Jenne, Peter, Jeff, Terra
We took charge measurements on the ITMs by driving 20.1 Hz into H1:SUS-ITMX/Y_L3_DRIVEALIGN_L2L_EXC with 100k cts and looked at the coupling to DARM. We stepped up and down the ESD bias voltage from zero and found the bias that gave zero coupling to get charge measurements, where Vcharge= (20/218) * bias * 40. ITMX zeroed with bias = 3k, ITMY zeroed with bias = 2.5k. See bias stepping ITMX and ITMY spectra attached.
ITMX charge: 9.15 V, ITMY charge: 7.6 V
ITMX:
| BIAS offset | RMS AMPL (m) | PEAK AMPL (m) | PHASE (deg) |
|---|---|---|---|
| 0 | 4.9x10-15 | 6.9x10-15 | 37 |
| 50K | 7.6x10-14 | 1.1x10-13 | -142 |
| 100K | 1.6x10-13 | 2.6x10-13 | -142 |
| -50K | 8.5x10-14 | 1.2x10-13 | 38 |
| -100K | 1.7x10-13 | 2.4x10-13 | 38 |
ITMY:
| BIAS offset | RMS AMPL (m) | PEAK AMPL (m) | PHASE (deg) |
|---|---|---|---|
| 0 | 5.4x 10-15 | 7.6x10-15 | -142 |
| 50K | 9.3x 10-14 | 1.3x10-13 | 38 |
| 100K | 1.9 x 10-13 | 2.7x10-13 | 38 |
| -50K | 1.0 x 10-13 | 1.4x10-13 | -142 |
| -100K | 2.0x 10-13 | 2.8x10-13 | -142 |
Approximating alpha: The first term in the expression for the force produced by the ESDs is the attractive force between the ESD fringe fields and the test mass: F = alpha(Vbias - Vsignal)2, where alpha is a constant of proportionality. With the known bias voltage Vb, signal drive voltage Vs, drive frequency f, and now the peak amplitude xpp , we used the largest bias offset (100k) to approximate alpha for both ITMs. Work is attached.
ITMX: alpha = 1.78 x 10-11 N/V2, ITMY: alpha = 1.85 x 10-11 N/V2
These LHO ITM force coefficients agree with LLO's. Using Valera and Den's 2015 measurements (and assuming an 80 Hz ESD drive), I calculated alpha for LLO ITMX: alpha = 1.46 x 10-11 N/V2