[Ushiba, Komori]

Abstract:

The combined contribution of coil driver noise, suspension horizontal thermal noise from sapphire fibers, and thermal noise coupling from the pitch mode of blade springs may explain the current DARM sensitivity observed in the 60–100 Hz range.
To confirm this estimation, it is essential to measure the Q-values of the sapphire fibers and blade springs, as well as the beam mis-centering.

Details:

Inspired by the coil driver noise estimation described in klog:31771, I have calculated the combined effect of this noise and the current suspension thermal noise.
The coil driver noise was estimated under the following conditions:

- Output voltage noise (V/√Hz):
In the current observation state, one dewhitening filter (the one closest to the DAC) is active for all four test mass actuators.
Therefore, the thermal noise from two 16 kΩ resistors directly drives the test masses.
The output voltage noise can thus be calculated as √(4*kb*T*R)*2 ~ 2.3e-8 V/√Hz per test mass.
This calculation aligns with the three 16-kΩ resistor thermal noise model described in klog:31771.

- Actuator efficiency (N/V):
The actuator efficiency, given in units of N/A, was measured as 2 mN/A in the cryostat design paper.
Considering the combined resistance of 80 Ω in the coil driver (as per the coil driver design) and 17 Ω in the coil itself (per the actuator summary in the JGW wiki), the actuator efficiency in N/V is approximately 2e-3/97 ~ 2.1e-5 N/V.

- Mechanical susceptibility (m/N):
The test mass is modeled as a free mass with a susceptibility of 1/(mw^2), where m is mass of the test mass (22.8 kg).

For the suspension horizontal thermal noise and pitch coupling from the blade springs, the following parameters were assumed:

- Horizontal Q-value of sapphire fiber:
The mechanical loss is assumed to be dominated by thermo-elastic loss, consistent with the estimation from the line width of the first violin mode (klog:25080).
The assumed Q-value is approximately 1e4.

- Pitch Q-value of blade springs:
Based on previous measurements (klog:25931), the average Q-value of the ITM pitch mode is 7e3.

- Beam spot mis-centering:
A mis-centering of 1 cm was assumed, based on the square root of the quadratic sum of the mis-centering across the four test masses.
This value is reasonable given the intentional vertical beam spot offset on the ITMs.
For reference, the beam radius at the test masses is approximately 3.5 cm.

Using these assumptions, I created a plot (attached) showing the contributions of the three noise sources to the DARM sensitivity.
The coil driver noise, suspension horizontal thermal noise, and pitch coupling noise from blade springs all contribute almost equally to the DARM sensitivity in the 60–100 Hz range, with their combined total closely matching the measured spectrum.

To improve the accuracy of this estimation, it will be necessary to directly measure the Q-values of the sapphire fibers and blade springs, as well as quantify the exact amount of beam mis-centering.