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Entry  Thu Feb 14 12:38:51 2019, Ching Pin, Mechanics, , comsol modelling Screenshot_from_2019-02-14_12-47-11.pngScreenshot_from_2019-02-14_15-07-40.pngScreenshot_from_2019-02-14_15-41-41.pnggraph.pdf
    Reply  Fri Feb 15 21:05:31 2019, Ching Pin, Mechanics, , comsol modelling Screenshot_from_2019-02-15_21-40-01.png
       Reply  Tue Feb 19 19:52:53 2019, Ching Pin, Mechanics, , comsol modelling Screenshot_from_2019-02-19_19-52-10.png
          Reply  Fri Mar 1 19:33:40 2019, Ching Pin, Mechanics, , comsol modelling Screenshot_from_2019-03-01_19-35-32.pngScreenshot_from_2019-03-01_19-36-02.pngScreenshot_from_2019-03-01_19-46-25.png
             Reply  Mon Mar 4 17:22:07 2019, Ching Pin, Mechanics, , comsol modelling Screenshot_from_2019-03-04_19-13-28.pngScreenshot_from_2019-03-04_19-14-41.pngScreenshot_from_2019-03-04_19-15-37.pngScreenshot_from_2019-03-04_19-15-56.png
                Reply  Wed Mar 6 09:51:18 2019, Ching Pin, Mechanics, , comsol modelling Screenshot_from_2019-03-06_09-31-24.png
                   Reply  Thu Mar 7 10:10:37 2019, Ching Pin, Mechanics, , comsol modelling Screenshot_from_2019-03-07_10-10-47.png
Message ID: 131     Entry time: Thu Feb 14 12:38:51 2019     Reply to this: 132
Author: Ching Pin 
Type: Mechanics 
Subject: comsol modelling 

So I did a simple comsol model of laser heating of a silicon disk, with only radiation, to see the temperature variation at steady state, which could be the limiting factor for high Q at 123 K, due to the thermalelastic effect. 

The model just uses a simple 2 inch disc, at 0.028 cm thick, with the flats not incorporated in yet. 

I had to search for silicon thermal conductivity and heat capacity at low temperatures, settling with k= 800 W/(m K) and C_p= 300 j/(kg K) from refering to papers. Will check LIGO documents for more accurate versions.

I put an arbitary boundary condition of constant temperature of 123 K on a spot .2 mm in radius, to simulate a beam.

Other arbitary values include 77 K for ambient and a surface emissivity of 0.5.

The laser is off center, because that it where the laser will enter the current setup.

We can see that the power required is .02 W, which seems reasonable.

The model is consistent with the analytic model I made with the laser beam at the centre of the disc. See last two figures.


I'm still trying to get the time dependence to work, as it is just giving me nonsense right now. 


Some thoughts: beam radius affects the temperature variation quite significantly, with a fat beam (1 mm radius) having half the temperature variation as a beam of .2 mm radius

I think the halo is just a trick of the eye, but I could be wrong. 


Things to do: 

Find the time scale of the system, as we want to modulate the laser to adjust the temperature, which will then be run though the mode ringer to measure Q to find the zero crossing

Change the heat source to be an actual laser

Add in the solid mechanics part

Add in the sapphire lens underneath

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