Transient signal propagation through an inhomogeneous plasma

The propagation of a transient electromagnetic field through a cold, isotropic, lossless, inhomogeneous plasma is considered. The electron density of the plasma decreases exponentially in the direction of propagation. For incident transient signals whose Laplace transforms are regular at infinity and whose only singularities are poles, the transient electric field propagated through the plasma can be expressed as a sum of exponential waves at discrete complex frequencies. The characteristic frequencies of the inhomogeneous plasma are related to the zeros of the modified Bessel function of the first kind of fixed argument and variable order. When the Laplace transform of the incident signal is not well-behaved at infinity, approximate methods may be used to evaluate the transient electric field. The propagation of a step sine wave and of a quasi-monochromatic Gaussian pulse are considered. It is found that for plasmas characteristic of reentry boundary layers, the effect of the plasma layer on dispersion is very small. The principal effect of the layer is to attenuate a signal propagated through it.