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Thermal noise calculations for cryogenic optics

Thermal noise calculations for cryogenic optics. R. Nawrodt, I. Martin, A. Cumming, W. Cunningham, S. Rowan, J. Hough ET-WP2 Workshop, La Sapienza - University of Rome 26th/27th February 2009. Overview. sources of thermal noise bulk material + coatings up scaling to necessary size

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Thermal noise calculations for cryogenic optics

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  1. Thermal noise calculations for cryogenic optics R. Nawrodt, I. Martin, A. Cumming, W. Cunningham, S. Rowan, J. Hough ET-WP2 Workshop, La Sapienza - University of Rome 26th/27th February 2009

  2. Overview • sources of thermal noise • bulk material + coatings • up scaling to necessary size • suspensions • problems, open questions

  3. Motivation [Punturo, ET talk at the LSC meeting, Amsterdam 2008] thermal noise limited

  4. Thermal Noise • Brownian Noise • Bulk • Coating • Suspension • Thermoelastic Noise • Bulk • Coating • Suspension • Photothermal Noise • Coating  Bulk

  5. Modelling Thermal Noise • Reference geometry = advanced detector optics • aim: cross check with existing calculations w0 = 60 mm D = 340 mm L = 200 mm D/2w0 = 2.8

  6. Bulk Material (1) • demands: • low thermal noise • suited for coatings (surface treatment, polish...) • big sizes available (materials: Fused Silica, CaF2, Si, Sapphire) • thermal noise contribution: • Brownian thermal noise • thermoelastic noise

  7. Bulk Material (2) • Brownian Thermal Noise • reminder: • origin - thermal energy • fluctuation-dissipation-theorem gives spectral distribution • idea: low loss material will concentrate Brownian noise around the internal resonances (which are above the detection band)

  8. Bulk Material (3) • Brownian Thermal Noise • infinite half space • finite mirror material (analytical calculation) [Liu, Thorne 2000]  … Poisson ratio, Y … Young’s modulus, T … temperature, f … frequency, substrate ... mechanical loss of the substrate, w … beam radius (1/e2 definition) [Liu, Thorne 2000, Bondu, Hello, Vinet 1998] correction term nearly temperature independent and < 1 Thus, the infinite half space always gives an upper limit.

  9. Bulk Material (4) • Brownian Thermal Noise (cont’ finite mirror) [Liu, Thorne 2000] J0 … Bessel function of order zero m … m‘th zero of the zero order Bessel function J1(m)

  10. Bulk Material (5) • Brownian Thermal Noise • finite mirror material (FEA, ANSYS) direct use of Levin‘s approach [Levin 1998] ANSYS

  11. Bulk Material (6a) • Brownian Thermal Noise • Young’s modulus

  12. [McGuigan 1978] Bulk Material (6b) • Brownian Thermal Noise • Mechanical loss impurity effects (e.g. doping, oxygen) Material properties collected and summarized for ET homepage.

  13. Bulk Material (7) • Thermoelastic Noise • reminder: • origin – entropy production during heat flux between compressed and expanded regions causes thermoelastic loss • a given temperature fluctuation T is converted into a displacement fluctuation x by means of the thermal expansion coefficient  • dependent on material thermal properties

  14. Bulk Material (8) • Thermoelastic Noise (Material properties) [Hull 1999] Collection of extracted data as txt-files and Origin-files for ET homepage.

  15. Bulk Material (9) • Thermoelastic Noise • finite/infinite test mass • problem: Most of the calculations use the adiabatic assumption. [Liu, Thorne 2000]

  16. Bulk Material (10) • Thermoelastic Noise adiabatic limit: a temperature fluctuation stays in time 1/f within the beam diameter 2w valid if: 2w laser w = Ö2 r0 substrate (adiabatic limit)

  17. Bulk Material (11) • Adiabatic limit T<80 K: crystalline materials violate adiabatic assumption amorphous materials still fulfil assumption

  18. Bulk Material (12) • Thermoelastic Noise • beyond the adiabatic limit [Rowan et al. 2000, Aspen Meeting] [Cerdonio et al. 2001]

  19. Bulk Material (13) • Bulk Material Comparison (300 K) fSiO2 = 4×10-10 fSi = 3×10-9 fSapphire = 3×10-9 TE Brownian

  20. Bulk Material (14) • Bulk Material Si(111) (20 K) fSi = 5×10-10 TE Brownian

  21. Bulk Material (15) • Bulk Material Comparison (20 K) fSiO2 = 1×10-3 fSi = 5×10-10 fSapphire = 3×10-9

  22. Bulk Material (16) • Bulk Material - e.g. Si(111), f=100 Hz, real measured values properties extracted from: McGuigan 1978 Touloukian 1972 Hull 1999

