Proposal of a next-generation GW detector using huge mirrors abstract April 10, introduction 1 2 design parameters and sensitivity 2 3 mirror c
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1 Proposal of a next-generation GW detector using huge mirrors abstract April 10, introduction 1 2 design parameters and sensitivity 2 3 mirror considerations huge substrate availability mirror curvature[2] mirror thermal noise[3] mirror internal modes (n=0) structural damping noise[4] thermoelastic noise[8] thermo refractive noise[9] photon-thermal noise[8] mechanical loss from coatings [10] pendulum motion[11, 12] high-power source consideration high power laser availability thermal lensing[14, 15] future works 8 6 discussion 9 7 conclusion 9 8 appendix noise sources[16] projective sensitivities
2 8.2.1 LCGT [17] LIGO II [18] introduction 200Mpc (1.4M 1.4M ) SNR=10 h [1/ 100Hz ( current TAMA h [1/ 700Hz 1.5kHz[1] radiation pressure noise shot noise (thermal lensing mirror thermal noise mirror suspension thermal noise curvatute(r 90km), polish, coating, annealing, metrology 2 design parameters and sensitivity (synthesized fused silica) φ60cm t50cm, m=300kg (ρ =2.2) 2
3 ARM L=3km LIGHT SOURCE λ = 1064nm P laser =300W Recycling gain 80 P eff =15kW (BS input) FP CAVITY F=100 τ s =0.64ms r 0 =7.5 cm MIRROR m=300kg 2r m =60cm t =50cm R 1 = R 2 =90km E = Pa σ=0.17 φ m =( ) 1 T m =300K SUSPENSION ω p /2π =0.5Hz φ p =( ) 1 T p =300K SEISMIC x 0 =10 8 m G =(2π/ω) 8 3 mirror considerations fused silica properties α = [1/K] β = [1/K] C = [J/kg/K] κ =1.4[W/m/K] ρ = [kg/m 3 ] σ =0.17 E = [Pa] 3.1 huge substrate availability Heraeus can deliver 800 mm diameter silica which is the standard of National Ignition Facility (by Riccardo). 3.2 mirror curvature[2] L: baseline, R i : curvature beam size : wi 2 = Lλ g1 g 2, π g i 1 g 1 g 2 g i =1 L R i (i =1, 2)(1) L=3km R 1 = R 2 = 90km (δ = rm 2 /(2R 2)=0.5µm) g 1 =1,g 2 =0.97 w 1 w 2 7.5cm r 0 (at r = r 0, 1/e in amplitude) transvers mode : ν n;lm = c 2L [n +(l + m +1)γ], γ = 1 π cos 1 g 1 g 2 (2) γ = TAMA L=300m, R 1 =, R 2 =450m, g 1 =1, g 2 =0.333 γ=0.30 3
4 Strain sensitivity h 1 Hz total shot noise mirror thermal suspension thermal radiation pressure seismic Frequency f [Hz] Large mirror interferometer K. Tsubono Mar.1,
5 10 20 Strain sensitivity h 1 Hz TAMA300 LIGO I LCGT LIGO II LM Frequency f [Hz] designed sensitivities K. Tsubono Mar.1,
6 R 1 = R 2 = 90km r 0 =6.3cm conforcal(r 1 = R 2 = L) r 0 =3.2cm 3.3 mirror thermal noise[3] mirror internal modes (n=0) lowest mode 5.05kHz 2nd mode 5.26kHz 3rd mode 5.93kHz... thanks to Numata structural damping noise[4] (intrinsic) φ(ω) h = 2 4k B T m φ m (1 σ 2 ) [1/ Hz] (3) L πer0 ω = [1/ = 10Hz (4) if φ m = [5, 6] (5) [7] r 0 r m =0.25 h <7% (6) thermoelastic noise[8] h = 8 α(1 + σ)t κk B L ρcω r0 3 (7) = [1/ = 10Hz (8) 6
7 3.3.4 thermo refractive noise[9] coating h = 2 β eff λt L r 0 k B π ωρcκ β eff = n2 2 β 1 + n 2 1 β 2 4(n 2 1 n2 2 ) (9) β 1 = dn 1 dt,β 2 = dn 2 dt T i O 2 n 1 =2.2, β 1 = K 1 (12) S i O 2 n 2 =1.45, β 2 = K 1 (13) β eff = (14) h = [1/ = 10Hz (15) (10) (11) photon-thermal noise[8] coating h = 8 α(1 + σ) c Pa L ρcr0 2ω πλ (16) mirror absorption: P a 1W (17) h = [1/ = 10Hz (18) mechanical loss from coatings [10] h 1 r 0 (19) beam spot 3.4 pendulum motion[11, 12] pendulum mode: ω p = g/l ω p /2π=0.5Hz l=1.0m Silica fiber N=4, d f stress σ p 4mg d f = πnσ p (20) σ p =0.5GPa (achievable tensil strength) d f =1.4mm f violin = 1 2l σp ρ = 240Hz (21) 7
8 dilution effect of loss ENπd 4 f φ p = 32mgl 2 φ f = φ f = φ f (23) thermoelastic loss φ th = ωτ d 1+(ωτ d ) 2 (24) = Eα2 T 1+σ Cρ 1 σ (25) thermal diffusion coefficient : D = κ Cρ (26) fiber case :τ d = d 2 f /(13.55D) f d =1.1Hz (27) φ th = (10Hz/f) φ f = φ bulk + φ th + 8d s φ bulk (28) d f d s : surface dissipation depth < 200µm φ th (φ bulk 10 8 ) φ p = (10Hz/f) f>10hz φ p < 10 8 (22) 4 high-power source consideration 4.1 high power laser availability 300W or even 1kW is no problem if 100W is OK (by Mio). 4.2 thermal lensing[14, 15] most serious problem for high power interferometer! sagitta :s λ L (29) 2π R thermal expansion:δs α 4πκ P a < β 4πκ P a for silica (30) shot noise thermal lensing BS active compensation sensing & compensating 5 future works high power in MC high power PD scattering noise 8
