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The Wave Equation and the Green's Dyadic for Bounded Magnetoplasmas

### Abstract

In studies of electromagnetic wave propagation and radiation in magnetoplasmas, the wave equation takes the form of a dyadic‐vector Helmholtz equation. The investigation here shows that the dyadic‐vector Helmholtz equation is solvable by the separation method in four cylindrical coordinate systems. Solutions in the form of complete sets of eigenfunctions are possible when boundary surfaces are present. For problems involving current sources in the plasma, the Green's dyadics for finite or semifinite domains can be constructed from the complete sets of eigenfunctions which are solutions to the homogeneous equation. The Green's dyadic for infinite domain is also shown to be obtained from that for a semifinite domain through a limiting process.

© 1964 The American Institute of Physics

Received 04 February 1964
Revised 24 April 1964
Published online 22 December 2004