aLIGO LHO Logbook

H1 ISC (ISC, SUS)

georgia.mansell@LIGO.ORG - posted 12:51, Tuesday 19 June 2018 - last comment - 12:51, Tuesday 19 June 2018(42572)

ETMX ESD force co-efficient measurement using optical levers

Georgia, Sheila

Summary

I have run a script that dithers the test mass ESD in pitch and yaw, in combinations with and without signal and bias offsets, and looks at the coupling to the optical lever to measure three combinations of the four force co-efficients (alpha, beta, beta_2, and gamma).

I take the transfer functions from pitch, yaw, and bias drive (at a single drive frequency) to pitch and yaw on the optical lever, use the sus model to convert this to Newtons of force on the test mass per volt of ESD drive, and calculate the parameters from this. This follows a similar method to Sheila’s in-lock charge measurements (see alog 38387 and 38608), but looking at the oplev signal rather than DARM.

Results so far

The parameters I’ve measured on ETMX are

	pit	yaw
alpha [N/V^2]	4.0e-9	3.7e-9
beta-beta2 [N/V]	2.0e-7	1.2e-7
gamma [N/V^2]	-4.0e-9	-3.6e-10
V_eff [V]	12.6	8.5

The numbers I calculate for Veff roughly agree with the usual Kissel-style V_eff measurement, the latest results from this I’ll post first thing tomorrow. For some reason I am still trying to pin down these are all off by an order of magnitude compared to the values of alpha, gamma and beta-beta2. I also might have lost track of signs somewhere.

Maths

The force on the test mass as a function of bias and signal (ESD electrode) voltages is given by:

For longitudinal measurements, we could drive bias voltage while changing the offset on the bias. To determine these parameters in pitch and yaw we need to always either drive or offset the signal, as the bias cannot be varied quadrant by quadrant. Hence in this type of measurement we can only determine alpha, gamma, and beta - beta_2.

Driving the bias, with offsets in either the bias or signal, the force on the test mass linear with the drive, , is:

Driving the signal, with offsets in either the bias or signal, the force on the test mass linear with the drive, is:

The measurements required to calculate alpha, beta-beta2, and gamma are:

1.Drive signal, no signal or bias offsets , which applies a force on the test mass:

2.Drive signal, with a signal offset

Non-image files attached to this report

1213040346DrivesLabelled.pdf

1213040346oplevLabelled.pdf

Comments related to this report

georgia.mansell@LIGO.ORG - 21:01, Monday 18 June 2018 (42573)

Link

My log post keeps getting cut off so it continues here:

2.Drive signal, with a signal offset

, which applies a force on the test mass:

3.Drive signal, with a bias offset

, which applies a force on the test mass:

Method

The scripts to drive and analyse this measurement are found at:

opt/rtcds/userapps/trunk/sus/common/scripts/quad/opLevChargeMeasurements

Drives are applied to the signal path through the L3_DRIVEALIGN_P2P_EXC and L3_DRIVEALIGN_Y2Y_EXC channels.

To do a longitudinal beta-beta_2 measurement the bias is excited via the L3_LOCK_BIAS_EXC.

The signal offset is applied to the L3_LOCK_P_OFFSET and L3_LOCK_Y_OFFSET and the bias offset to the L3_LOCK_INBIAS channels.

The matlab script takes the optical lever pitch and yaw outputs, as well as the L3_MASTER_OUT_DC_DQ, and two of the ESD quadrants MASTER_OUT channels, to compute the transfer functions in radians/count.

This is converted to radians/V, accounting for the DAC V/cnt (20/2^18), and the high voltage chassis gain (40, I think this is true of the signal path too as this measurement was taken in high voltage mode).

Finally the transfer function is converted to N/V, using the sus model (from /ligo/svncommon/SusSCN/sus/trunk/Common/SusMogelTags/Matlab) to convert radians to Newtons.

I've attached some hastily made plots showing the time series drives to the ESD bias and two quadrants, and the time series of the optical lever. The pitch has some additional noise that I suspect is coming from an upper stage of the quad. The highest SNR and coherence is found in the signal drive with bias on (unsurprising) but there was very coherence >.95 for the other parts of the measurement. Note that I've just chopped up the parts of the measurement I used to calculate the alpha/beta-beta2/gamma co-efficients and in the actual measurement process I am ramping these signals on and off approriately.