The present aim is the calculation of the TE noise like Liu and Thorne. Although, the results of Liu and Thorne are for the case of an infinite mirror, in our case, we try
to model a test mass with large dimensions in an attempt to get closer to the result due to Liu and Thorne
Following my previous post - The presents results given by the COMSOL simulations gave the same profile as Liu and Thorne's result which has a frequency dependence
of 1/omega^2 but was displaced from the analytic result by a constant factor which was dependent on the applied pressure on the face of the test mass which should not be
the case.
Following the steps followed Liu and Thorne, we had constructed the test mass as a cylinder, large compared to the beam spot size. An oscillating pressure was applied
to one of the faces and the from the temperature gradient generated in the process due to strains, one can calculate the work dissipated. The process involves integrating
the gradient of temperature over the entire geometry and taking the time avrage. However, this did not give the correct results, so it was decide to extract the Fourier coefficient
of the signal and perform the integration on it, as done in the case of TR niose by Koji Arai.
I mention the steps it was done -
> The data extracted was stored in a 3D array in matlab. using mphinterp - each dimension for r, z, t
> The number of radial slices and z slices is defined by the user previously
> For each r,z value there was a time signal.
> The fourier coefficient corresponding to the pressure oscillation frequency was extracted from the last three cycles
(In theory only one cycle should suffice)
> The above step was done so that random data( which is small in magnitude) generated by COMSOL is avoided.
> The fourier coefficients are stored in a 2D array corresponding to r and z values.
> The integration was performed using trapz twice once on each dimension to get the total volume integral
> The rest of the calculation is same as the previous script - plugging in the prefactors in the formulae and plotting
**The primary problem with this script is that the data extraction takes significant amount of time - For a mirror with 200 times the radius of the beam spot and 200 radial slices, it takes close to 6 minutes
to evaluate work dissipated for each frequency. The script solves for 16 frequency values. The results for small number of radial slices does not follow the straight line profile. For larger number of slices
the program takes a longer time. The results have not been checked yet. |