1. 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)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 00 Scattered Beam  t )

2. The seismic spectrum: High Q (Q=1000-2000) Peaks from fans

3. 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)

4. 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)

5. 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) = A 0 *sin(2π*f 0 ), which has A 0 > 1e-8 m Give rise to a “shoulder noise” in spectrum that: – Extends up to f max = 4π/ *A 0 *f 0 – Has RMS amplitude (H bs ) 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)

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

7. We deduce two simple rules for up-conversion noise in the detection band (f max > 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 (H bs ) RMS = K*sqrt(2)/sqrt(f max ) 10) 2) Simple rule to avoid the onset of up-conversion noise inside the ITF detection band (f max > 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.