This is an estimate of the required RIN for the CTN experiment, so that Chas can set the appropriate loop gain and shape for the ISS boxes. This estimate relies on computing the equivalent RIN level set by the expected coating Brownian noise of the cavities.

Amplitude spectral density of CTN coating Brownian noise

From figure 6 of the CTN upgrade document (T1200057-v11), the anticipated ASD of frequency noise due to coating Brownian noise is (0.25 Hz/rtHz) / f^1/2.

Calculation of transfer function from intensity to frequency

The spectral density of displacement noise induced by beam intensity flucations was computed by Cerdonio et al. (2001), PRD 63: 082003 (see eq. 24). Based on this, Tara has written Matlab code (PSL:1014) which numerically computes the transfer function of relative intensity noise to frequency noise for a fused silica cavity. Tara and Sarah (2012 SURF student) measured this transfer function using an AOM and one of Tara's 8″ cavities and found OK agreement (PSL:1029); the discrepancy is greatest near 1 Hz, where the calculated transfer function is 6 times higher than the measurement.

Computation of equivalent RIN

To compute the equivalent intensity fluctuations, I've taken the coating Brownian noise spectrum given above and divided it by the RIN-to-frequency transfer function as computed with Tara's Matlab code. [In this code I've replaced 8″ with 1.45″ and upped the finesse from 7500 (measured value) to 10000 (value assuming a transmissivity of 300 ppm and no losses).] I've then divided this by 2 mW (the assumed power incident on the CTN cavity) to get an equivalent RIN corresponding to the coating Brownian noise. This is shown in the second attached figure, along with yesterday's unsuppressed RIN measurement. The first figure shows the intensity-to-frequency transfer function. I've also included the data and code used to generate the plots (some of it is duplicated from yesterday's post).

Based on discussions with Chas, it sounds like we want to stabilize the RIN to be at least a factor of 10 below the equivalent RIN level shown in the second attachment.