Figure 1, is the spectrum of the RFC error signal once the CARM SLOW loop is engaged. There is large peak at 150mHz in the remaining frequency noise.
In order to check if the OMC will be able to follow this frequency noise fluctuation I have measured the OMC1 length locking loop this morning by injecting noise, while the OMC1 was locked on the recombined ITF.
07:17 UTC (9min) noise injection into the OMC1 error point, first with 300e-7 level, and then halfway through increased to 900e-7 (arbitrary units).
Figure 2, measured open loop TF. The unity gain is at 4Hz, so the gain is a factor ~6 higher than designed for this loop which should have a UGF of 2Hz.
Note there is a lot of phase margin, not sure why, probably used to have a sharp low-pass in the signal demodulation, it will probably need to be added back to prevent reinjecting sensing noise above 10Hz.
Below 0.1Hz the coherence drops, but the gain of the loop should be at least 100, using 100 for the performance estimation below (green line).
Figure 3, the blue line is the frequency noise as measured by the RFC in figure 1, but calibrated into equivalent OMC length cavity noise.
The calibration is done assuming a calibration into frequency of 6e4 Hz/V of LSC_RFC_6MHz_I, and then from frequency to cavity length 1.44963*0.124/2.82e14 m/Hz.
Then the red line is the frequency noise divided by the OMC closed loop gain abs(1-OLTF). The lock RMS is 6e-14m, one order of magnitude better than needed.
In black is the same but with the OMC loop at the gain I expect it to operate in low noise conditions (gain 6 times smaller), it is at 4e-13m, which is the same as the best achieved measurements so far.
In conclusion, the CARM_SLOW loop performance should already be good enough for the OMC to be able to follow the frequency noise fluctuations, but a factor few more suppression of the 150mHz bump wouldn't hurt.
