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AdV-COM (1/√f noise)
mwas - 16:26 Friday 05 April 2024 (63854) Print this report
CP thermal noise question

The rigid mounting of the CP into a metal structure highlighted by Enrico and Antonino raises the question of what is the thermal noise of the CP, as the rigid mounting (VIR–0128A–12, section 10.3.3) is likely increasing the loss angle orders of magnitude above the loss angle of fused silica (1e-8).

An example of thermal noise computation in transmission of an optic was done 15 years ago for GEO: LIGO-T0900209. One of the noise listed there is transmissive substrate brownian noise which depends on the loss angle. For the GEO beam splitter the optical length noise is 2e-20 m/rtHz at 100Hz. Neglecting the differences in the geometry, for Virgo this is attenuated by a factor 5e-3 as the beam splitter is outside the Fabry-Perot arm cavities, and after dividing by the 3km arm length correspond to a strain noise of 3e-26 1/rtHz that is negligible.

However if the loss angle of the CP is not 1e-8 but 1e-3 due to the friction with the metalic frame that holds it, then the noise level in terms of strain becomes 1e-23 1/rtHz at 100Hz, comparable to the level of the 1/f^0.66 mystery noise.

A large caveat is that at first glance the coupling mechanism is not compatible with measurements. Plan wave simulations (Optickle) show that the BS to h(t) coupling is independent of the SR reflectivity. The CP optical length noise should couple the same way as the beam splitter position noise, and changing SR reflectivity changes the DARM optical gain in a similar way as misaligning SR. Experimentally we see the noise change in h(t) as a function of SR alignment, while in this scenario of optical length noise in the short Michelson this doesn't happen according to plane wave simulations. But it is possible that changing SR reflectivity is not a good approximation of the effect of misaligning SR. It would interesting to check with Finesse simulations, how the BS to h(t) coupling changes with SR misalignment.

Nonetheless, It would be interesting to evaluate what is the expected CP thermal noise when the mounting frame is taken into account, and think if it is feasible to measure experimentally the quality factor of one of its bulk modes, for example the drum mode. As even if doesn't explain the mystery 1/f^0.66 noise, it could be a source of additional noise that hides just beneath it.

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mwas - 12:24 Tuesday 14 May 2024 (64250) Print this report

In simulations done 10 years ago by Matteo Lorenzini and Paola Puppo the quality factor of the CP drum mode should be ~400. Using equation 1 from  LIGO-T0900209 this correspond to a high optical length noise for the CPs.

Figure 1 shows the optical length noise of one CP

FIgure 2 shows the expected contribution of two CPs to h(t). This a factor 2 below the current sensitivity curve and if confirmed it is a major issue.

Attached is also the Octave code that produces these figures

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mwas - 21:21 Tuesday 21 May 2024 (64322) Print this report

An example of excess thermal noise when mounting a mirror in a metal frame has been abserved at the AEI 10m prototype facility: .

The inferred substrate Brownian noise when the mirror is glued inside a metal frame 7e-18 m/rtHz. When the mirror is just clamped with screws the noise is even higher, and shows mechanical resonances (at a few kHz).

It is a very different case for the CP, but shows that a mount can change the substrate thermal noise to levels that would be sufficient to explain the mystery 1/f^{2/3} noise.

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