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

Simple estimation

Φ(t) << 1h = sqrt(f_sc) * T/L * δx

f_sc = |overlap integral|2 * RAR

Simple estimationon each surface of lenses

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/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.→ so 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 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.

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 problem with relative motion