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Time‐Dependent Green's Function for Electromagnetic Waves in Moving Conducting Media

### Abstract

This paper treats the problem of radiation from sources of arbitrary time dependence in a moving conducting medium. The medium is assumed to be homogeneous and isotropic, with permittivity ε, permeability μ, and conductivity σ, and to move with constant velocity v with respect to a given inertial reference frame. v may have any value up to the speed of light. It is shown how the Maxwell‐Minkowskiequations for the electromagnetic fields in the moving medium can be integrated by means of a pair of vector and scalar potential functions analogous to those commonly used with stationary media. The wave equation associated with these potential functions is derived, and an associated scalar Green's function is defined. The solution for the Green's function is obtained in closed form, by means of a technique making use of the relation between the fundamental solution of a radiation problem and that of a corresponding Cauchy initial‐value problem. The resulting Green's function is found to consist of an oblate spheroidal shell, similar to that which occurs in a lossless medium, plus a residue which persists after the shell. In addition, the Green's function is exponentially damped in both space and time, an effect not present in a lossless medium.

© 1968 The American Institute of Physics

Received 15 March 1967
Published online 21 December 2004