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##### LIGO-G030036-00-R

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**Thermal Noise in Advanced LIGO Core Optics**Gregory Harry and COC Working Group Massachusetts Institute of Technology - Technical Plenary Session - March 17-20, 2003 LSC Meeting - Livingston, LA LIGO-G030036-00-R 1**Outline**• Sensitivity impact • Coating thermal noise • Relevance for material downselect • Silica annealing • Sapphire status • Modeling (analytical and FEA) • Direct thermal noise measurements LIGO-G030036-00-R LIGO-G030036-00-R 2**Significance for sensitivity**BNS Range 120 Mpc BNS Range 200 Mpc 3 LIGO-G030036-00-R**Coating thermal noise**Status • Tantala/silica coating studied on silica - fcoat = 2.8 +/- 0.7 10-4(in modal Q measurements) - tantala dominates loss • Various other materials tried -niobia/silica, tantala/alumina, alumina/silica - none have consistently improved loss • Some work on sapphire substrates • Figure of merit developed • d fcoat ( Ypar/Ysub + Ysub/Yperp) LIGO-G030036-00-R 4**Coating thermal noise**Recent results • Special coating developed at SMA/Virgo - tantala doped to reduce stress in coating - fcoat = 2.8 10-4 undoped tantala/silica - fcoat = 1.8 +/- 0.1 10-4 MIT - fcoat = 1.5 +/- 0.7 10-4 Glasgow - Young's modulus and optical absorption unchanged • Annealed alumina/silica sample measured - 2.1 +/- 0.6 10-4 Glasgow - results pending at Syracuse • Coated sapphire next (Glasgow) LIGO-G030036-00-R 5**Coating thermal noise**Future plans • New material being developed at SMA/Virgo - index similar to tantala - Young's modulus similar to silica - working to get optical absorption down • Further work with doped tantala/silica • Correlate loss with coating stress • Explore effects of annealing • Measure coating thermal noise directly LIGO-G030036-00-R 6**Material downselect**Substrate loss BNS Range vs Q for Ycoat = 100 GPa and fcoat = 1X10-5 7 LIGO-G030036-00-R**Material downselect**Coating loss BNS Range Ycoat = 70 GPa BNS Range Ycoat = 200 GPa Coating f Coating f 8 LIGO-G030036-00-R**Material downselect**Coating Young's modulus BNS Range with fcoat = 5 X 10-5 BNS Range with fcoat = 1 X 10-5 Coating Young's modulus Coating Young's modulus 9 LIGO-G030036-00-R**Substrate thermal noise**Silica status • Empirical understanding of • silica loss is developing • Lossy surface layer limits Q • Annealing can dramatically • increase Q • High Q in polished sample • - 54 106 • High Q in flame drawn sample • - 200 106 • See silica discussion Thursday • afternoon 10 LIGO-G030036-00-R**Substrate thermal noise**Sapphire status • Thermal noise dominated by thermoelastic damping • Modal Q's typically about 200 106 (S. Rowan, V. • Mitrofanov, et al) • Q's span 65 to 400 106(K. Numata, P. Willems, et al) • Low frequency dependence to loss unknown • Anisotropy of loss not well understood • See talk by G. Billingsley 11 LIGO-G030036-00-R**Substrate thermal noise**Recent Q results on sapphire Two 40 kg samples measured for Q at Caltech by Phil Willems, 6 modes each - white (“good”) sapphire two degenerate modes show high Q Q1 = 200 106 Q2 = 180 106 - pink (“not”) sapphire shows high Q of 260 106 }Sets limit on anisotropy of loss • 1/Q vs mode for both samples • Results fit two parameter model for single bulk f and surface (barrel) f very well LIGO-G030036-00-R 12**Other loss sources**Bonding and charging • Silicate bonding to silica suspension • Bonded silica samples measured for Q at Glasgow and • Syracuse using different geometries • Loss very high in bond region (f ~ 100 - 10-2) • Calculations indicate will not effect thermal noise in advanced LIGO (Syracuse sample bonded in Glasgow) • Charging of optics • Modeling and Q measurements suggest will not limit thermal noise • Could be a source of other noise sources • May need more study 13 LIGO-G030036-00-R**Thermal noise modeling**Analytical models we have • Non-modal, direct thermal noise calculation(Yu. Levin) Better Paradigm than modal Q for thermal noise • Finite sized, uncoatedmirrors(Liu and Thorne, Bondu et al) • Infinite sized, coatedmirrors(Nakagawa / Gretarsson et al) • Anisotropic coatings (assuming isotropic layers) fcoat+ = Ycoat / d (d1f1 / Y1 + d2f2 / Y2 ) • Thermoelastic damping in coatings(M. Fejer, S. Rowan) • - sets limit on how low coating loss can be - creates preferential matching of coatings and substrates - see talk by Sheila Rowan later on Thursday 14 LIGO-G030036-00-R**Thermal noise modeling**Models we need • Finite sized, coatedmirrors N. Nakagawa is thinking about this problem FEA models indicate thermal noise goes down • Multiple coatings on substrate • have secondary coating below first coating • mechanical impedance matching • one coating with low absorption, one with low loss no one is thinking about this problem • Anisotropic substrate used for sapphire, may not be necessary • Inhomogeneous loss distribution probably better done by finite element analysis (FEA) • (Coating thermal noise with Mexican hat beam) • not strictly necessary 15 LIGO-G030036-00-R**Thermal noise modeling**Finite element analysis Code we have OCEAN - coating, bonding, and surface loss Q (D. Crooks, et al) invaluable for coating and bonding loss efforts I-DEAS – inhomogeneous, anisotropic modal Q, and thermal noise(D. Coyne) good agreement with Nakagawa theory, being used for initial LIGO TAMA - inhomogeneous thermal noise (K. Numata, K. Yamamoto, et al) shows thermal noise lower than Nakagawa theory for finite mirrors What we need A sharable version of TAMA code Further development of most codes 16 LIGO-G030036-00-R**Direct measurement of thermal noise**Thermal Noise Interferometer (Caltech) • Designed to measure thermal noise in silica and sapphire • Silica mirrors in place • Sapphire mirrors on hand • Measured noise close to tantala/silica coating thermal noise • Development ongoing • See TNI Technical Advisory • Committee session from • Tuesday Coating thermal noise 17 LIGO-G030036-00-R**Direct measurement of thermal noise**University of Tokyo experiments • K. Numata thesis experiment • Measure Brownian and thermoelastic • BK7 glass for Brownian, f independent • CaF2 for thermoelastic, good • agreement with theory • Trying to measure coating noise • K. Yamamoto thesis experiment • Examined nonhomogeneous • loss • Good agreement with Levin LIGO-G030036-00-R**Thermal noise prospectus**What we need to do from here • Reduce coating thermal noise to acceptable level • Determine if high Q can be obtained in large, polished • silica optics • Continue to study sapphire • Further development of theories to turn Q’s into thermal • noise predictions • Confirm thermal noise predictions with direct • measurements 19**Conclusions**• Thermal noise is a crucial problem in advanced LIGO • Coating thermal noise reduction is proceeding • Material downselect depends on many factors • Silica and sapphire both are possible choices • Work remains on thermal noise modeling • Direct thermal noise measurements are beginning to • provide input 20 LIGO-G030036-00-R