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Entry  Thu Jan 31 14:00:00 2013, Kristen Holtz, Notes, PMC, PMC Longitudinal Testing and Modal Analysis PMCphoto_circclamps.JPGPMC_ringdown_Jan28.JPGPMC_unconstrainedringdown_Jan28.JPGPMC_Excitation_Diagram_1-28-13.JPG
    Reply  Wed Mar 27 01:52:34 2013, tara, Notes, PMC, PMC Longitudinal Testing and Modal Analysis pmc_eigen.png
       Reply  Sun Mar 31 03:03:28 2013, tara, Notes, PMC, PMC Longitudinal Testing and Modal Analysis psl_log.pngpsl_log2.png
          Reply  Sun Mar 31 14:42:05 2013, Evan, Notes, PMC, PMC Longitudinal Testing and Modal Analysis 
             Reply  Sun Mar 31 20:06:16 2013, tara, Notes, PMC, PMC Longitudinal Testing and Modal Analysis 
       Reply  Mon Apr 1 20:59:19 2013, tara, Notes, PMC, PMC Longitudinal Testing and Modal Analysis 
          Reply  Thu Apr 4 23:55:12 2013, Evan, Notes, PMC, PMC Longitudinal Testing and Modal Analysis mirrorsag_coarse.pdfmirrorsag_fine.pdf
    Reply  Thu Apr 4 11:44:14 2013, Evan, Notes, PMC, 270 Hz clamped PMC twisting mode pmc_clamp_twist_mode.jpg
Message ID: 1141     Entry time: Thu Apr 4 23:55:12 2013     In reply to: 1137
Author: Evan 
Type: Notes 
Category: PMC 
Subject: PMC Longitudinal Testing and Modal Analysis 


These are plots of the sagging of the front and back mirrors as a function of the longitudinal positions of the mounting holes (these positions are measured from the back of the PMC). The first plot is a coarse search, and the second is more targeted toward a region of lower sagging.

I generated these plots by taking Tara's Comsol model of the PMC body, assigning fixed displacement to the three mounting holes, and assigning a body load to the PMC body equal to the weight of the steel. Then, I extracted the displacements of four points on the front edge and four points on the back edge of the PMC borehole (these edges are where the faces of the mirrors will make contact with the body). I then took some cross-products with these points in order to get the unit normals that would result when the mirrors are placed against the deformed body. I then compute the angle between the deformed unit normals and the undeformed unit normals to get the sag of the mirrors in radians.

I'm a bit uneasy about how precision is handled in the Comsol/Matlab combination used to generate these plots. The Comsol GUI has no problem reporting displacements all the way down to 10^-24 meters, but anything smaller than 10^-15 meters or so gets truncated to exactly 0 when the results are reported in Matlab. When propagated through to the sagging computation, this means any sagging smaller than 10^-8 radians or so also gets rounded to exactly 0. You can see in the second set of plots that there are large swaths of exactly the same light blue and periwinkle, which seems to indicate a low level of precision in the computation. There's probably some obvious Comsol/Matlab setting that I'm missing, but I haven't been able to find it so far.

Regardless, it appears there is an optimum range of hole placements for the PMC body: 10 cm for the front holes and 3 cm for the back holes, give or take a centimeter or so.


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.


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.


  • 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.


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.

Attachment 1: mirrorsag_coarse.pdf  225 kB  | Hide | Hide all
Attachment 2: mirrorsag_fine.pdf  228 kB  | Hide | Hide all
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