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Thermal Noise Design of KAGRA Sapphire Suspensions

This paper discusses the design and expected thermal noise of the KAGRA sapphire suspensions for gravitational wave detection. Topics include the main interferometer, vibration isolation, and cryogenics.

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Thermal Noise Design of KAGRA Sapphire Suspensions

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  1. Design and expected thermal noise of the KAGRA sapphire suspensions Kazuhiro Yamamoto Institute for Cosmic Ray Research, the University of Tokyo 23 May 2013 Gravitational Wave Advanced Detector Workshop @ Hotel Hermitage, La Biodola, Isola d’Elba, Italy 1 1

  2. 0. Abstract Although there are many topics, but here, I will explain (1)Main interferometer (2)Vibration isolation (3)Cryogenics for KAGRA.

  3. Contents • Introduction • Design • Expected thermal noise • Recent experiments • Summary

  4. Introduction Room temperature second generation interferometer Fused silica mirror suspended by fused silica fibers 4 4 4 4

  5. Introduction KAGRA (Cryogenic second generation) Sapphire mirror suspended by sapphire fibers Firstfeasibility study T. Uchiyama et al., Physics Letters A 242 (1998) 211. Sapphire fiber : High Q-values and large thermal conductivity 5 5 5 5 5

  6. 2. Design Strength Sapphire fibers should support the weight of sapphire mirror. Mirror : 23 kg Number of fibers : 4 Tensile strength : 400 MPa Safety margin : 7 Fiber diameter must be larger than 1.1 mm. 6 6 6 6 6

  7. 2. Design Thermal conductivity Fibers should transfer heat (about 1 W). Crystal (sapphire, silicon, diamond) and pure metal (Al, Cu, Ag) : Thermal conductivity is extremely high (> 1000 W/m/K). Q-values of pure metal is low. Crystals with high Q-values are candidates (sapphire, silicon). G. Ventura and L. Risegari, “The art of Cryogenics Low-Temperature Experimental Techniques”, Elsevier (2008) p76. 7 7 7 7 7

  8. 2. Design Thermal conductivity Sapphire : Thermal conductivity is maximum around 30 K. Temperature of KAGRA mirror will be around 20 K. Specification sapphire suspension Number of fibers : 4 Length of fibers : 0.3 m Heat generated in a mirror : 1 W Mirror temperature : 23 K Temperature at top end of fiber : 16 K Thermal conductivity : 5500 (T/20K)3 W/m/K Fiber diameter must be larger than 1.6 mm. This requirement is severer than that of strength. 8 8 8 8

  9. 3. Expected thermal noise Assumption and design Assumption : Upper ends of fibers are fixed rigidly. Resonant frequencies (except for violin modes) are different from the actual system. However, the thermal noise above the resonant frequency is the same. Design: Number of fiber : 4 Fiber length : 0.3 m Fiber diameter : 1.6 mm Q-values of sapphire fibers : 5*106 9 9 9 9

  10. 3. Expected thermal noise Degrees of freedom Horizontal motion along optical axis Pendulum and violin modes Vertical motion Gradient of interferometer baseline is 1/300. for discharge of water in the mine. Rotation (Pitch and Yaw) Distance between optical axis and center of gravity of mirror is 1 mm. 10 10 10 10

  11. 3. Expected thermal noise Degrees of freedom 11 11 11 11

  12. 3. Expected thermal noise Resonant frequencies and Q-values Resonant frequencies Q-values Pendulum 1 Hz? 1.5*106?? 1st violin 220 Hz 8 *106??? Vertical 109 Hz 5*106 Pitch 23.4 Hz 5*106 Yaw 1.4 Hz 2*107 In the cases of Pendulum (and violin) and Yaw, loss dilution factors by gravity were taken into account. 12 12 12 12

  13. 3. Expected thermal noise Horizontal and vertical motion 13 13 13 13

  14. 3. Expected thermal noise Horizontal and vertical motion Between 100 Hz and 200 Hz, there are 1st violin mode and vertical mode. Room temperature interferometer : 1st violin ~ 300 Hz vertical mode ~ 10 Hz Thick fiber to transfer heat ! Thicker fiber : Lager thermal noise (pendulum mode) Longer fiber : Lower violin mode, lower vertical mode -> Smaller heat transfer Shorter fiber : Higher violin mode, higher vertical mode -> Fiber should be longer than mirror radius. Note : These peaks make Signal to Noise Ratio of matched filter for neutrons star coalescence smaller (several per cent). 14 14 14 14

