Wave propagation in a transient plasma - Development of a Green's function

The effect of a transient plasma on a source wave, when the rise time of the electron density profile is comparable to the source wave period, is considered. The problem is not amenable to a sudden-switching approximation or an adiabatic approximation. It is investigated by developing a causal Green's function for temporally unlike media. A perturbation series based on the Green's function gives the solution to the desired accuracy. As compared to the numerical methods that give the total fields, this method has the intrinsic advantage of processing the forward propagating and backward propagating waves explicitly. The validity of the method is illustrated by comparing the perturbation solution to the exact solution of a linear profile. The scattering coefficients for a "hump profile," which has no obvious exact solution, are obtained to illustrate the general applicability of the new approach.