Q EDIT: THIS IS WRONG. I LOCKED PRC ON THE CARRIER

 As Koji measured the other day: MICH and PRCL seem very degenerate in the 3f REFL PDs. 

I'm using this as a motivation to do some simulation in MIST and try to understand the best way to implement the 3F locking scheme. Hopefully my thinking below isn't nonsense...

First, I modeled the PRC with no arm cavities and the estimated cavity length I got with the PRM kick measurement, and looked at the REFL sensing matrix.

This agrees with the observed degeneracy. I then modeled the case of the PRC length that gives coincident SB resonance, again with no arm cavities.

Now there is good separation in REFL165. (REFL33 still looks pretty degenerate, however). This raised the question, "What does the angle between MICH and PRCL in REFL165 do as a function of macroscopic PRC length?" 

• We see ~90 degrees at coincident resonance
• Shortening the cavity, which we did to account for the arms, quickly shrinks the angle
• Presuming we moved to make the cavity 4cm shorter implies we had ~45 degrees between MICH and PRCL in REFL165 before the move. (Is this consistent with earlier observations?)

To me, this implies that locking the PRC on 3F from scratch won't be simple. However, the whole point of the PRC length choice is to have coincident SB resonance when the arms are resonating.

So: even if we're not spot on, we should be relatively close to the PRC length where having arms resonant gives us simultaneously resonant upper and lower sidebands, where MICH and PRCL should be orthogonal-ish. I.e. building up a little bit of IR power in the arms may start to break the degeneracy, perhaps allowing us to switch from 1F to 3F locking, and then continue reducing the CARM offset. 

So, I ultimately want to model the effect of arm power buildup on the angle between MICH and PRCL in the 3f PDs. This is what I'm currently working on. 

So far, I have reproduced some of the RC modeling results on the wiki to make sure I model the arms correctly. (I get 37.7949 m as the ideal arm length for a modulation freq of 11.066134 MHz vs. 37.7974m for 11.065399 MHz as stated on the wiki). Next, I will confirm the desired PRC length that accounts for the arms, and then look at the MICH vs PRCL angle in the REFL PDs as a function of arm power or detuning.