Simulation model of Back-scattered light Noise from AdV CryoTrap

(deduced from Vinet, Brisson, Braccini article PRD on scattered noise)Case is: light diffused by mirror, then scattered back to mirror by CT

walls, finally diffused back into ITF beam)• Non linear • z(t) is CryoTRAP walls vibration along beam axis• K is the coupling factor, also deduced from above PRD, see computation in Antonio’s document (link)

•TESTED with: K = 2E-25 z(t) = measured displacement spectrum of VIRGO CryoTrap

>>> THIS provides just an EXAMPLE!WE ASK FOR: Validation by experts,Wait for realistic seismic noise measurement of AdV CryoT bubbles make realistic projection to check proposed CT design, isolation sys ...

Undisturbed Beam

Total field

scA

0A 0

Scattered Beam

(t)

• The seismic spectrum:

High Q (Q=1000-2000)Peaks from fans

• Linear VS not-linear approximation:LINEAR approx. z(t) << /(4π) = 1E-7m (let us translate it as: z(t) < 1E-8m)Angle is small and sin() (t) = 4pi/ * z(t)

• factor 1/sqrt(2) comes from averaging over the static phase angle PHI0

• Low frequency microseism (always present) Smoothes the high-Q lines (fans...) (see RED vs GREEN,GREEN is done filtering out the Low frequency part of the seismic noise, highpass filter)

• Low frequency microseism (always present) Smoothes the high-Q lines (fans...) (see RED vs GREEN)•GREEN is done filtering out the Low frequency part of the seismic noise, highpass filter)

Upconversion noise• For vibration noises z(t) > 1e-8 m(it happens seldom, see seism spectrum, but it might happen with new CT,

mech resonances excited by bubbles...?)

• Some simple rules for upconversion: (see docs by Bas, Edwige,...):A quasi monocromatic peak z(t) = A0*sin(2π*f0), which has A0 > 1e-8 m

Give rise to a “shoulder noise” in spectrum that:– Extends up to fmax = 4π/ *A0*f0

– Has RMS amplitude (Hbs )RMS =

(the energy of the peak gets spread over a frequency band up to fmax, thus the RMS amplitude reduces by 1/sqrt(fmax). The factor sqrt(2) seems needed from simulations, although I did not find the explanation)

Shoulder by the micro-seismic peak: (f0=0.35Hz, A0= 8E-6 m)shoulder extends up to fmax 35Hz, and it has amplitude (Hbs)RMS 4e-26 as predicted by Eq. 5 and Eq. 6.

We deduce two simple rules for up-conversion noise in the detection band (fmax > 10 Hz):

1) Up-conversion noise is under control: long as K guarantees a safe limit for the linear approximation, the up-conversion noise in the

AdV detection bandwidth is limited as well: in fact its spectral amplitude is (Hbs )RMS = K*sqrt(2)/sqrt(fmax ) < K (being fmax > 10)

2) Simple rule to avoid the onset of up-conversion noise inside the ITF detection band (fmax > 10Hz):

a) avoid CT walls vibrations with frequency f > 10Hz and amplitude z exceeding 1E-8m;

b) avoid CT walls vibrations with frequency f < 10Hz and amplitude z, such that:

f * z > /4π*10, or velocities v > /2*10, i.e avoid velocities greater than 5E-6 m/s.

example This means that a possible resonance mode of CT seismic isolation sys which for example is at f=5 Hz should have amplitude z < 1E-7m.