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Internal thermal noise in the LIGO test masses: A direct approach

Levin, Yu. (1998) Internal thermal noise in the LIGO test masses: A direct approach. Physical Review D, 57 (2). pp. 659-663. ISSN 2470-0010. doi:10.1103/PhysRevD.57.659.

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The internal thermal noise in LIGO’s test masses is analyzed by a new technique, a direct application of the fluctuation-dissipation theorem to LIGO’s readout observable, x(t)=(longitudinal position of test-mass face, weighted by laser beam’s Gaussian profile). Previous analyses, which relied on a normal-mode decomposition of the test-mass motion, were valid only if the dissipation is uniformally distributed over the test-mass interior, and they converged reliably to a final answer only when the beam size was a non-negligible fraction of the test-mass cross section. This paper’s direct analysis, by contrast, can handle inhomogeneous dissipation and arbitrary beam sizes. In the domain of validity of the previous analysis, the two methods give the same answer for Sx(f), the spectral density of thermal noise, to within expected accuracy. The new analysis predicts that thermal noise due to dissipation concentrated in the test mass’s front face (e.g., due to mirror coating) scales as 1/r02, by contrast with homogeneous dissipation, which scales as 1/r0 (r0 is the beam radius); so surface dissipation could become significant for small beam sizes.

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Additional Information:©1997 The American Physical Society Received 21 July 1997 This work would not have been possible without discussions and help from Vladimir Braginsky, Ron Drever, Darrell Harrington, Nergis Mavalvala, Fred Raab, Glenn Soberman, and Kip Thorne. In particular, Glenn Soberman suggested the method of integration in Eq. (A4), and Kip Thorne carefully reviewed the manuscript and made a few significant corrections and suggestions. This work was supported in part by NSF Grant No. PHY-9424337.
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Deposited On:06 Oct 2006
Last Modified:08 Nov 2021 20:23

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