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Message ID: 898     Entry time: Wed Apr 4 23:58:43 2012
Author: tara 
Type: Notes 
Category: NoiseBudget 
Subject: thermal noise from spacer + support  

Following the calculation from Kessler, I estimated brownian noise from the spacer and the o ring support from our setup. From the cursory check, it seems that we don't have to worry about both sources too much.

      Kessler et al. refined the calculation for brownian noise of a spacer from Numata's et al and included  Brownian noise of viton supports. For spacer's noise, they corrected the result for a cavity with a hole along the cavity's axis, and also did the FEA simulation with COMSOL for the mirrors that are smaller than the diameter of the spacer. For their chosen geomtry, the noise from the spacer, as obtained from FEA, can be 30% larger than the analytical result.

    So, as a quick check for our cavity, I used their analytical result and increased the result by 30% to get an estimate. The new spacer noise is about an order of magnitude below the coating noise, so it should not be a problem.

    For viton noise calculation, they assumed a 4-point supported cavity, and calculated the energy stored in shear deformation, then used fluctuation-dissipation theorem(FDT) to compute the displacement fluctuation. However, our cavity is supported by two o-rings wrapping around the cavity's groove and sitting on two  U-shape teflon pieces. I don't know the exact thickness of our o-rings, so I use (1/8)" = r_o . Assuming that the surface area is  pi* cavity's radius * r_o *sqrt(2), and thickness of the o ring under pressure = 1.5 r_o. [add pic], I can get the noise contribution from the support. Parameters for O-rings' are assumed to be the same as those of viton in the paper. The result is about the same as substrate's Brownian noise, which is not very threatening for our experiment. I believe that the actual number will be even lower, since my estimation exaggerates, to get the upper bound, the surface area of the o ring to be half of the spacer's perimeter times the ring's thickness. The actual shear deformation should be localized in smaller area.

 Parameters for our cavities can be found here.




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