I calculated some requirement for the beam jitter at the output of the PMC. A rough estimate shows that we need the angular stability at the PMC about half nano radian so that the frequency noise of the beam locked to the refcav is less than 10^-2 Hz/rtHz.

==Background==

PMC also reduces beam jitters from the laser, so that the beam alignment to the cavity is kept centered. Since the laser is locked to the reference cavity, any misalignment of the input beam will cause the beam to sense the change of the cavity length.

So vibration that shakes the PMC will change the alignment of the output beam. With stiff material, the seismic induced deformation of the PMC will be reduced.

==Calculation==

• calculate the ray tracing matrices from the PMC to the cavity. I assume that only the angle of the output beam changes due to PMC sagging, because of a long distance from the PMC to the refcav, with several mirrors in between. This gives me the position and the angle of the beam going to the cavity.
• find out what is the change of the cavity length (dL), when the input beam is translated by dx, with angle theta.
• convert displacement noise to frequency nosie (dL -> df), as a rough estimate I choose the requirement for df to be less than 10^-2 Hz/rtHz (about the level of the estimated coating noise). This step is not really necessary, but I feel that it is easier to compare the noise in Hz/rtHz unit rather than m/rtHz.
• The required angular stability at the PMC is ~ 0.5 nano rad. This number seems to be too strict. I will double check it.

==next==

Eavn is working on COMSOL to find out the angular tilt of the output beam due to PMC sagging. Optimum support points will be determined to minimize beam jitter due to seismic.