Based on measurements of the DARM OLTF and the EY PUM/test crossover that Jeff and I took last week, we can estimate the current value of the EY ESD actuation coefficient. It is 1.45×10−10 N/V2, with a 20 % uncertainty. This is an 80 % increase compared to the previous value (0.8×10−10 N/V2) which was measured at the end of May.
This number mostly relies on the crossover measurement, since above 10 Hz, the effect in the OLTF of changing the actuation coefficient is largely the same as changing the optical gain. Additionally, this number requires us to assume a number for the PUM actuation coefficient. Here I assume that it has not changed since the May calibration (i.e., I use 7.0×10−13 m/ct at dc).
Note that the modeled crossover doesn't really agree well with the measurement above 80 Hz. More investigation is required, particularly since during ER7 we already knew there was an issue with the DARM model around 10 Hz. (This discrepancy is why I say the uncertainty in the coefficient is no better than 20 %.)
To generate this number, I took Jeff's ER7 calibration script and made a version (H1DARMXO.m) that models the crossover. Both scripts (and the parameters file for the July 25 measurement) live in the CalSVN under Runs/PreER8/H1/Scripts/DARMOLGTFs. All parameters were left the same as their ER7 values except for the optical gain (I use 1.0×106 ct/m), the DARM pole (I use 330 Hz), and the EY L3 drive strength (I use 11×10−15 m/ct at dc). By tuning the L3 drive strength to match the measured crossover, we can extract the ESD actuation coefficient, assuming the rest of the L3 signal chain has been well-characterized. This is how I get the number quoted above.
The 80 % increase is sort of consistent with the 70 % increase that we saw when retuning the L3 digital gain post-vent. Strictly speaking, that was a measurement of the relative strengths of EX and EY. However, the DARM OLTF (with the retuned EY L3 gain) stayed roughly the constant before and after the vent, indicating that this 70% increase really is a change in EY.
I would like to clarify the relationship between the above entry and Sudarshan's entry.
The above entry is making a statement about a number (in N/V2) which characterizes the force applied to the test mass given a certain amount of voltage applied to the ESD (both its bias and its quadrants).
Sudarshan's entry is making a statement about a number (in m/ct) which characterizes the test mass displament given a certan number of counts in the DARM control signal. Therefore, it includes not only the above ESD strength (in N/V2), but also the mechanical response of the test mass, the electronic driver transfer function, the DAC, and the digital control filters for EY. In particular, it includes the digital EY L3 drivealign gain, which was changed from 50 ct/ct to 30 ct/ct after the vent in order to compensate for an unknown* increase in some other part of the EY actuation chain. Therefore, we expect Sudarshan's number to be small; if the compensation had been done perfectly, we would expect 0% change.
*Although it is unknown, I hypothesize that it is due to the discharging of EY resulting in an increase in the ESD actuation coefficient (in N/V2).