  23. Coating Material (1) • Demands: • low thermal noise • low optical absorption (thermal load) • conventional stack – high difference in refraction index • large coatings needed with properties at the limit what is currently available

  24. Coating Material (2) • Brownian Thermal Noise • infinite/finite • important parameters mostly unknown for coating materials (Y, , …) • Thermoelastic Noise • infinite/finite • important thermal parameters unknown • Photothermal Noise • absorption measurement needed for all new coatings

  25. Coating Material (3) • Brownian Thermal Noise (infinite) [Harry et al. 2002] If two different mechanical loss values exist then the Brownian thermal noise of a coating is dependent on the ratio of Young’s moduli at the interface. Lowest loss occurs if Y=Y’.

  26. Coating Material (4) • Brownian Thermal Noise (finite) ANSYS as an alternative multilayer stack is treated as a two-layer-system analytical approaches [Cunningham, Torrie] [Somiya, Yamamoto, LIGO-P080121-00-Z]

  27. Coating Material (5) • Brownian Thermal Noise unknown parameters: Y’,  and || often: approximations  = || measurements: see next two talks

  28. Coating Material (6) • Thermoelastic Noise (multilayer stack) [Braginsky, Fejer et al. 2004] The adiabatic limit for amorphous materials (silica, tantala) is low even at cryogenic temperatures  no limit/correction.

  29. Coating Material (7) • Thermoelastic Noise (material properties) • most parameters unknown for coatings • some measurements available (e.g. densitiy, absorption) [Morgado, 1st ET Meeting, Cascina 2008] • coatings often approximated by bulk material values Measurements of thermal and mechanical properties needed.

  30. Coating Material (8) • Photothermal Noise [Cerdonio et al. 2001] • absorption of coatings governs photothermal noise Ta2O5:TiO2 absorption, ~ 1 ppm [Harry 2007]

  31. Coating Material (9) • example (15 double layers Ta2O5:TiO2 / SiO2) advanced geometry 20 K sample temperature l = 1064 nm fTa2O5 = 9×10-4 fSiO2 = 6×10-4 fSi = 5×10-10 Si(111) 15 double layers

  32. Coating Material (10) coating dominates

  33. Comparison to Goal 4 mirrors contributing, L = 10 km

  34. How to achieve the ET sensitivity? • increasing beam size: assuming advDet. aspect ratio m ~ w3 ROC

  35. How to achieve the ET sensitivity? • increasing beam size: • smaller influence of the coatings (e.g. waveguide mirrors, beam-profile) 60 mm beam radius would be sufficient

  36. How to achieve the ET sensitivity? • increasing beam size: • results agrees with estimates by S. Hild for upscaling existing techniques in GWINC [Hild et al. arXiv: 0810.0604v2] • big substrate, coating with dia. 800 mm needed • big mass will cause problems in the suspension

  37. Suspension Material (1) • Demands: • low thermal noise • high thermal conductivity (extraction of thermal load of residual absorption, ~ 1 ppm, ~ 1 W) • high breaking strength • available ?

  38. Suspension Material (2) • Brownian Thermal Noise • Thermoelastic Noise • fibres, ribbons • Thermal Aspects • Connecting Bulk and Suspension?

  39. Suspension Material (3) breaking strength of Si is dependent on treatment (200 MPa – 6 GPa) 1 circular fibre diameter: 25 mm2 … 1 mm2 30% of maximum value: ~ 2.5 mm2 4 fibres: ~ 0.7 mm2 per fibre ~ 1 mm diameter 500 kg

  40. dia. Suspension Material (4) • Thermoelastic Noise [Cagnoli, Willems 2002]  for Si unsuited for compensation

  41. AdvLIGO fibre thermal noise reduction • techniques developed for advDet. -> ET suspension • FE assisted analysis of refined fibre models, fibre shapes, fibre neck shapes, tapered fibres • additional aspects of heat extraction needs to be taken into account [Cumming 2008]

  42. Challenges • high coating thermal noise • compensation: large beam diameter, large substrate • large substrate mass causes problems in the suspension • possible reduction: finite size correction, reconsidering aspect ratio of substrat, better/no dielectric coatings, lower temperatures • unknown parameters of coatings (thermal, mechanical) cause uncertainties which might change the result significantly

  43. Suggestions • database for material properties (paper + data files) • common reference curve for thermal properties  comparison between different calculations • implementation of temperature dependent material properties in a GWINC code (cryoGWINC?)

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