  15. 3. Expected thermal noise d Pitch and yaw rotation 15 15 15 15

  16. 3. Expected thermal noise Pitch and yaw rotation Yaw rotation does not matter. Around 20 Hz, there is pitch mode. Room temperature interferometer : pitch mode ~ 3 Hz Thick fiber to transfer heat ! Pitch mode frequency depends on distance between fibers (d). This distance must be as small as possible (10 mm~30 mm). Note : If this mode is lower than 30 Hz, the effect on Signal to Noise Ratio of matched filter for neutrons star coalescence is small. 16 16 16 16

  17. 4. Recent experiments Our old measurement : Q-values (0.25 mm in diameter) KAGRA fiber : 1.6 mm in diameter Q-values are 5*106. KAGRA requirement T. Uchiyama et al., Physics Letters A 273 (2000) 310. 17 17 17 17

  18. 4. Recent experiments Our old measurement : Thermal conductivity Size effect : Conductivity is proportional to fiber radius. Mean free path of phonon is limited by fiber radius. KAGRA fiber : 1.6 mm in diameter T. Tomaru et al., Physics Letters A 301 (2002) 215. 18 18 18 18

  19. 4. Recent experiments Sapphire fibers with nail heads are necessary to suspend mirrors. Test sample (T. Uchiyama) 19

  20. 4. Recent experiments T. Uchiyama asked MolTech GmbH (Germany). Sapphire fibers have already come ! Length = 350 mm diameter = 1.8 mm Almost as needed in bKAGRA. Need to check the quality and improvement . 20 20

  21. 4. Recent experiments Ettore Majorana asked IMPEX HighTech GmbH (German company). They made similar fibers (nail heads on the both ends).

  22. 4. Recent experiments Ettore Majorana asked IMPEX HighTech GmbH (German company). They made similar fibers (nail heads on the both ends).

  23. 4. Recent experiments Quality check Q-value Measurement in Glasgow and Jena Plan for measurement in Rome and Tokyo (Christian Schwarz and Gerd Hofmann’s visit from Jena to export measurement system) Christian will present poster on Friday morning. Thermal conductivity Measurement in Jena Plan for measurement in Rome and Tokyo Christian will present poster on Friday morning. Strength Discussion with Glasgow (Thanks for E. Hirose)

  24. 4. Recent experiments Apparatus to measure Q-values in cryostat of Jena G. Hofmann http://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/DocDB/ShowDocument?docid=1638

  25. 4. Recent experiments Apparatus to measure Q-values in cryostat of Tokyo (ICRR) G. Hofmann http://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/DocDB/ShowDocument?docid=1638

  26. 4. Recent experiments Q measurement in Jena Moltech G. Hofmann http://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/DocDB/ShowDocument?docid=1638 Preliminary result It is comparable with KAGRA requirement !

  27. 4. Recent experiments Q measurement in Jena IMPEX G. Hofmann http://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/DocDB/ShowDocument?docid=1638 Preliminary result It is slightly larger than KAGRA requirement !

  28. 4. Recent experiments Thermal conductivity measurement in Jena G. Hofmann http://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/DocDB/ShowDocument?docid=1638

  29. 4. Recent experiments Thermal conductivity measurement in Jena It is same as KAGRA requirement (size effect) C. Schwarz T. Tomaru et al., Phys. Lett. A 301 (2002) 215. Preliminary result Moltech

  30. 4. Recent experiments Thermal conductivity measurement in Jena Preliminary result C. Schwarz It is smaller than KAGRA requirement, but same order of magnitude. Moltech

  31. 4. Recent experiments Profile measurement in Glasgow As grown sample We have ground samples.

  32. 4. Recent experiments Strength test Discussion with Glasgow (4th of April) Stretch and bend test Some fibers were sent to Glasgow. Crystal structure X ray apparatus in Jena

  33. 4. Recent experiments Bonding between fibers and mirror Bonding should be investigated. Rebecca Douglas presents a poster in this session. Other type sapphire suspension Eric Hennes will report it on Friday morning.

  34. 5. Summary Construction of KAGRA interferometer is in progress. Total length of exavated tunnels is about 2 km. All vacuum tubes has already been manufactured. Cryostat cooling test was finished sucessfully. Test for vibration isolation system (Type-B) will start on this autumn at TAMA site.

