Summary:

MC2 M3 coils were balanced using pringle injection into MC2, using MC2 TRANS QPD as the angle sensor and IMC_L_IN1 as length sensor at 9Hz.

(This measurement might have been limited at sub-% level imbalance due to cheesy electronics coupling from MC2 M3 drive to some of MC2 M1 OSEM sensors, resulting in shaking of the entire suspension. This is a small effect anyway but will be discussed in a different alog. Note that I could have killed this coupling by implementing notches for M1 damping filters.)

Anyway, I reduced pringle to length and yaw coupling by more than 20dB (note that yaw sensing is related to PIT balance in pringle excitation). Old balance was not good for PIT.

Due to this (and 7% overestimate that existed in all LHO calculations prior to Jun/20/2018, alog 42594), to correctly interpret MC2 PIT spot position measurements from the past, you need to first divide the centering number by 1.07 and subtract 2.2mm. Sign convention I'm using is positive=high.

For example, Sheila's measurement showed that MC2 spot was too high by 7.6mm (alog 42350), according to this new measurement it was in reality something like 7.6/1.07-2.2=4.9mm.

But I don't know if this is the only systematic in A2L spot position measurement. P2L coupling of HSTS model might matter, I'll have a look.

Details:

I used MC2 TRANS as angle sensor due to higher S/N though I looked at IMC WFS RF and DC as well as IM4 trans. I used IMC_L_IN1 for length. For pringle excitation, since I used DTT I just injected into four coils independently, with 12k exc into each at 10Hz, with 180 deg phase offset to LL and UR.

First attachment left bottom shows coil gains before adjustment, left top is after, and the right plot shows the coupling before and after the adjustment. Note that, by doing pringle injection, your PIT coil/magnet imbalance shows up as YAW motion, and vice versa. Length and YAW signal decreased by more than 20dB.

UL+UR gain divided by LL+LR gain used to be 1.14 before, now after balancing it's 1.02. So the force balance for PIT used to be 1.14/1.02.

In the second attachment, which is a modification of Koji's cartoon in http://nodus.ligo.caltech.edu:8080/40m/2863, alpha-primed is the imbalance due to coil imbalance. I changed the sign convention from Koji's original so positive alpha means the node is high.

If we ignore cross term of alpha*alpha', the centering offset becomes 2*beta/D*(alpha+alpha') = 39.3mm*(alpha+alpha') for HSTS.

Before I started changing coil balance, it used to be that

(1-alpha')/(1+alpha')=1.14/1.02, i.e. alpha'=-5.6E-2.

Natural rotational node (i.e. no A2L correction, alpha=0) was 39.3mm*(-5.6E-2)=-2.2mm.