The Computation of the Frequencies and Fields of a Cavity Resonator Containing a Magnetoplasma Dielectric

摘要

The computational procedures for obtaining the resonant frequencies, spatial parameters, and fields of a cavity resonator containing a cold, uniform, collisionless magnetoplasma dielectric are presented. The calculation of frequencies and spatial parameters involves the simultaneous solution of three equations. Two equations are rational in the three variables, and the third is transcendental in two of the variables. The transcendental functions have infinitely many real zeros and poles. An analysis is given to determine ranges of values of the spatial parameters and regions in the space of plasma parameters and frequency where solutions may exist. The method of solution starts with a trial value of frequency, the calculation of corresponding values of spatial parameters from two of the equations, and observation of the sign of the third function. A solution is determined by a change of sign of the third function. The transcendental functions are quotients of Bessel functions, and they are economically computed from continued fractions. The spatial paremeters enter into the field expressions as part of the arguments of Bessel functions. These functions, which have complex arguments, are computed from integral formulas. (Author)