Exact Solution for the Eigenfrequencies of a Microwave Cavity Partially Filled with a Magnetized Plasma

Pure TE and TM waves do not, in general, exist in a microwave cavity partially filled with a magnetized plasma. The scalar wave equations are coupled (the equation for Ez has a term involving Hz and vice versa). Uncoupling of the two equations results in two fourth-order wave equations which are biquadratic. The solution of this equation can be obtained by factoring the fourth-order expression into the product of two second-order wave equations. The result is two solutions for Ez and Hz. From these terms, all other field components may be found. A set of six boundary conditions on the field components gives a determinantal expression for the eigenvalues. These can be presented in mode chart form and show the splitting of degenerate modes along with resonances at the electron-cyclotron frequency. The technique is applicable to any form of the dielectric tensor if it can be specified in complex notation.