I realized that we have not checked the eigenmodes of 1.45" cavity yet, so I used comsol to find out several modes. The lowest mode is ~ 46kHz, and the first longitudinal mode is about 60kHz. The frequencies are high enough so that the thermal noise calculation in dc- 10kHz frequency band can be done with quasi-static assumption.

1) I tried a simple cylindrical shape, with the dimension of the spacer. The result for the first longitudinal mode is 74KHz, the analytical result is ~ 77kHz, see PSL:1135. It seems that COMSOL's result and the analytical results are comparable.

2) Then I simulated the whole reference cavity. The lowest body mode is ~ 47kHz. The body expand-contract radially, and should not change the cavity beamline length that much. The first longitudinal mode is ~ 60kHz. The color on the surface shows the rms displacement from all direction.