1. LIGO-G020062-00-Z Thermal noise in sapphire - summary and plans Work carried out at: Stanford University University of Glasgow Caltech MIT

2. LIGO-G020062-00-Z Timescales Core optics –Design Requirements Review June 2002 –Sapphire silica downselect/Preliminary Design ReviewNovember 2002 R & D areas –Sapphire absorption ( thermal compensation ) –Coating absorption –Fabrication issues ( size/quality ) –Polishing etc –Thermal noise performance

3. LIGO-G020062-00-Z Thermal noise performance –“Intrinsic” thermal noise Intrinsic dissipation Attachments Coatings Polishing Electrostatic drive Others??? –Thermo-elastic thermal noise How accurate is our knowledge of relevant material properties? –(J. Camp et al - Caltech) –(R. Lawrence et al - MIT) Scaling with beam size as expected? –(E. Black et al - Caltech) In frequency band of interest: To intermediate mass Sapphire Mass ~ 40kg Fused silica ribbons or fibers Fused silica ears Expect thermoelastic to be dominant provided intrinsic thermal noise is low enough

4. LIGO-G020062-00-Z Intrinsic thermal noise Estimated using measurements of Q/loss factors of samples of sapphire made at high frequencies, assume structural damping Original measurements (Braginsky/Mitrofanov et al) – Q’s > 4 x 10 8 in samples ~ few cm diam. X 10cm long. Various cuts measured. –Russian sapphire - varying optical quality Recent measurements (Rowan et al, Willems) –Q ~ 2.7 x 10 8 in sapphire from Crystal Systems Inc. –“C-axis cut” (ie c-axis = axis of cylindrical sample) –Commercial polish (Waveprecison Inc., Insaco) Spec. for Adv. LIGO: Q = 3 x10 8 Provided this is met - thermo-elastic noise is dominant

5. LIGO-G020062-00-Z Intrinsic dissipation C - axis sapphire from Crystal Systems Inc, with visible flaw Q ~ 10 8 (Willems et al)

6. LIGO-G020062-00-Z Intrinsic dissipation Stanford/Glasgow : c-axis / m-axis companion sapphire pieces Both = 12.7cm diameter 5.4cm thick Nominally Hemex (central 7cm dia.), CSI white grade Polished by same vendors to same specifications Q/loss measurements so far - work in progress –m-axis piece ~ 5 x 10 6 (***PRELIMINARY***) –Companion c-axis sample to be measured Measure Q factors for different pieces (“full-size” a-axis piece ordered by U. Gla - possibility of Q tests) Several smaller m-axis, a-axis pieces (3” by 1”) to be measured Other samples - masses for TNI to be measured at Caltech???

7. LIGO-G020062-00-Z Interpretation of results Our thermal noise estimates use measured Q (or  (  o )), assume structural damping Following Levin and others: –Estimation of thermal noise in interferometer requires knowledge of response of test mass to Gaussian force on front face –Energy dissipation through imaginary part of Young’s modulus of test mass Sapphire has anisotropic material properties (trigonal) Stress/strain relations described through the elasticity tensor for the material - 6 independent elastic constants In principle: each elastic constant can have imaginary (dissipative) part Gaussian pressure on front of test mass exercises some set (or all) of these elastic constants (different set for different cuts of sapphire)

8. LIGO-G020062-00-Z Interpretation cont. Each mode of a test mass also samples a set of the elastic constants Each mode samples the constants differently In principle by –(a) measuring the Q of a number of modes of sapphire samples and –(b) calculating for each mode how much energy was stored in different types of deformation One could then back out loss factors associated with each elastic constant and use to calculate expected thermal noise. NB: for this type of analysis to have any validity, measured Q’s have to be some genuine measure of the internal dissipation of the material. i.e. not limited by suspension losses or any extrinsic mechanism

9. LIGO-G020062-00-Z Interpretation cont. Instead measure Q of c-axis and m, a cuts However earlier experiments (see Braginsky/Mitrofanov measurements) expect Q’s of ~ 10 8 in each case - suggests detailed reverse engineering of elastic loss coefficients unlikely to prove helpful. Nb: requirement is to be less than thermo-elastic noise Needs checked - expts underway - see earlier in presentation

10. LIGO-G020062-00-Z Attachments Fused silica ‘cone’ Sapphire rod Fused silica fibers Approach: measure Q (loss factor) of the fundamental resonant mode of a suspended sample before and after the bonding of a silica attachment to the sample. Estimate loss associated with the bonding ~3cm

11. LIGO-G020062-00-Z Attachments Silica/silica bonds Silica/sapphire bonds Fused silica mass M = 0.5kg Bond area = 0.8cm 2 Sapphire mass M = 0.28kg Bond area = 0.5cm 2 Fused silica attachment estimated loss ~ 3 x 10 -8 Expect loss scales linearly with bond volume ( or area if thickness held constant) LIGO II: total area = 2 x (3 x 1) = 6 cm 2 estimated loss ~ 3 x 10 -8 * Preliminary result Expected loss = 7.5 x 10 -8 Expected loss = 3.6 x 10 -7 Effect of loss depends on ratio of energy stored in bond to energy stored in mass For given bond area expect effect to scale with mass supported: 40kg Expected loss = 1.3 x 10 -9 Expected loss = 2.5 x 10 -9 Spec. for intrinsic loss of fused silica –3 x 10 -8 Specification for intrinsic loss of sapphire (ignoring thermo-elasticity) –3 x 10 -9 Do not expect excess loss introduced by silicate bonding to be a significant effect in either case

12. LIGO-G020062-00-Z Attachments - in progress Experimental plans: –Repeat above measurements on further sapphire samples –Large a-axis sample on order (U. Gla) for bonding/suspension tests Modeling plans: –Above analyses are based on effect of bonds on Q –However, clearly loss from bonds is spatially localized –Work from variety of places (Levin, Nakagawa, Yamamoto et al) points out this inhomogeneous loss needs different treatment than for modal model eg: loss located on circumference may be less important than Q measurements suggest - but no full analytical treatment available –Work ongoing (Fejer in prep.) on analytical treatment to allow effects of spatially inhomogeneous loss on thermal noise of test masses to be calculated.

13. LIGO-G020062-00-Z Coatings Crystal Systems m-axis sample Dimensions 7.6cm dia x 3cm thick Q’s of 5 modes measured - sample then coated by REO (Ta 2 O 5 /SiO 2 ) –HR @1064nm –AR @ 1064nm Q’s re-measured for each mode nb: Barrel polish “rippled” and coatings run over on to large portion of barrel Coating loss analysed using methods similar to talk by Sneddon et al: Phi coating =1x10 -4 to 10 -3 ********Preliminary******* Further sapphire samples to be studied as part of coating mechanical loss program S. Rowan, P. Sneddon 7.6cm m-axis sapphire sample, on loan from LIGO project, through crossed polarizers. Dark spots are small amounts of Al, used as mirrors

14. LIGO-G020062-00-Z Coatings - in progress Use FE methods to calculate energy stored in coating vs substrate Need to take into account anisotropy of sapphire Suitable modifications to current models underway (D.Crooks)

15. LIGO-G020062-00-Z Other noise sources? Excess loss from electrostatic drive? Others ????

16. LIGO-G020062-00-Z Summary Q measurements and modeling studies underway allowing diagnosis of elastic loss at high frequencies from: –Intrinsic loss –Loss from attachments –Coating loss As always we make assumptions about frequency dependence of damping (typically structural) In the end, a direct measure of thermal noise will be necessary