We have done some analysis of the Reference Cavity using COMSOL. We got the design parameters for the reference cavity from [[http://www.ligo.caltech.edu/docs/D/D980670-00.pdf|D980670]]


=== Basic Model Parameters ===
 * '''T = 273 + 38 K''' (reference cavity can is kept at 38 C)
 * Spacer and mirrors made of Corning Fused Silica (7940) - in reality its probably 7980?
 * Uses: Structural Mechanics module, Heat Transfer module, & Materials Library

=== Eigenmodes ===
 1. Remove gravity
 1. No constraints (as if there's no wire)

 [[/EigenmodePlots]]

=== Vertical Sensitivity ===
 1. Constrain the grooves on the bottom in all 3 DOF.
 1. Add a load force on the spacer. F/V = -9.81 * 2200 (comsol likes a force/volume)

Deformation of the cylinder shows the actual shape. Color indicates displacement along the cavity axis.

The displacement of the left mirror is ~0.17 nm. The overall cavity length gets shorter by ~0.35 nm making a strain of dL/L = (3.5e-10)/0.20 = 1.7 x 10^-9^. So the sensitivity of the cavity length to vertical acceleration is ~2 x 10^-10^  / (m/s^2^) or 53 kHz / (m/s^2^). Next we have to consider the limited vibration isolation characteristics of the reference cavities stack and spring pendulum.

For comparison, the Ye/Hall vertical football cavities have a sensitivity of 10-20 kHz/(m/s^2^).
Not such a big difference if it turns out that the measured sensitivity is as good as the model.

[[Sag from Gravity|{{attachment:refcav1.png||height=300}}]]
[[Zoomed color scale|{{attachment:refcav1-zoom.png||height=300}}]]
[[Zoom on one end|{{attachment:refcav1-zoom2.png||height=300}}]]

The sensitivity of the cavity to [[/Horizontal_Accelerations]] (beamline (X) and non-beamline (Y)) are much smaller than the vertical direction.

=== Thermal Noise ===

=== Temperature Noise ===
The reference cavity's vacuum can is actively stabilized with a PID loop of ?? Hz BW. Is it an integrator?

The sensor noise of the AD590 temperature sensors is 40 pA/rHz (according to the data sheet) which corresponds to 40 uK/rHz. If were able to stabilize to this level (which I doubt), the inside temperature fluctuations would then be in the 10 nK/rHz regime because of the passive filtering of the can.

IF true, the strain noise of the cavity spacer would be (10 nK/rHz)*(5e-7 (dL/L)/K) = 5e-15 / rHz. ''This is a LOT more than either the coating thermal noise or seismic noise''.

Here's the measured temperature noise at some random room at the AEI [[attachment:tempnoise.pdf]]. We can assume that the 'ambient' line is typical of a basic room.