I estimated power recycling gain with the results of arm loss measurement.
From elog 11818 and 11857, round trip losses including transmittivity of ETM of Y arm and X arm (let us call them and ) are 229+13.7=243 ppm and 483+13.7=495 ppm, respectively.
How I calculated:
I used the following formula.
Amplitude reflectivity of an arm cavity :
(see elog 11816)
Amplitude reflectivity of FPMI :
With power transmittivity of PRM and amplitude reflectivity of PRM , power recycling gain is
I assumed , , and , and then I got
PRG = 9.8.
Since both round trip losses have relative error of ~ 4 % and PRG is proportional to inverse square of up to the leading order of it, relative error of PRG can be estimated as ~ 8 %, so PRG = 9.8 +/- 0.8.
According to elog 11691, which says TRX and TRY level was ~125 when DRFPMI was locked, power recycling gain was at the last DRFPMI lock.
Measured PRG is lower than PRG estimated here, but it is natural because various causes such as mode mismatch between PRC mode and arm cavity mode, imperfect contrast of FPMI, and so on could decrease PRG, which Eric suggested to me.
Added on Dec 9
If were as small as , PRG would be 16.0. PRC would be still under coupled.