12 12 12 12

  13. 2.KAGRA+ Summary of future plan committee Fortunately, thermal noise does not matter although we do not assume any tricks. Thanks for cryogenic technique, even current mirror thermal noise is enough small for KAGRA+. 13 13 13 13 13 13 13 13 13

  14. 2.KAGRA+ Summary of future plan committee Fortunately, suspension thermal noise does not matter although we do not assume any tricks. Cryogenic technique is useful to reduce mirror thermal noise. 14 14 14 14 14 14 14 14 14

  15. 2.KAGRA+ Summary of future plan committee Fortunately, suspension thermal noise does not matter although we do not assume any tricks. Cryogenic technique is useful to reduce mirror thermal noise. 15 15 15 15 15 15 15 15 15

  16. 2.KAGRA+ Summary of future plan committee Fortunately, suspension thermal noise does not matter although we do not assume any tricks. Cryogenic technique is useful to reduce mirror thermal noise. 16 16 16 16 16 16 16 16 16

  17. 2.KAGRA+ From here, I mention my personal (too ambitious) comments for middle term (10 years). Thick fiber is an issue. Even if thermal noise is not so large, suspension assembly is difficult. For example, … 17 17 17 17 17 17 17 17 17

  18. 2.KAGRA+ From here, I mention my personal (too ambitious) comments for middle term (10 years). Thick fiber is an issue. Even if thermal noise is not so large, suspension assembly is difficult. For example, … Matteo’s talk (Monday afternoon) 18 18 18 18 18 18 18 18 18

  19. 2.KAGRA+ From here, I mention my personal (too ambitious) comments for middle term (10 years). Thick fiber is an issue. Even if thermal noise is not so large, suspension assembly is difficult. For example, … 19 19 19 19 19 19 19 19 19

  20. 2.KAGRA+ We must introduce sapphire blade spring into KAGRA current sapphire suspension to compensate fiber length difference because fiber stretch with mirror weight load is only 20 mm. 20 20 20 20 20 20 20 20 20

  21. 2.KAGRA+ Solution for thick fiber issue (although not easy) (1)Low heat absorption in mirror (2)Higher thermal conductivity of sapphire fiber 21 21 21 21 21 21 21 21 21

  22. 2.KAGRA+ (1) Low heat absorption in mirror If heat absorption in mirror (not only substrate but also coating) is 10 - 30 times smaller, the fiber can be as thin as possible (More thinner fibers can not support mirror). 22 22 22 22 22 22 22 22 22

  23. 2.KAGRA+ • Low heat absorption in mirror • If heat absorption in mirror is 10 - 30 times smaller,… • Substrate : ~ 1ppm/cm • Coating : < 0.1 ppm • Substrate : Small absorption (a few ppm/cm) in small sample was reported. So not impossible … • Coating : It is exactly challenge … 23 23 23 23 23 23 23 23 23

  24. 2.KAGRA+ Thick fiber is an issue. (2) Higher thermal conductivity of sapphire fiber Size effect : Thermal conductivity is proportional to fiber diameter . Thermal conductivity is proportional to phonon mean free path which is limited by fiber diameter. It sounds like upper limit of thermal conductivity. But, .. 24 24 24 24 24 24 24 24 24

  25. 2.KAGRA+ Thick fiber is an issue. (2) Higher thermal conductivity Phonon is diffused on fiber surface as like molecules in vacuum duct. But when phonon reflection is specular as like light, thermal conductivity could be larger. Thermal conductivity (limited by size effect) of silicon is (a few times) larger when fiber surface is polished . Phys. Rev. 186, 801 (1969) 25 25 25 25 25 25 25 25 25

  26. 3.Thermo-optic noise Thermo optic noise Noise by coupling of temperature fluctuation and (1) thermal expansion (a) (2) temperature coefficient of refractive index (b) of coating. Limit of coating thermal noise 26 26 26 26 26 26 26 26 26

  27. 3. Thermo-optic noise Issue of evaluation of thermo-optic noise We do not know well a and bof coating (especially, cryogenic temperature) ! Measurement is not so easy … Coating (thin layer) material properties could be different from those of bulk. 27 27 27 27 27 27 27 27 27

  28. 3.Thermo-optic noise We got excellent (extremely small) power spectrum densities from gravitational wave detector or thermal noise interferometer. These power spectrum gives upper limit of thermo-optic noise. So, we can derive constrain on a and b. It would be great if thermal noise interferometer gives small upper limit. 28 28 28 28 28 28 28 28 28

  29. 3.Thermo-optic noise Constrain on a and b : Room temperature Thermal noise interferometer Fused silica mirror : U - Tokyo [K. Numata et al., Phys. Re. Lett. 91 (2003) 260602]. Sapphire mirror : Caltech [E.D. Black et al., Phys. Re. Lett. 93 (2004) 241101]. 29 29 29 29 29 29 29 29 29

  30. 3.Thermo-optic noise Constrain on a and b : Room temperature Average of thermal coefficient of two materials in coating. 30 30 30 30 30 30 30 30 30

  31. 3.Thermo-optic noise Constrain on a and b : Room temperature Thermo optic noise depends on elastic properties of substrate. So, slope in graph depends on substrate. 31 31 31 31 31 31 31 31 31

  32. 3.Thermo-optic noise Constrain on a and b : Room temperature When we measure at least two kinds of substrate mirror, allowable area is finite. 32 32 32 32 32 32 32 32 32

  33. 3.Thermo-optic noise Constrain on a and b : Room temperature Constrain is larger than typical a and b. But they are NOT AMAZINGLY large. 33 33 33 33 33 33 33 33 33

  34. 3.Thermo-optic noise Constrain on a and b : Room temperature If coating loss angle (coating Brownian noise) is on the order of 10-5, we could ace thermo-optic noise. 34 34 34 34 34 34 34 34 34

  35. 3.Thermo-optic noise Constrain on a and b : Cryogenic temperature Calculation (Not experiment) Kazuhiro assumes thermal noise interferometer whose power spectrum density is dominated by coating Brownian noise (coating loss angle is 4*10-4). 35 35 35 35 35 35 35 35 35

  36. 3.Thermo-optic noise Constrain on a and b : Cryogenic temperature Constrain is much larger than typical value. It suggests thermo-optic noise does not matter at cryogenic temperature. 36 36 36 36 36 36 36 36 36

  37. 4.Summary • KAGRA+ thermal noise • Thermal noise itself in white paper does not • matter. • Kazuhiro’s comment : Smaller absorption mirror • or higher thermal conductivity sapphire fibers • are necessary to simplify assembly. • 2. Thermo-optic noise • Thermal noise interferometers can give • constrain on a and b of coating, which are • important parameters to evaluate thermo-optic • noise. • At room (cryogenic) temperature, thermo-optic • noise could be an issue in near future (is not • problem at all). 37 37 37 37 37 37 37 37

  38. Thank you for your attention ! 38 38 38 38 38 38 38 38

  39. 1.Introduction ( Surface polish could enhance. Phys. Rev. 186, 801 (1969) Takayuki’s paper refer H.M. Rosenberg, Low Temperature Solid State Physics: SomeSelected Topics, Clarendon, Oxford, 1963;Also, J. Hough, Pointed out the Size Limitation of the ThermalConductivity in thin Sapphire Fiber, private communication at2000 Aspen Winter Conference of GW Detection. 39 39 39 39 39 39 39 39 39

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