Sheila, Alexa, Evan
Summary
We have transitoned CARM from digital normalized REFLAIR9I to analog REFLAIR9I, with a 4 kHz bandwidth and 50 degrees of phase. An OLTF is attached [the last data point is spurious, so ignore it]. This lock started at about 2015-02-09 12:24:00 UTC. We are leaving the IFO locked.
There is plenty of phase to push the bandwidth higher, but we have encountered large offsets induced by switching on the common-mode and summing-node boards.
We can also improve the low-frequency fluctuations of the CARM error signal by introducing an integrator somewhere; we need more dc gain.
Details
Analog REFLAIR9I is plugged into input B2 on the summing-node board (SNB), with polarity "off". The output of B goes into input #2 on the common-mode board (CMB), with positive polarity. Digital normalized REFLAIR9I is plugged into input A1 on the SNB, with polarity "on". The output of A goes to input #1 on the CMB. [See LHO#16489 for a review.]
According to our reckoning, the shape of the digital CARM loop at the start of the transition is roughly 1/f above a few hertz. At a few hertz and below, it has a number of boosts and integrators which make it tricky to engineer a stable crossover with the analog signal.
Transition procedure is as follows, starting right after the guardian has brought the interferometer into resonance.
- With the B2 gain at 0 dB on the SNB, input B2 engaged on the SNB, and the input #2 gain at 0 dB on the CMB, we engage input #2.
- Step up B2 gain to 8 dB on the SNB.
- Turn off double integrator in digital CARM path (FM2 in REFLBIAS: it is two zeros at 2 Hz and two poles at 0.01 Hz).
- Step up B2 gain to 14 dB on the SNB.
- Remove zero-pole pair in digital CARM; it is a 1.6 Hz pole and 20 Hz zero. We remove this pair by engaging FM1 on REFLDCBIAS.
- Step up B2 gain to 17 dB on the SNB.
- Engage analog compensation filter in the CMB. It is a pole at 40 Hz and zero at 4 kHz.
- Ramp down digital CARM gain all the way to zero using the input matrix.
- Increase the analog CARM gain by 10 dB using the CMB slider. This is the point at which we saw disconcertingly large offset jumps. The total jump was 6 ct of REFLAIR_A_RF9_I_NORM. For comparison, the peak-to-peak fringing of this signal during digital CARM is 6 ct pkpk.
- We also saw a huge offset jump when turning off A1 on the SNB, which analogizes the digital CARM loop. In retrospect, this is probably because we had an integrated history on the output of this loop (since we turned the loop off at the LSC input matrix, not at the loop's output).
- To tune the error signal offset to zero, we have shifted around the common offset slider on the CMB
Also, the use of DHARD WFS (pitch and yaw) has removed the need for touching up the ETMs. However, since the AS36Q WFS feedback to the BS has not worked for the past couple of days, the BS had to be touched up by hand every so often.
In fact this lock lasted about 2.5 hours.
The lock broke due to a ~ 5kHz oscillation in the CARM loop (first plot). The second plots shows several locking attempts from last night. The drop in the sideband power observed during the first long lock last Friday , correlated with the increase of the carrier build-up during acuqisition, is not present anymore now that the locking sequence is much faster, so it might have been some thermal-induced effect. The third plot shows the trend of the power recycling sideband and carrier power, whose fluctuations are well correlated with angular PIT motion of the BS (ASC BS loops not yet closed, as Evan was saying).
Here are some numbers for arm buildup on resonance, recycling gain and stored arm power for last night's lock:
-IMC input power was 2.81W. Given modulation depths of Γ9 = 0.219(12) and Γ45 = 0.277(16), from alog 15674, the power in the sidebands is (Γ92+Γ452)/2=6%, there was 2.64W carrier power into IMC. 88% of this power is transmitted through the PSL-IMC-Faraday chain to PRM as measured in alog 13495.
-Arm buildup (X-arm) was 1200 x single arm power (1210 at the beginning of the lock). LSC-TR_X_QPD_B_SUM_OUTPUT was an average of 1035(10) cts during the lock stretch. This QPD is already roughly calibrated to arm buildup, but can be corrected for new input power levels as per Evan's alog 16450, so [arm buildup]=TR_X_QPD_B_SUM_OUTPUT*(10.95/2.82)*(3/10).
-Recycling gain was 36 W/W. [Recycling gain]=[arm buildup]/[PRM transmissivity], assuming PRM transmissisivty of 2.97% from galaxy page.
-X-arm cavity gain is 276 W/W. G_arm=( ti / (1-ri*re) ) ^2. Transmissivities Ti=1.39% and Te=3.6ppm according to galaxy webpage. re=sqrt(1-Te-Le) where Le is the x-arm loss is assumed to be 120(30)ppm based on alogs 16082, 15937, 15919.
-Power stored in the X-arm was 11.5kW. P_arm=[carrier power into PRC]*[recycling gain]*[0.5 (beamsplitter)]*[arm cavity gain]=2.64*0.88*36*0.5*276.
I made a typo in the equation for recycling gain, which should read: [Recycling gain]=[arm buildup]*[PRM transmissivity]