I took Aidan's COMSOL model for the ITM from a couple years ago and updated it with some more details:

1. Through radiative cooling only, the ITM is cooled to 103 K. Taking it to 123 K will be accomplished by adding a ring heater to the ITM.
2. Assume 3 W of heating from main laser beam onto ITM HR face.
3. Emissivity of ITM barrel is 0.95. Emissivity of HR* and AR faces is 0.5.
4. The CP and the Inner Shield are kept fixed at 80 K. This is to simulated the effect of having conductive cooling with cold straps. This needs to be checked in more detail by actually modeling thermal straps.
5. Emissivity of the CP is 0.9.
6. The total length of the inner shield is 5 m. The CP is at z = 0 m and the ITM is at z = 2.25 m. We should check what the result would be if the shield is ~1m shorter or longer.

In the attached image, I have made one quadrant of the tubular cryo shield transparent just for clarity - the actual modelled tube is 3 cm thick, made of aluminum, has an emissivity of 0.95 on the inside and 0.03 on the outside (to simulate what we would get from polished aluminum or gold coating).

This files is in our GitLab: https://git.ligo.org/rana-adhikari/CryogenicLIGO/blob/master/FEA/ITM-ColdShield-CP.mph

*I am suspicious of just using a single emissivity number for the AR and HR coatings. Since we are concerned with wavelengths which are long w.r.t. the coating thickness, it may be that the HR and AR coatings have a complicated wavelength dependence in the 5-50 micron band.