craig.cahillane@LIGO.ORG - posted 18:58, Monday 07 October 2019 - last comment - 23:22, Sunday 20 December 2020(52343)
DARM plant closer to Ward model, arm and SRC losses unable to fully explain the plant
This is a continuation of alog 48366. I tried fitting the Ward DARM model to the "2019 08 19 August Spots No SRCL Offset" DARM plant measurement. I thought SRC losses might be sufficient to explain the lowering of the Q of the DARM spring resonance. While the SRC losses do lower the DARM spring resonance, it also lowers the DARM pole frequency, as is expected (fDARM = farm (1 + rSRM)/(1 - rSRM)). The level of SRC losses needed to explain the lowered DARM spring Q is far too high to be realistic (~10-15%). These sorts of losses would lower the DARM pole far too much (~310 Hz for 10% losses). Allowing an MCMC to try to fit the Ward model to the measurement produces the pdfs below.Fit Parameters: Phi = Detuning Angle ~ 89.5 degs Zeta = Homodyne Angle ~ 90 degs Pbs = Power on the Beamsplitter = Input Power * PRG ~ 32 * 44 = 1.4 kW Losses in the Arms ~ 100 ppm Losses in the SRC ~ 1 % ?? Losses in the OMC (including OFI, tip-tilts, etc) ~ 10 %The walkers want to lower the DARM spring Q by reducing the power on the beamsplitter and lock at some incorrect homodyne angle. The power on the beamsplitter the MCMC wants is far too low (PRG would be ~30). In the posted corner plots, I have plotted my "initial guess" parameter values as the red lines. We trust the homodyne angle and power on the beamsplitter guesses here pretty well, but the losses guesses are not well-informed. The priors on the parameters are-90 < phi > 270 [degs] 85 < zeta > 95 [degs] 0 < Pbs > 2000 [W] 0 < arm_loss > 500e-6 0 < SRC_loss > 1 0 < post_SRM_loss > 1SRC losses were implemented as scattering losses in the SRC, i.e.TSRM = 32%, RSRM = 1 - TSRM - LSRC. Dan Brown has produced a Finesse model of this same effect, with similar results to be reported soon. We are in the process of checking the overall gain of the Ward model versus the Finesse model. Relevant code lives in the darmplant git repo.
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Quick update: I've taken a look at Dan Brown's code, and we've gotten a decent agreement between the finesse model of LHO and the analytic Ward model. Starting from Eq 3.83 of Rob Ward's thesis, we multiplied E_zeta by E_LO to get watts of DARM response, where E_LO = sqrt(20 mA/resp/QE), where responsivity = 0.856 A/W, and quantum efficiency QE = 0.98. 20 mA is the amps on the DCPD sum which is servoed using the DARM offset. Using the same parameters in the Ward model and Finesse, I put in an additional overall scaler of sqrt(2) into the Ward model to get a overall gain matchup. Unclear where this factor is coming from yet. Parameters used for comparison: Phi = 89.35 deg Zeta = 90.0 deg E_LO^2 = 0.0238 watts L = 3994.4692 m ls = 56.01 m T SRM = 0.32 T ITMX = 0.015 T ETMX = 5e-06 Pbs = 1417 W Arm Loss = 9e-05 SRC Loss = 0.05 Talking to Dan, the small wiggle at 4 Hz comes from a small MICH offset. Remains to be seen if a larger MICH offset (which could be believable given the ~0.6 degree SRCL detuning we see nominally at LHO), could explain some of these discrepancies.
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btw i found the factor of sqrt(2) it comes from the definition of quadratures in Buonanno and Chen 2001, they define their quadratures like (a(w) + a^*(w)) / sqrt(2). if you want to measure actual sideband power fluctuations at w you have to include the sqrt(2) when returning to real units of watts.