I did the calculation to estimate the required power for heating up the cavity by 20 K above room temperature. More details are coming.
Since we plan to tune the beat frequency by tuning the cavity length with thermal expansion, we need to know how much power is needed to heat one cavity up by 20K above room temp (see LIGO-1200057 for more detail).
To simplify the calculation, I use 2-D model for the cavity and the shield. Assuming the system is in equilibrium. In the calculation, I considered the effect from reflected radiation from both the shield, and the cavity itself.