Download - Backscattering TMS
Backscattering TMS
Junko Katayama
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
BRTGPT
ETM
QPD
B1 B2
B3 B4
G1 G2
G3 G4
TMS
Transmission Monitor System
Simple estimation
Φ(t) << 1h = sqrt(fsc) * T/L * δx
fsc = |overlap integral|2 * RAR
Simple estimationon each surface of lenses
Including radiation pressure
• h = G*sqrt(fsc*T*Pcav/Pin)/L*4pi/λ*δx
(G is given by Aso-san)
• Transfer Function (Simple pendulum)TF = 1/(1-ω2/ω0
2+iω/ω0*1/Q)
Including radiation pressurewith TF
up-conversion
Esc*eiΩt[cos(φ(t))+isin(φ(t))]φ(t) << 1h = G*sqrt(f_sc*T*Pcav/Pin)/L*4pi/λ*δx
φ(t) >> 1Up-conversion ; φ(t) → sin(φ(t))
Pφ(ω) → Psinφ(ω) ≡ Pa(ω)
Pφ(ω)
autocorrelation function
From Aso-san slides ‘ScatteringWorkshop’
already know
want to know
Pφ(ω) & Pa(ω)
Pφ(ω) & Pa(ω)adding peek
up-conversion with TF
at low frequency :ETM moves larger, as much as the seismic motion→ We should consider the relative motion between ETM and TMS elements.
using relative motionbetween ETM and TMS
xrelative = (xETM2 + xTMS
2)1/2
ETM element
xETMxTMS
up-conversion with TFcomparing normal & using relative motion
From last slide, we can say that the consideration of relative motion makes almost no difference in the noise estimation.
..we can find this reason in the next two slides. ETM motion and its contribution to h are enough smaller than TMS motion at > 1 Hz.
up-conversion with TFcomparing normal & using relative motion
comparing ETM & TMS motion
ETM contribution to h
Conclusion
• TMS should be suspendedSimple pendulum is enough for TMS
• ETM motion is quite smaller than TMS motion → no need to consider the relative motion