Eigenvalues of a Microwave Cavity Filled with a Plasma of Variable Radial Density

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Abstract
A solution to the eigenvalue problem of a cylindrical plasma of variable radial density placed coaxially within a cylindrical cavity has been obtained. The solution is based on a model constructed by dividing the plasma into a series of concentric shells, in each of which the plasma density is assumed to be constant but not necessarily equal to that of any other shell. Maxwell's equations are solved exactly for the electro‐magnetic fields in each shell. The boundary relations at the inner and outer surface of each shell and at the cavity walls result in a set of simultaneous equations which may be solved numerically for the eigenfrequencies if the cavity dimensions, number of shells, and density in each shell are specified. For a given density profile, which may be obtained from experiments, the frequency shift of the system for a given mode may be determined as a function of the density of the central shell. A 10‐shell model has been used to solve for the frequencies of the first 10 modes of a cylindrical cavity.