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Message ID: 372     Entry time: Mon Oct 25 21:46:26 2010
Author: tara 
Type: Notes 
Category: NoiseBudget 
Subject: thermal expansion noise due to RIN  
I write up the calculation for thermo elastic noise due to RIN. The result from pure thermo elastic noise is 0.012 Hz at 10Hz.

We are concerned with extra noise due to absorption from RIN in the cavity. Because, currently,
it seems to be the limiting noise source in our experiment.
This extra noise comes in two forms, thermo-elastic (TE) and thermo-refractive (TR), and they
are supposed to cancel each other, although not entirely.

As a starting point, I calculate the effect from TE only.

I use a half-infinite model, with coating thickness d ~4.4 microns.
I treat the multiple-layer coatings as a single layer coating with average thermal properties
between Ta2O5 and SiO2.

*I use the results from this paper,
to calculate thermal expansion coefficients of thin film, and the average
thermal properties of the coating.

I analytically calculate the transfer function of the heat response inside the mirror.
Then I use MATLAB code to plot and calculate the effect numerically.

The result turns out to be very small. It can be either,
I might make some mistake in the code, or
TE effect is small, and we are doomed by TR.

Thank you Greg Ogin for his insight about heat equation.

I'll think about TR next.

DYM: We should strive to make the elog a beautiful easily parsable wonder of the interwebs: it automatically dumps the contents of your .m file, and pdf's should be thumbnailed only when there is a reason to thumbnail them (plots: yes, reports / text docs: no)
Attachment 1: heatRIN.m  5 kB  Uploaded Mon Oct 25 22:47:24 2010  | Hide | Hide all
%% this calcualte the two different medium
%%thermal fluctuation from sine heat
%% Tara 2010_10_23

%coating compound(SiO2 and Ta2O5) thermal properties
k1 = 2.22; %W/mK
C1 = 1.83e9; %J/m^3K
thermal_co1 = 5.8e-6; %(this is calculated outside the code) 
                       % use the result from Evans' paper
%substrate thermal properties, SiO2
... 226 more lines ...
Attachment 2: RIN2.pdf  101 kB  Uploaded Mon Oct 25 23:22:47 2010  | Hide | Hide all
RIN2.pdf RIN2.pdf RIN2.pdf RIN2.pdf RIN2.pdf
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