[Yokozawa, Ushiba, TYamamoto, Komori]

Abstract:

We designed a new PRCL filter to suppress residual PRCL displacement and improve the DARM sensitivity.
While the new filter successfully allowed us to reach the observation state, the DARM sensitivity remained unchanged.
The noise observed in the DARM sensitivity around 20 Hz is likely due to direct coupling from PRC angular motion, rather than through PRCL displacement.

Our Trial:

Motivated by the possibility that PRCL-to-DARM coupling could limit the DARM sensitivity broadly around 20 Hz (klog:33357), I designed a new PRCL filter following the concepts outlined in klog:33419.
I prepared the filters for the three states, the PRMI 3F, transition to 1F, and observation.
However, in our first attempt, the lock failed at the PRMI 3F stage (klog:33425).
To address this, I modified the filters so that the initial filter for PRMI 3F locking closely resembles the conventional one, while the final filter for the observation state remains aligned with the newly designed filter from klog:33419.
With this update, we successfully reached the observation state using the new filters.

Measurements of the PRCL open-loop transfer function (OLTF) and closed-loop transfer function (CLTF) were consistent with our design (Fig.1 and Fig.2).
Please note that a gain adjustment of 0.6 dB and a time delay of 0.48 ms were applied to align the modeled curves with the measurements.
We also modeled the PRCL-to-DARM coupling, assuming radiation pressure coupling at low frequencies and a phenomenological constant coupling at higher frequencies (Fig.3).
This coupling model was used to project PRCL displacement into the DARM sensitivity.

I expected the PRCL contribution to DARM noise to improve from the level shown in the blue curve to that shown in the cyan curve in Fig.4, after applying the new filter.

Results and Discussion:

Despite successfully engaging the new filters, the DARM sensitivity showed no improvement (Fig.5).
This suggests that the noise around 20 Hz is likely due to angular motion of the PR mirrors, rather than displacement through PRCL.
The angular motion may be directly coupling into the DARM signal, not through PRCL.
As a result, the PRCL spectrum itself is likely dominated by angular motion, which cannot be suppressed via displacement feedback.

Further evidence of this is seen in the change in the PRCL sensitivity before and after applying the new filter (Fig.6).
This variation should not occur, as the current calibration method is filter-independent.
This inconsistency supports the idea that the PRCL spectrum is contaminated by motion from other degrees of freedom.

Given these results, We propose reverting to the conventional PRCL filter and focusing on reducing angular motion in the PRC by optimizing local control filters.