Jenne, Craig We are wondering why our range did not go up when we increased the power from 30 to 35 watts. Assuming responsivity = e λ / (h c) = 0.858 A/W, I used the 330 Hz PCALY line to find the optical gain today (April 9, 2019) and before the 30 to 35 W power input increase (which happened March 18, 2019):35 W DARM Optical Gain = 3.87 mW/pm 30 W DARM Optical Gain = 3.71 mW/pm Optical Gain Increase = 4.3 %I checked the actual input power measured according to IM4 as well:35 W Input Power = 30.8 W incident on PRM 30 W Input Power = 26.5 W incident on PRM Power Input Increase = 16.0 %We servo the DARM offset to always keep 20 mA on our OMC DCPDs. DARM offset decreases like the sqrt(Antisymmetric Power) increases: Pas ~ DARM offset2:35 W DARM offset = 10.1 pm 30 W DARM offset = 11.0 pm DARM offset Decrease = 8.1 %Checked the power recycling gain:35 W PRG = 45.0 30 W PRG = 46.3 PRG Decrease = 2.8 %According to Kiwamu Eq 11, DARM optical gain goes likedPas/dLDARM = 8 * k2 * Input Power * DARM offset * PRG * Signal Recycling Gain * Arm Reflectivity Derivativewherek is the wave number 2π/λ PRG = (tPRM/(1 - rARM * rPRM))2 SRG = (tSRM/(1 + rARM * rSRM))2 Arm Reflectivity Derivative = drArm/dφ = ( tITM2 rETM / (1 - rITM rETM)2 )2DARM Optical Gain goes linearly with PRG, DARM offset, and Input Power. From the changes above, we find our DARM optical gain should have increased by around 4 %. This is pretty much what we see. So why didn't the range increase? My guess is, it did, but on the night of the power increase we didn't see any immediate improvements due to bad spot positions and TCS for higher power. Later with the calibration changes and other commissioning tasks happening at the same time we got confused about what our range really was. In any case, we did win with the power increase (after ~month of ASC/TCS commissioning), and we have no reason to believe that going up further would not help us.
Craig and I have also been looking at what we expect our optical gain to be given what we know about our interferometer.
One thing to recall (thank you Sheila for finding this factor of 2!) is that we usually call DARM (Lx-Ly), but Kiwamu's equations are based on a DARM definition of (Lx-Ly)/2. In our usual notation, our DARM offset is roughly 10pm, but in the Kiwamu notation it is 5pm. This factor divides out when looking at an optical gain ratio as Craig does, but is important for trying to calculate the expected optical gain.
In the 'more typical' DARM notation that we use, Kiwamu's derived equation becomes:
Also of note is that this equation doesn't include any output losses, such as transmission through the OFI, mode matching to the OMC, and perhaps unknown others, which I will include to give a more realistic estimate of our expected optical gain.
If we say that the power circulating in the arm cavities is given by
P_arm = P_in/2 * J0(Gamma1)^2 * J0(Gamma2)^2 * PRG * arm reflectivity derivative, we can solve for the arm reflectivity derivative (difficult to directly measure) in terms of measured power circulating in the arm (easier to directly measure). This lets us compare our expected optical gain and that measured in Craig's alog.Rewrite: dP_as / dL_DARM = 2 * k^2 * P_in * DarmOffset * PRG * SRG * J0(Gamma1)^2 * J0(Gamma2)^2 * OutputLosses * (2 * P_arm / P_in * 1/PRG * 1/J0(Gamma1)^2 * 1/J0(Gamma2)^2 )^2
k = 2*pi/1064e-9 1/m
P_in = 31.3 W (injected to PRM measured by IM4 trans, when 35W injected to vacuum)
P_arm = 184 kW (average of our 2 arms, alog 47722)
DarmOffset = 10.1 pm
Gamma1 = 0.160 (alog 47113 for 9 MHz)
Gamma2 = 0.182 (alog 47113 for 45 MHz)
T_etm = 3.85 ppm (power transmission, average of 2 ETMs from as-built page)
T_itm = 1.46 % (power transmission, average of 2 ITMs from as-built page)
T_prm = 3 % (from as-built page)
T_srm = 32.34% (from as-built page)
Loss_arms = 75 ppm (we don't have a good measurement of this, so using a value that gives a PRG of 44.5)
Calculated PRG = 44.5
Calculated SRG = 0.09 (Assumes R = 1-T, L_SRC = 0)
Power reflectivities of the arms are R = 1 - T - Loss/2, so that I am splitting the total loss in the arm between the ITMs and ETMs. Somewhat arbitrary, doesn't really change things if I put all the loss on the ETMs.
The OutputLosses is somewhat hard to say what they should be. If I say that the SRG is only 70% of the ideal, and we have an additional 20% in losses from the SRM to the OMC and in OMC mode matching, then I get an optical gain value of 3.88 mW / pm, which is very close to Craig's measurement of 3.87 mW/pm. But, that seems like a lot of losses at our output. If instead I say that our losses are perhaps more realistic, with SRG 80% of ideal, and 10% extra losses from SRM to OMC and in OMC mode matching, then I get an optical gain value of 4.99 mW / pm, which would imply that we're missing about 30% of our potential optical gain.
Things also start to get a bit tricky with such a big change in optical gain, since we servo our DARM offset such that the OMC DCPDs see 20 mA of photocurrent.
Unfortunately, not having a very good idea of a number of output losses means that I don't really have a good conclusion here on how much optical gain we're missing out on due to (potentially) non-optimal spot positions in the arm cavities, which means it's hard to say what we might gain in range with (potentially) better spot positions.