We measured test mass L2P to L3P and L3P to L3P transfer functions with high resolution (0.01 Hz bandwidth). For the convenience of modeling, we also fitted the measurements in zpk forms.

The measurement results and the fitted tfs are attached as figures. The zpk representation of the p2p tfs are attached as text files. Here we have scaled the DC level of each tf so that its magnitude should be in [rad / Nm]. We also used this information to update the L3P/L2P filter (i.e. FM2) in ASC-PRC_D/CHARD_P.

To generate a plant modified by the Sidles-Sigg radiation pressure torque, we can use the simple formula

       Plant_n (P_arm) = Plant_n (0W) / [1 + R(P_arm) * Plant_L3 (0W)]

where:

       Plant_n (P_arm) is the Sidles-Sigg modified SUS TF (P or Y) from stage n (L2 or L3) to L3 evaluated at (P_arm) W of circulating power in [rad/Nm]

       Plant_L3 (0W) is the L3 stage A2A TF at 0 W (i.e. free pendulum)

       R(P_arm) = -2 * P_arm/c * dy_dth * Plant_L3 (0W), with dy_dth = -4.5e4 [m/rad] for the hard mode, and +2.1e3 [m/rad] for the soft mode for aLIGO geometry.