Resonant Electromagnetic Modes Research Articles

On the electromagnetic resonant frequencies of the earth ionosphere cavity

The earth ionosphere cavity is capable of supporting resonant electromagnetic modes (Schumann modes) at extremely low frequencies. The usual formula for the frequencies of these resonances is deduced from the waveguide mode theory in which propagation is essentially tangential to the earth's surface. Here an alternative formulation in terms of outwardly and inwardly propagating radial waves is presented and shown to result in the same formula as found from the waveguide mode theory for all reasonable <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</tex> -region ionosphere parameters.

Evaluation of the zeros of cross-product Bessel functions

Computational results for the characteristic values and solutions of Bessel's equation are presented. Specifically, the results pertain to the first two solutions subject to the Neumann boundary condition at r = a,b and to the first solution subject to the Dirichlet condition, when (b-a)/(b+a) is small (0.1, 0.01, and 0.001). Approximate analytic formulas are derived to complement the computational results. The possible application of the data to phenomena involving the interaction of an intense circulating beam and the electromagnetic fields within a particle accelerator is indicated, as is also the utility of the results for estimation of the loss-factor, Q, for resonant electromagnetic modes of possibly high order within a toroidal vacuum chamber of rectangular cross section. (auth)