9 6 discussion further improvement if T/Q 1/10 (advanced detector) narrowband improvement (dual recycling, RSE, etc) 7 conclusion proposal of a next-generation interferometric laser interferometer 1. huge mirrors (M = 300kg, φ =60cm) 2. large spot size (r 0 =7.5cm) 3. high power illumination (P BS = 15kW) (R&D) φ W thermal lensing compensation (active,scanned beam heating?, idea ) 9
10 Strain sensitivity h 1 Hz total shot noise mirror thermal suspension thermal radiation pressure seismic Frequency f [Hz] Large mirror interferometer(advanced) K. Tsubono Mar.1,
11 10 20 Strain sensitivity h 1 Hz LIGO I LCGT LM300 LM300 advanced TAMA300 LIGO II Frequency f [Hz] designed sensitivities K. Tsubono Mar.1,
12 8 appendix 8.1 noise sources[16] 1. SHOT NOISE λ h = ( 1 4πcP BS τs 2 + ω 2 )[1/ Hz] (31) (τ s = 2LF πc : cavity storage time) 2. MIRROR THERMAL NOISE structure damping model h = 2 4k B T m φ m (1 σ 2 ) L πer0 ω [1/ Hz] (32) (r 0 : beam radius) 3. SUSPENSION THERMAL NOISE h = L 2 4kB T p ωpφ 2 p mω 5 [1/ Hz] (33) (ω p : resonant freq. of the pendulum) 4. RADIATION PRESSURE NOISE h = 2 b 8π PBS L mω 2 cλ [1/ Hz] (34) (b = F 2π ) 5. SEISMIC NOISE x seismic = x 0 ( 1Hz f x 0 = m vibration isolation ratio G(ω) ) 2 [m/ Hz] (35) h = 2 4π 2 L ω 2 x 0G(ω)[1/ Hz] (36) 8.2 projective sensitivities LCGT [17] LIGO II [18] 12
13 10 20 Strain sensitivity h 1 Hz total shot noise mirror thermal suspension thermal radiation pressure seismic Frequency f [Hz] LCGT 13
14 10 20 Strain sensitivity h 1 Hz total shot noise mirror thermal suspension thermal radiation pressure seismic Frequency f [Hz] LIGO II 14
15 [1] M. Ando et al. Stable Operation of a 300-m Laser Interferometer with Sufficient Sensitivity to Detect Gravitational- Wave Events within Our Galaxy Phys. Rev. Lett (2001)(in press). [2] H. Kogelnik, T. Li Laser beams and resonators Proc. IEEE 54 (1966)1312. [3] Kazuhiro Yamamoto Ph.D. thesis, Study of the Thermal Noise Caused by Inhomogeniously Distributed Loss, December [4] Y. Levin Internal thermal noise in the LIGO test masses : a direct approach Phys. Rev. D57(1998)659. [5] [6] S. D. Penn et al., High Quality Factor Measured in Fused Silica [7] Y. T. Liu, K. S. Thorne Thermoelastic Noise and Homogenious Thermal Noise in Finite Sized Gravitational-wave Test Masses Phys. Rev. D62(2000) [8] V. B. Braginsky, M. L. Gorodetsky, S. P. Vyatchnin Thermodynamical Fluctuation and Photo-thermal Shot Noise in Gravitational Wave Antennae Phys. Lett. A 264 (1999)1. [9] V. B. Braginsky, M. L. Gorodetsky, S. P. Vyatchnin Thermo-refractive Noise in Gravitational Wave Antennae Phys. Lett. A 271 (2000)303. [10] K. Yamamoto, M. Ando, K. Kawabe, K. Tsubono Thermal Noise Caused by the Inhomogeneous Loss in the Mirrors Used in the Gravitational Wave Detectors Phys. Lett. A (in preparation). [11] A. M. Gretarrson et al., Pendulum Mode Thermal Noise in Advanced Interferometers: a Comparison of Fused Silica Fibers and Ribbons in the Presence of Surface Loss Phys. Lett. A 270 (2000)
16 [12] G. Cagnoli et al., Very High Q Measurements on a Fused Silica Monolithic Pendulum for Use in Enhanced Gravity Wave Detectors Phys. Rev. Lett. 85 (2000)2442. [13] A. M. Gretarrson, G. M. Harry Dissipation of Mechanical Energy in Fused Silica Fibers Rev. Sci. Instrum. 70 (1999)4081. [14] W. Winkler, K. Danzmann, A. Rudiger, R. Schilling Heating by Optical Absorption and the Performance of Interferometric Gravitational-wave Detectors Phys. Rev. A44(1991)7022. [15] K. Strain, et al., Thermal Lensing in Recycling Interferometric Gravitational Wave Detectors Phys. Lett. A 194 (1994)124. ( ) [16] [17] K. Kuroda et al., Large-scale Croyogenic Gravitational Wave Telescope Int. J. Mod. Phys. 8 (1999)557. [18] E. Gustafson, D. Shoemaker, K. Strain, R. Weiss, LSC White Paper on Detector Research and Development Sep LIGO T D. [19]
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