I wanted to put my optomechanical instability hypothesis to the test. So I decided to cut the input power to the IMC by ~half and try locking the PRFPMI. However, this did not improve the stability of the buildup in the arm cavities, while the control was solely on the ALS error signal.
Basically, with some tweaks to loop gains, it worked, see Attachment #1. Note that the lower right axis shows the IMC transmission and is ~7500 cts, vs the nominal ~15,000 cts.
Cutting the input power did not have the effect I hoped it would. Basically, I was hoping to zero the optical CARM offset while the IFO was entirely under ALS control, and have the arm transmission be stable (or at least, stay in the linear regime of REFL11). However, the observation was that the IFO did the usual "buzzing" in and out of the linear regime. Right now, this is not at all a problem - once the IR error signal is blended in, and DC control authority is transferred to that signal, the lock acquisition can proceed just fine. And I guess it is cool that we can lock the IFO at ~half the input power, something to keep in mind when we have the remote controlled waveplate, maybe we always want to lock at the lowest power possible such that optomechanical transients are not a problem.
I also don't think this test directly disputes my claim that the residual CARM noise when the arm cavities are under purely ALS control is smaller than the CARM linewidth.
What does this mean for my hypothesis? I still think it is valid, maybe the power has to be cut even further for the optomechanics to not be a problem. In Finesse (see Attachment #2), with 0.3 W input power to the back of the PRM, and with best guesses for the 40m optical losses in the PRC and arms, I still see that considerable phase can be eaten up due to the optomechanical resonance around ~100 Hz, which is where the digital CARM loop UGF is. So I guess it isn't entirely unreasonable that the instability didn't go away?
After this work, I undid all the changes I made for the low power lock test. I confirmed that IMC locking, POX/POY locking, and the dither alignment systems all function as expected after I reverted the system.