LIGO Document T1400225-v1

Modeling mirror shape to reduce substrate Brownian Noise in interferometric gravitational wave detectors

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T - Technical notes
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This paper is a report on the effect of varying mirror shape upon Brownian noise is the test mass substrate. Using finite element analysis, it was determined that by using frustum shaped test masses with a ratio between the opposing radii of about 0.7 the frequency of the principle real eigenmodes of the test mass can be shifted into higher frequency ranges. For a fused silica test mass this shape modification could increase this value from 5951 Hz to 7210 Hz, and in a silicon test mass it would increase the value from 8491 Hz to 10262 Hz, in both cases moving the principle real eigenmode to a frequency further from LIGO bands, reducing slightly the noise seen by the detector. The Brownian thermal noise in the optimized substrate was calculated in order to demonstrate that it is lower than in a cylindrical substrate.
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