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Entry  Wed Jun 13 19:00:26 2012, Sarah, DailyProgress, Laser, Transfer Functions 12x
    Reply  Fri Jun 22 22:34:28 2012, tara, DailyProgress, NoiseBudget, RIN coupling to Frequency noise 
    Reply  Wed Jun 27 18:51:56 2012, Sarah, DailyProgress, Laser, Transfer Functions Slide1.pngtf_oa_calc_measured.pngTF_allfreq.pngTF_fit_allfreq.pngnb_allfreq.png
       Reply  Fri Jul 6 18:59:49 2012, tara, DailyProgress, Laser, Transfer Functions IMG_1447.jpgRIN_Fnoise.pngRIN_Fnoise.png
          Reply  Tue Jul 10 02:55:37 2012, tara, DailyProgress, Laser, Transfer Functions 
             Reply  Mon Jul 16 19:08:34 2012, tara, DailyProgress, NoiseBudget, Transfer Functions (RIN to Frequency noise via photothermal) 
                Reply  Tue Jul 17 19:05:32 2012, tara, DailyProgress, NoiseBudget, Transfer Functions (RIN to Frequency noise via photothermal) 7x
                   Reply  Tue Jul 24 17:02:35 2012, Sarah, DailyProgress, NoiseBudget, Transfer Functions (RIN to Frequency noise via photothermal) 8x
                      Reply  Fri Aug 3 02:46:15 2012, tara, DailyProgress, NoiseBudget, Transfer Functions (RIN to Frequency noise via photothermal) RIN_coupling_2012_08_03.pngRIN_coupling.fig
                         Reply  Tue Aug 13 21:45:51 2013, tara, DailyProgress, NoiseBudget, Transfer Functions (RIN to Frequency noise via photothermal) farsi_2013_08_13.pngfarsi_2013_08_13.figRIN_TO_algaas.pngRIN_TO_algaas.fig
                            Reply  Fri Aug 16 04:35:58 2013, tara, DailyProgress, NoiseBudget, Transfer Functions (RIN to Frequency noise via photothermal) RIN_req_algaas.pngRIN_req_algaas.fig
                            Reply  Thu Aug 22 13:36:19 2013, tara, DailyProgress, NoiseBudget, Transfer Functions (RIN to Frequency noise via photothermal) fasi_2013_08_22.pngFarsi_compare.fig
          Reply  Wed Jul 11 11:13:38 2012, Sarah, DailyProgress, Laser, Transfer Functions 7x
          Reply  Sun Jul 15 23:20:32 2012, tara, DailyProgress, NoiseBudget, Transfer Functions (power fluctuation to Frequency noise via photothermal effect) Farsi_compare.pngFarsi_compare.fig
             Reply  Thu Jul 19 03:01:26 2012, tara, DailyProgress, NoiseBudget, Transfer Functions (power fluctuation to Frequency noise via photothermal effect) Farsi_compare.pngFarsi_compare.fig
                Reply  Thu Jul 19 23:56:45 2012, rana, DailyProgress, NoiseBudget, Transfer Functions (power fluctuation to Frequency noise via photothermal effect) 
                   Reply  Fri Jul 20 01:32:45 2012, tara, DailyProgress, NoiseBudget, Transfer Functions (power fluctuation to Frequency noise via photothermal effect) 
Message ID: 1027     Entry time: Fri Jul 20 01:32:45 2012     In reply to: 1025
Author: tara 
Type: DailyProgress 
Category: NoiseBudget 
Subject: Transfer Functions (power fluctuation to Frequency noise via photothermal effect) 

1) The coating term is account for thermal expansion only(TE), no thermo refractive has not been included yet.

Farsi treats the effect from TR by assuming that all the TR contribution comes from the first few layers with 180 degree phase different from TE. From their result, TR contribution is much smaller in our frequency band, so I haven't included it in the calculation yet.

2) I agree that our fixed spacer setup will have different result. I'll think about it. Since the coupling is high at low frequency, and the thermal diffusion length is large  ~sqrt(k/C/2pif), which is ~ 1.7 cm [sqrt(1Hz/f)],  (SiO2 material properties) This is certainly comparable to the radius of the mirrors, and any effect on the edge may not be negligible.

Mistake!!, the heat diffusion length is sqrt[ k/ (rho*C*2pif) ] ,  where k is heat conductivity (W/mK), rho is mass density, C is specific heat per kg. This gives 367 um x sqrt(1Hz/f) in fused silica, which is ~ 1.2 mm at 0.1 Hz, and it is still small compared to the mirror's size. Then the boundary condition of our optics might not be as bad as I thought.  I'm thinking about using COMSOL to estimate the effect due to heat escaping from the substrate to the spacer. However, I expect that the boundary effect will help us a bit. The contact area at the spacer will provide additional heat bath for the substrate and reduce the heat at the spot area, thus reducing the thermal expansion effect. Plus, the expansion of the spacer/the substrate at the contact area will be in the opposite direction of that on the spot area. The expansion at the spot area will make the cavity shorter, while the expansion of the spacer/contact area will make the cavity longer. So I think the calculation will still give us the upper bound level, the shape at low frequency ( around 0.5 Hz and below), may change due to the longer heat diffusion length and the boundary effect is not negligible.

Quote:

 

 Does the coating term include the thermo-optic cancellation between thermo-refractive and thermo-elastic? I think you have to use the Evans/Ballmer paper for that (i.e. the GWINC code that I sent you before).

I am surprised if we can use these other papers without modification since the boundary conditions of our optic are fixed. The edge of the mirror doesn't move since its contacted to the spacer. How do you account for that?

 

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