Koji asked me to look at what the ideal RF modulation frequency is, for just the PRMI case (no arms). If we had a perfect interferometer, with the sidebands exactly antiresonant in the arms when the arms resonate with the carrier, this wouldn't be an issue. However, due to vacuum envelope constraints, we do not have perfect antiresonance of the sidebands in the arm cavities. Rather, the sideband frequencies (and arm lengths) were chosen such that they pick up a minimum amount of extra phase on reflection from the arms. But, when the arms are off resonance (ex, the ETMs are misaligned), the sideband frequencies see a different amount of phase.
We want to know what a rough guess (since we don't have a precise number for the length of the PRC since our last vent) is for the ideal RF modulation frequency in just the PRMI.
If I take (from Manasa's kind measurements from the CAD drawing yesterday) the relevant distances to be:
L_P[meters] = 1.9045 + 2.1155 + 0.4067
L_X[meters] = 2.3070 + 0.0254*n
L_Y[meters] = 2.2372 + 0.0359*n + 0.0254*n
L_PRCL = L_P + (L_X + L_Y)/2 = 6.7616 meters.
The *n factors (n=1.44963) are due to travel through glass of the BS, and the substrate of the ITMs.
I find the FSR of the PRC to be 22.1686 MHz. For the sidebands to be antiresonant, we want them to be 11.0843 MHz. This would correspond to a mode cleaner length of 27.0466 meters. Our current modulation frequency of 11.066134 MHz corresponds to a MC length of 27.091 meters. So, if we want to use this 'ideal' modulation frequency for the PRC, we need to shorten the mode cleaner by 4.4cm! That's kind of a lot.