Motivation:

We'd like to know how much actuation is required on the ETMs to lock the DARM degree of freedom. The "disturbance" we are trying to cancel is the seismic driven length fluctuation of the arm cavity. In order to try and estimate what the actuation required will be, we can use data from POX/POY locks. I'd collected some data on Friday which I looked at today. Here are the results.

Method:

• I collected the error and control signals for both arm cavities while they were locked to the PSL.
• Knowing the POX/POY sensing response and the actuator transfer functions, we can back out the free running displacements of the two arm cavities.
  • I used numbers from the cal filters which may not be accurate (although POX sensing response which was recently measured).
  • But the spectra computed using this method seem reasonable, and the X and Y arm asds line up around 1 Hz (albeit on a log scale).
  • In this context,  is really a proxy for  and similarly for L_Y so I think the algebra works out correctly.
  • I didn't include any of the violin mode/AA/AI filters in this calculation.
• Having calculated the arm cavity displacements, I computed "DARM" as L_y- L_x and then plotted its asd.
• For good measure, I also added the quadrature sum of 4 optics' displacement noise as per the 40m GWINC model - there seems to be a pretty large discrepancy, not sure why.

If this approach looks legit, I will compute the control signal that is required to stabilize this level of disturbance using the DARM control loop, and see what is the maximum permissible series resistance we can use in order to realize this stabilization. We can then compare various scenarios like different whitening schemes, with/without Barry puck etc, and look at coil driver noise levels for each of them.