  35. 5. Summary Young reserachers make their great efforts for KAGRA. Main Interferometer Cotrol with high power light (Yuta Michimura) Vibration Isolation Test for Pre-isolator (Takanori Sekiguchi) Cryogenics Initnial cooling time (Yusuke Sakakibara) Vibration of shield (Dan Chen) Sapphire fiber (Gerd Hofmann) Coating mechanical loss (Kieran Craig) TOBA for low frequency band (Ayaka Shoda)

  36. Acknowledgement ELiTES: ET-LCGT interferometric Telescope Exchange of Scientists Grant for collaboration aboutcryogenic between KAGRA and ET European 7th Framework Programme Marie Curie action (Mar. 2012 - Feb. 2016) European people can visit Japan for KAGRA.

  37. Vi ringrazio molto per la vostraattenzione ! Vielen Dankfuer Ihre Aufmerksamkeit ! Thank you for your attention !

  38. 4. Sapphire fibers Q measurement in Jena (cool) and Glasgow (300K) Moltech It is slightly smaller than KAGRA requirement ! Y. Sakakibara Preliminary result

  39. 4. Sapphire fibers Thermal conductivity measurement in Jena Thermal conductivity of IMPEX fibers will be measured soon.

  40. 7. For future Some items for future research (not perfect list) (a)Investigation material properties (Q, thermal conductivity, strength etc.) of coating, fiber and so on. (b)Sapphire bonding, Sapphire fiber clamp (c)Control and damping scheme Actuators and sensors at cryogenic temperature (d) Mechanical and thermal simulation for payload (e) Vertical spring in cryostat (f) Reduction of initial cooling time Thermal resistance of clamp .... (g) Baffles for scattered light in radiation shield (h) Assembly procedure 40

  41. 8. Summary Cryostat : Assembly is in progress. Cooling test is coming soon. Cryogenic duct : Optimum position of 5 buffles Future work : scattered light Cryocooler unit : Cooling test and vibration measurement : OK Cryogenic payload Preparation for 1/4 cryostat to check payload performance is in progress. Current main R&D topics Inital cooling time, Sapphire fiber with nail head, Coating mechanical loss, Vibration of shield

  42. 8. Summary ELiTES has already started and supports the development of KAGRA cryogenic system. If you want to join our mission, let us know.

  43. 2. Issues (1)How to assemble Details of construction, clean room …. (2)Strength Tensile strength, development of clamp, sapphire bonding … (3)Control and damping system to reduce fluctuation and instability Actuators (what and where), resonant mode (frequency and Q) and so on

  44. 2. Issues (4)Cooling Temperature of mirror (below 20 K), initial cooling time, heat resistance of clamp … (5)Noise Thermal noise, vibration via vibration isolation system and heat links …

  45. 4. Sapphire fibers After Yusuke left …. Clamp for IMPEX fibers in Jena

  46. 4. Challenges for cryogenic 1. Issues of cooling : Reduction of heat load (Absorption in mirror) In order to keep mirror temperature … Absorption in mirror : less than 1 W Coating : 0.4 W (1 ppm) Substrate : 0.6 W (50 ppm/cm) Our target of substrate : 20 ppm/cm 46 46 46 46

  47. Sensitivity of KAGRA Thermal noise Assumption (1) : Upper ends of fibers are fixed rigidly. Resonant frequencies (except for violin modes) are different from the actual system. However, the thermal noise above the resonant frequency is the same. Assumption (2): Number of fiber : 4 Fiber length : 0.3 m Fiber diameter : 0.16 mm Q-values of sapphire fibers : 5*106 Horizontal motion along optical axis Pendulum and violin modes Loss dilution by tension (gravity) must be taken into account. 47 47 47 47

  48. Sensitivity of KAGRA Thermal noise Vertical motion Gradient of interferometer baseline is 1/300. Q-values of stretch is assumed to be 5*106. Pitch motion Distance between the optical axis and center of gravity of mirror is 1 mm. Q-values of stretch is assumed to be 5*106. Yaw motion Distance between the optical axis and center of gravity of mirror is 1 mm. Q-values of shear is assumed to be 5*106. Loss dilution by tension (gravity) must be taken into account. 48 48 48 48

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