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Finite mirror effects in advanced interferometric gravitational wave detectors

Lundgren, Andrew P. and Bondarescu, Ruxandra and Tsang, David and Bondarescu, Mihai (2008) Finite mirror effects in advanced interferometric gravitational wave detectors. Physical Review D, 77 (4). Art. No. 042003. ISSN 2470-0010. doi:10.1103/PhysRevD.77.042003.

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Thermal noise is expected to be the dominant source of noise in the most sensitive frequency band of second-generation, ground-based gravitational-wave detectors. Reshaping the beam to a flatter, wider profile which probes more of the mirror surface reduces this noise. The “Mesa” beam shape has been proposed for this purpose and was subsequently generalized to a family of hyperboloidal beams with two parameters: twist angle alpha and beam width D. Varying alpha allows a continuous transition from the nearly flat (alpha=0) to the nearly concentric (alpha=pi) Mesa beam configurations. We analytically prove that in the limit D-->[infinity] hyperboloidal beams become Gaussians. The ideal beam choice for reducing thermal noise is the widest possible beam that satisfies the Advanced LIGO (Laser Interferometer Gravitational-wave Observatory) diffraction loss design constraint of 1 part per million (ppm) per bounce for a mirror radius of 17 cm. In the past the diffraction loss has often been calculated using the clipping approximation that, in general, underestimates the diffraction loss. We develop a code using pseudospectral methods to compute the diffraction loss directly from the propagator. We find that the diffraction loss is not a strictly monotonic function of beam width, but has local minima that occur due to finite mirror effects and leads to natural choices of D. For an alpha=pi Mesa beam a local minimum occurs at D=10.67 cm and leads to a diffraction loss of 1.4 ppm. We then compute the thermal noise for the entire hyperboloidal family. We find that if one requires a diffraction loss of strictly 1 ppm, the alpha=0.91pi hyperboloidal beam is optimal, leading to the coating thermal noise (the dominant source of noise for fused-silica mirrors) being lower by about 10% than for a Mesa beam while other types of thermal noise decrease as well. We then develop an iterative process that reconstructs the mirror to specifically account for finite mirror effects. This allows us to increase the D parameter to 11.35 cm for a nearly concentric Mesa beam and lower the coating noise by about 30% compared to the original Mesa configuration.

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Additional Information:©2008 The American Physical Society. (Received 19 October 2007; published 20 February 2008) We thank Yanbei Chen for guidance, useful discussion, and for foreseeing many of the issues presented in this paper. We are grateful to Geoffrey Lovelace for useful discussions regarding the noise calculations. Our calculations make use of the GNU Scientific Library [30], IT++ [31], and the AMD Core Math Library [32]. We thank our advisors James York, Éanna Flanagan, Ira Wasserman, Saul Teukolsky, Dong Lai, and Barry Barish for support and encouragement. This work was partially supported by funds from the following sources: Sofja Kovalevskaja Programme from the Alexander Von Humboldt Foundation, NSF Grant Nos. AST-0707628, AST-0606710, and PHY-0652952. A.P.L. and R.B. were supported to attend the GR18/Amaldi7 conference, which was helpful to this work, by a combination of Cornell, NSF, and IUPAP/ISGRG travel grants. R.B. and M.B. are grateful to Jayashree Balakrishna and Gregory Daues for their friendship and continuous support.
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ID Code:9658
Deposited By: Archive Administrator
Deposited On:21 Feb 2008
Last Modified:08 Nov 2021 21:01

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