Craig has been making long low excitation measurements of all the arm ASC loops (see alogs 67518, 67488, 67187). I have been applying my ASC models to match these measurements.
All of these measurements are made at the "blend" point, or A point of the ASC loop. In this case, G_ol = {loop}_{dof}_A_IN1/{loop}_{dof}_A_IN2 = optical gain * L2_ct2N *(digital control + RPC) * S_L2 / (1 + Rh(60W input) * S_L3). L2_ct2N is a calibration from counts to Newtons, based on G1100968 (6.3e10 N/ct).
S_L2 and S_L3 refer to the free pendulum L2 or L3 suspension transfer functions. I have made recent measurements of those to confirm they match the modeled transfer functions from Brett Shapiro. Rh(60W input) is the radiation pressure factor for a hard degree of freedom at a given amount of circulating power. Rh = (2*P_circ /c) * dy/dTheta(hard), where dy/dTheta(hard) is the eigenvalue of the angle-to-spot-position matrix for the hard mode (4.5e4 m/rad from the aLIGO g factors).
The digital control and RPC (radiation pressure compensation) are known values. For the CHARD measurements, I have recent measurements of the optical gain. However, I can only estimate the optical gain for DHARD. This leaves the circulating power (and DHARD P optical gain) as a free parameter I can adjust to match the model to the measurement. The CHARD optical gain measurements were made at 2W, but correcting for the modulation depth reduction at high power gives a value that matches well to the measurement.
Bottom line: the ASC arm measurements suggest that the circulating power in the arms is about 290 kW at 60W PSL input. Our current calibration, based on the PRG and arm gain estimates 340-380 kW at 60 W PSL input.
Estimating the arm power from ASC measurements is certainly not the most exact method we have on hand. I do think it's an interesting data point to have in our continued quest to figure out what our arm power is. I have attached my modeled OLGs at 290kW and 340kW compared with Craig's measurements for CHARD and DHARD P.
A caveat to these measurements is that they were made early enough on in the lock that the power was changing as the IFO thermalized. I have attached screenshots of the power trends for the CHARD P and DHARD P measurements, using the start times that Craig listed in his alog as t0 on the scope. For both the CHARD P and DHARD P measurements, the RPC gain stayed constant during the measurement. This means that the the suspension plant slowly changed throughout the measurements, but the compensation did not. During the hour long measurement, the power changed by about 20 kW. It would be better to capture these OLGs at a time many hours into the lock to ensure the thermalization is complete.
Craig also has a measurement of the CHARD Y loop. It also suggests 290 kW, but I am not including it in this alog as we have made several changes to the loop and I would like to remeasure. I will continue to update this alog as we make more ASC measurements using this unbiased method.
Craig just posted an alog with a DHARD Y measurement. I have attached another side by side comparison with 290 kW and (this time) 380 kW. I used a high power than the ones above to see if I could match the upper split peak. It is possible that these split peaks are due to differing powers in the arms.
This measurement does fit with 290 kW, but it is much less conclusive than the other measurements. I will try to fit the split peak feature by applying different arm powers in each arm.
Again, I had to adjust my assumed optical gain of DHARD Y based on matching the measurement. This measurement suggests that the DHARD Y optical gain is about 3.9e10 ct/rad.
