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Optimizing Suspension Systems for KAGRA's Future Plans

This presentation discusses KAGRA's current thermal noise issues and proposes future plans to enhance suspension systems and optics. Topics include sapphire mirror cooling, heat absorption in mirror, and recommendations for improving KAGRA's performance. The analysis covers the impact of thicker fibers, heat absorption considerations, and the need for innovative solutions to minimize thermal noise. The summary emphasizes the importance of suspension design in reducing noise interference. Findings suggest potential methods for addressing thick fiber challenges and optimizing mirror performance.

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Optimizing Suspension Systems for KAGRA's Future Plans

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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 themo-topic 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 going to write 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) Power at BS is about 2 times larger than that of bKAGRA (current design). High Frequency (HF) 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+ 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 (Current design). 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). We need thicker fibers (about 2mm in diameter). 9 9 9 9 9 9 9 9 9

  10. 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 We need thicker fibers (about 2mm in diameter). 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 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, suspension thermal noise does not matter although we do not assume any tricks. 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. 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. 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. 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 as 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+ We must introduce blade spring Into KAGRA current sapphire suspension compensate fiber length difference because fiber stretch with mirror weight load is only 20 mm. 18 18 18 18 18 18 18 18 18

  19. 2.KAGRA+ Solution for thick fiber issue (although not easy) (1)Low heat absorption in mirror (2)Higher thermal conductivity 19 19 19 19 19 19 19 19 19

  20. 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 fiber can not support mirror). Substrate : Small absorption (a few ppm/cm) in small sample was reported. So not impossible … Coating : It is exactly challenge … 20 20 20 20 20 20 20 20 20

  21. 2.KAGRA+ Thick fiber is an issue. (2) Higher thermal conductivity Size effect : Thermal conductivity is proportional to fiber diameter . Phonon mean free path is comparable with diameter. It sounds like upper limit of thermal conductivity. But, .. 21 21 21 21 21 21 21 21 21

  22. 2.KAGRA+ Thick fiber is an issue. (2) Higher thermal conductivity It is assumed that phonon is duffed on fiber surface as like molecules in vacuum duct. But phonon reflection is specular as like light, thermal conductivity could be larger. Thermal conductivity (limited by size effect) of silicon is larger when fiber surface is polished . Phys. Rev. 186, 801 (1969) 22 22 22 22 22 22 22 22 22

  23. 3.Thermo-optic noise Thermo optic noise Noise by coupling of (1) thermal expansion (a) (2) temperature coefficient of refractive index (b) of coating and temperature fluctuation. Limit of coating thermal noise 23 23 23 23 23 23 23 23 23

  24. 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 are different from those of bulk. 24 24 24 24 24 24 24 24 24

  25. 3.Thermo-optic noise We got excellent (extremely small) power spectrum densities from gravitational wave detector or thermal noise interferometer. They are 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. 25 25 25 25 25 25 25 25 25

  26. 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]. 26 26 26 26 26 26 26 26 26

  27. 3.Thermo-optic noise Constrain on a and b : Room temperature Average of thermal coefficient of two materials in coating. 27 27 27 27 27 27 27 27 27

  28. 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. 28 28 28 28 28 28 28 28 28

  29. 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. 29 29 29 29 29 29 29 29 29

  30. 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. 30 30 30 30 30 30 30 30 30

  31. 3.Thermo-optic noise Constrain on a and b : Room temperature If this loss is on the order of 10-5, we must face thermo-optic noise. 31 31 31 31 31 31 31 31 31

  32. 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). 32 32 32 32 32 32 32 32 32

  33. 3.Thermo-optic noise Constrain on a and b : Cryogenic temperature Constrain is much larger than typical value. It suggest thermo-optic noise does not matter at cryogenic temperature. 33 33 33 33 33 33 33 33 33

  34. 3.Thermo-optic noise Constrain on a and b : Cryogenic temperature Constrain is much larger than typical value. It suggest thermo-optic noise does not matter at cryogenic temperature. 34 34 34 34 34 34 34 34 34

  35. 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 (not at all). 35 35 35 35 35 35 35 35

  36. 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. 36 36 36 36 36 36 36 36 36

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