Abstract
The problem of representing electromagnetic fields in an electron plasma subjected to large and rapid electron-density variations due to transient ionization processes is considered. The inherently nonlinear character of this problem, which arises in the Maxwell-Euler equations through the electron transport term ▿· (nV), is retained under the assumption that temporal variations of the electron density n are of first order in magnitude while spatial variations in n are of second order. That is, we asume V·▿n≪n▿·V and consequently, ▿· (nV)≃n▿·V, where V is the induced velocity field. With the aid of vector and scalar potentials, it is shown that, in this case, the set of ten coupled Maxwell-Euler equations describing a cold, isotropic, lossy, electron plasma with current and ionization sources can be reduced to a set of five integro-differential equations which are effectively decoupled. A method of solving these equations based on perturbation techniques is sketched for the case where the initial electron density is zero.
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