As part of the design of an experiment, I am trying to model the magnetic fields inside a hollow rectangular waveguide cavity. I have not had any problems calculating the cavity physical dimensions for the desired mode and resonant frequency, and I have obtained equations for the electric and magnetic fields. $$ \mathrm{For\;reference\;:\;}\begin{cases}f_c=2.87\;\mathrm{[GHz]}\\\mathrm{Cavity\;dimensions\;}(a\cdot b\cdot d)=7.39\cdot5\cdot7.39\;\mathrm{[cm]}\\\mathrm{Mode\;TE_{101}}\end{cases}$$
$$\mathrm{Fields\;\;:\;}\begin{cases}E_x=0\\E_y=-2 j f_c \mu a H_0\sin\left(\frac{\pi x}{a}\right)\sin\left(\frac{\pi z}{a}\right) \\E_z=0\\H_x=-H_0 \sin\left(\frac{\pi x}{a}\right)\cos\left(\frac{\pi z}{a}\right)\\H_y=0\\H_z=H_0\cos\left(\frac{\pi x}{a}\right)\sin\left(\frac{\pi z}{a}\right)\end{cases}\;\;\;\;\mathrm{with}\;\;h^2\equiv \left(\frac{\pi}{a}\right)^2+\left(\frac{\pi}{b}\right)^2$$
My problem is that these equations have the field amplitude $H_0$ as a free parameter, where I would like it to be determined by the power injected into the cavity. I imagine that the assumption of perfectly conductive walls has to be discarded, to account for the fact that power is being continuously injected and dissipated.
Is there an analytical method to calculate the field amplitude inside a resonant cavity from the injected power, or would this require numerical simulation using HFSS or similar finite-element modeling software? I am looking for ballpark, order-of-magnitude values, not exact results.
