I use COMSOL to simulate the mirror of RefCav.

I tried only DC heating from the beam. The mirror has finite size, absorbed power is radiated outside.

Next step will be using DC power + small fluctuation.

 The information about dT will be used to calculate phase shift due to thermoelastic and thermorefractive noise.

note about heat3.mph file

 COMSOL 4.0

MIRROR model for PSL
This is a note about file heat3.mph

1) Global definition
     1.1) parameters: most of them are self explanatory. Some that might need
                     clarification are
             a)  p0 is the total power absorbed on the surface
                  which is Power input x absorption x finess/pi 

                  = 10mW x 5ppm x 10^4/pi ~ 1.6 x10^-4 watt

             b) I0, (p0/2pi w^2) Intensity factor of the Gaussian beam, when integrated the
                   intensity over  the area, the total power will be p0

              c) Qin, gaussian beam profile on the mirror

2) Model 1

   2.1) Geometry 1
           a) a substrate with thickness, radius as specified in (1.1)
           b, and so on) multiple coating layers*
              *note: I tried both 3 doublets with 1 cap and effective 5 um coating, but when I mesh the geometry, it's out of memory.
              So I disabled all coatings, and use only substrate. Frank suggested I can reduce the
              mirror's size if the temperature across the surface drops fast enough. I haven't tried that
              *effective coating is a single layer, 5 um thick. Thermal expansion coeff and heat capacity is
               calculated from multiple layers of Ta2O5 and SiO2.
 
          c) Form Union-> choose Form a union then, click "Build All"  

  2.2) Materials
        a) SiO2 (fused quartz): from COMSOL library
             surface emissivity is 0.75 (taken from  <http://www.optotherm.com/emiss-table.htm> and

<http://www.google.com/url?sa=t&source=web&cd=2&ved=0CCIQFjAB&url=http%3A%2F%2Fwww.holanengineering.com%2Fsitebuildercontent%2Fsitebuilderfiles%2Femissivity_1.pdf&ei=JGBgTKr9IIL2tgOPj-ipCw&usg=AFQjCNHFASfDeyG6yvq-FNXuEUShtmH_2Q>

    b) Ta2O5, all parameters are from Evans etal paper.
            Note that the value from Evans' paper,
           the specific heat capacity for Ta2O5 is  2.1 X10^9 [Joule/m^3 kelvin]
             in comsol I defined
                specific heat capacity to be 2.1 x10^9[Joule/kg Kelvin] and,
                 mass density to be     1.0   [kg/ m^3] , so heat capacity per volume is the same.
     c) effective coating's properties from multiple layers of SiO2 and Ta2O5
   thermal conductivity
 
2.3) Heat Transfer(ht)
         a) heat transfer in solid: all domains
         b) thermal insulation : only coatings' edge
        c) initial values: all domains are set at 310 K
         d) boundary heat source: at the topmost surface, Qin is defined in (1.1) (gaussian beam)
         e) surface to ambient radiation: all surfaces except coatings' side
              *for surface emissivity value, I have to choose User difined to be 0.75. I tried "from material"
                but it didn't work even though I add the surface emissivity in material property already, see (2.2)
2.4) Mesh
       - choose free tetrahedral, and specify size as you want, click build all.

3) study
    a) right click on study, select compute. Sit back, relax and enjoy the result.

4) Results
    a) 3d plot group1 shows a 3D picture
    b) 3dplot Group2 shows a slice
    c) 1D temp center axis shows a temperature plot along the center axis