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Mirror Thermal Noise: Gaussian vs Mesa beams

Mirror Thermal Noise: Gaussian vs Mesa beams. J.Agresti, R. DeSalvo. LIGO-Virgo Thermal Noise Workshop. Mirror thermal noise problem:. Sapphire TM. Advanced-Ligo sensitivity Dominated by test-masses thermoelastic (S-TM) or coating (FS-TM) thermal noises. Fused Silica TM.

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Mirror Thermal Noise: Gaussian vs Mesa beams

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  1. Mirror Thermal Noise: Gaussian vs Mesa beams J.Agresti, R. DeSalvo LIGO-Virgo Thermal Noise Workshop

  2. Mirror thermal noise problem: Sapphire TM Advanced-Ligo sensitivity Dominated by test-masses thermoelastic (S-TM) or coating (FS-TM) thermal noises. Fused Silica TM Can we reduce the influence of thermal noise on the sensitivity of the interferometer? Without drastic design changes

  3. Mirror Thermal Noise: Thermoelastic noise Brownian noise Mirror surface Created by stochastic flow of heat within the test mass Due to all forms of intrinsic dissipations within a material (impurities, dislocations of atoms, etc..) Fluctuating hot spots and cold spots inside the mirror Expansion in the hot spots and contraction in the cold spots creating fluctuating bumps and valleys on the mirror’s surface Surface fluctuations Interferometer output: proportional to the test mass average surface position, sampled by to the beam’s intensity profile.

  4. Indicative thermal noise trends Noise spectral densities in the Gaussian beam case (infinite semi-space mirror) Substrate thermoelastic noise Coating thermoelastic noise Substrate Brownian noise Coating Brownian noise Exact results require accurate information on material properties and finite size effects must be taken in account.

  5. Diffraction prevents the creation of a beam with a rectangular power profile…but we can build a nearly optimal flat-top beam: Flat-top beam Gaussian beam The mirror shapes match the phase front of the beams.

  6. Thermal noise for finite sized mirrors: • Precise comparative estimation of the various thermal noise contributions for finite test masses (design optimization). • Noise suppression using Mesa beam.

  7. Thermal noise calculations Interferometer is sensitive to the test mass surface displacement Levin’s approach to Fluctation Dissipation Theorem Is the energy dissipated by the mirror in responce to the oscillating pressure

  8. Assumptions in our analysis BHV+LT (accurate) approximate analyical solution of elasicity equations for a cylindrical test mass Pressure distribution Quasistatic approximation for the oscillations of stress and strain induced by P. Adiabatic approximation for the substrate thermoelastic problem (negligible heat flow during elastic deformation). Brakes down for coating thermoelastic problem Perturbative approach Coating is an isotropic and homogeneous thin film

  9. Material properties:

  10. Ideas behind calculations • Fixed total mirror mass = 40 Kg. • The beam radius is dynamically adjusted to maintain a fixed diffraction loss = 1ppm (clipping approximation). • The mirror thickness is also dynamically adjusted as a function of the mirror radius in order to maintain the total 40 Kg mass fixed. • Calculation at the frequency 100 Hz Noise TE-s Noise B-s / B-c

  11. Substrate Brownian noise Substrate thermoelastic noise

  12. Coating Brownian noise Boundary condition

  13. Coating thermoelastic noise at the surface Boundary condition

  14. Results for Gaussian and Mesa beam

  15. Comparison between Gaussian and Mesa beam Gain factor Gain factor

  16. Sensitivity improvement

  17. Coating Thermo-refractive noise estimation • Infinite mirrors • Perfect square beam

  18. Finite size test mass correction for Gaussian Beam

  19. 5ppm Diff. loss

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