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Estimate of tilt instability of mesa-beam and Gaussian-beam modes for advanced LIGO

Savov, Pavlin and Vyatchanin, Sergey (2006) Estimate of tilt instability of mesa-beam and Gaussian-beam modes for advanced LIGO. Physical Review D, 74 (8). Art. No. 082002. ISSN 2470-0010. doi:10.1103/PhysRevD.74.082002.

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Sidles and Sigg have shown that advanced LIGO interferometers will encounter a serious tilt instability, in which symmetric tilts of the mirrors of an arm cavity cause the cavity's light beam to slide sideways, so its radiation pressure exerts a torque that increases the tilt. Sidles and Sigg showed that the strength T of this torque is 26.2 times greater for advanced LIGO's baseline cavities—nearly flat spherical mirrors which support Gaussian beams (FG cavities), than for nearly concentric spherical mirrors which support Gaussian beams (CG cavities) with the same diffraction losses as the baseline case: TFG/TCG=26.2. This has motivated a proposal to change the baseline design to nearly concentric, spherical mirrors. In order to reduce thermal noises in advanced LIGO, O'Shaughnessy and Thorne have proposed replacing the spherical mirrors and their Gaussian beams by "Mexican-Hat" (MH) shaped mirrors which support flat-topped, mesa shaped beams. In this paper, we compute the tilt-instability torque for advanced-LIGO cavities with nearly flat MH mirrors and mesa beams (FM cavities) and nearly concentric MH mirrors and mesa beams (CM cavities), with the same diffraction losses as in the baseline FG case. We find that the relative sizes of the restoring torques are TCM/TCG=0.91, TFM/TCG=96, TFM/TFG=3.67. Thus, the nearly concentric MH mirrors have a weaker tilt instability than any other configuration. Their thermoelastic noise is the same as for nearly flat MH mirrors, and is much lower than for spherical mirrors.

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Vyatchanin, Sergey0000-0002-6823-911X
Additional Information:©2006 The American Physical Society (Received 21 September 2004; revised 15 August 2006; published 9 October 2006) We are very grateful to Kip Thorne who could be regarded as the "father" of this paper; he posed the problem; it was his idea to use CM beams to reduce the tilt instability; and he took part in very fruitful discussions and gave us useful advice. We thank Thorne and Yanbei Chen for helpful advice about the wording of this paper. For useful scientific discussions, we thank Thorne, Chen, Juri Agresti, Mihai Bondarescu, Erika d’Ambrosio, Poghos Kazarian, and Richard O’Shaughnessy. The research reported in this paper was supported in part by National Science Foundation grants No. PHY-0098715 and PHY-0099568, by Russian Foundation for Fundamental Research grants No. 03-02-16975-a and by contracts No. and No. 40.700.12.0086 of the Industry and Science Ministry of Russia.
Issue or Number:8
Record Number:CaltechAUTHORS:SAVprd06
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6189
Deposited By: Archive Administrator
Deposited On:28 Nov 2006
Last Modified:08 Nov 2021 20:31

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