As Rana and Jan suggested, I thought about the effect of mirror's radius of curvature and DC tilt effect to cavity length noise. I ran a few simulation tests and the results were not changing much.
**==cavity length noise== **
The cavity length mainly changes from two effect
1) Actual position change:
2) Tilting of the mirror: If both mirrors tilt up or down together by theta, the cavity length will be longer by R*theta^2, see the attached picture. The calculation takes mirror's ROC and optical axis shifting into account.
So, to find the best place to support the cavity, the contribution from both effects should be minimize.
**==COMSOL Simulation: effects from different boundary conditions==**
We have been discussing about different boundary conditions for support points whether to use fixed in all direction, fixed in only vertical direction, point support, or finite area. So I decided to check the effect from the following condition
- Point like support, fixed in all direction
- Point like support, fixed only in vertical direction
- Area support, fixed in all direction (The size of the area does not change the result that much, see PSL:1061. This time I chose 1mm^2 which is 1.5x10^-3 [in^2].)
** ==result==**
** There are no significant differences among the chosen boundary conditions**. I varied the angle from 30, 45 and 60 degree, all the boundary conditions resulted in the same sagging behavior, so the best choice will be 30 degree as discussed in PSL:xx .The plot below shows the displacement per [m/s^2] of the mirror center along the beam line and tilt angle per [m/s^2] of the mirror, (the support angle is 30degree). With any boundary conditions, the optimum position will be quite the same (30 degree, 1.2" apart).
**==where is the optimum spot? what is the coupling from seismic to cavity length?==**
From the simulation, with our restriction on support position (angle between 30 to 60 degree, 0.5 - 1.2" apart), the mirror positions always extend the cavity length. Since tilt will always increase the cavity length, we cannot cancel the effect between translation and tilt. The best way is to minimize translation and choose zero tilt as before.
About the coupling, at the optimum spot where tilting is zero, there will be no tilting motion. Displacement noise will only come from translation of the mirrors. |