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Entry  Fri Jan 6 12:18:08 2012, tara, DailyProgress, NoiseBudget, Thermoelastic noise from substrate  TE_noise_compare.pngctn_nb.pngcerdonio.png
    Reply  Fri Apr 6 01:07:47 2012, tara, DailyProgress, NoiseBudget, Thermoelastic noise from substrate  corrected.pngbeat_145in.png
Message ID: 901     Entry time: Fri Apr 6 01:07:47 2012     In reply to: 780
Author: tara 
Type: DailyProgress 
Category: NoiseBudget 
Subject: Thermoelastic noise from substrate  

I corrected the code for substrate thermoelastic noise (TE) in my noise budget. The substrate thermoelastic of 8 inch cavity will not be a problem, but it will be comparable to coating thermal noise around 10 Hz for 1.45" cavity.

 

     After reviewing the papers about measurement of thermoelastic noise in substrate, I realized that I have not fixed my calculation for substrate TE as noted in both publications by Numata et al (2003) and Black et al (2004). Apparently, the calculation from Cerdonio et al(2003) uses different notion of beam radius, and misses one factor of pi.  The new result is plotted below. It is about a factor of 1.5 higher than the old one at adiabatic limit (high f), but it is still smaller than the estimated coating thermal noise, see figure 1.

 corrected.png

fig1: TE noise is corrected and plotted in comparison with the previous result.

     However, for a planned 1.45" long cavity, due to the smaller spot size on the mirror, TE noise is very close to the coating thermal noise around 3 Hz up to50 Hz, see figure 2 below. So this will be another issue to keep in mind.  Note: shot noise seems to be very high, I'll double check the result again if it is correct or not. I just changed the cavity length parameter and ran the code to get the result.

beat_145in.png

fig2: Noise budget for 1.45" long cavity.

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