Longitudinal propagation in a magnetized time-varying plasma: development of Green's function

The effect of a magnetized transient plasma on a circularly polarized source wave, when the rise time of the electron density profile is comparable to the source wave period, is considered. The problem has no exact solution and is not amenable to a sudden-switching approximation or an adiabatic approximation. It is investigated by developing a causal Green's function for magnetized time-varying plasma 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 scattering coefficients for a linear profile, which has no known analytical solution, are obtained to illustrate the superiority of the new approach.