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Backscattering TMS

This study examines the backscattering noise on the surfaces of BRT and GPT lenses, including the effects of radiation pressure, up-conversion, and the relative motion between ETM and TMS elements. Simple estimation methods and transfer functions are used to analyze and compare the contributions of ETM and TMS motion.

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Backscattering TMS

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  1. Backscattering TMS Junko Katayama

  2. What I did I computed the backscattering noise on the each surface of BRT and GPT lenses. • Simple estimation • Including radiation pressure • up-conversion • up-conversion using the relative motion between ETM and TMS elements

  3. TMS ETM BRT B1 B2 GPT G1 G2 G3 G4 B4 B3 QPD

  4. Simple estimation Φ(t) << 1 h = sqrt(f_sc) * T/L * δx f_sc = |overlap integral|2 * RAR

  5. Simple estimationon each surface of lenses

  6. Including radiation pressure • h = G*sqrt(f_sc*T*Pcav/Pin)/L*4pi/λ*δx (G is given by Aso-san) • Transfer Function (Simple pendulum) TF = 1/(1-ω2/ω02+iω/ω0*1/Q)

  7. Including radiation pressurewith TF

  8. up-conversion Esc*eiΩt[cos(φ(t))+isin(φ(t))] φ(t) << 1 h = G*sqrt(f_sc*T*Pcav/Pin)/L*4pi/λ*δx φ(t) >> 1 Up-conversion ; φ(t) → sin(φ(t)) Pφ(ω)→ Psinφ(ω) ≡Pa(ω) Pφ(ω)

  9. autocorrelation function already know want to know From Aso-san slides ‘ScatteringWorkshop’

  10. Pφ(ω) & Pa(ω)

  11. Pφ(ω) & Pa(ω)adding peek

  12. up-conversion with TF

  13. using relative motionbetween ETM and TMS at low frequency : ETM moves larger, as much as the seismic motion. → so we should consider the relative motion between ETM and TMS elements. ETM element xrelative= (xETM2 + xTMS2)1/2 xTMS xETM

  14. up-conversion with TFcomparing normal & using relative motion

  15. up-conversion with TFcomparing normal & using relative motion From last slide, we can see that there is almost no problem with relative motion between ETM and TMS. → We can see this reason in the next two slides. ETM motion and its contribution to h are enough smaller than TMS motion at > 1 Hz.

  16. comparing ETM & TMS motion

  17. ETM contribution to h

  18. Conclusion • TMS should be suspended Simple pendulum is enough for TMS • ETM motion is quite smaller than TMS motion → No problem with relative motion

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