Green's function for a switched plasma medium and a perturbation technique for the study of wave propagation in a transient plasma with a small rise time

The main effect of switching a medium (creating a temporal discontinuity in the properties of a medium) is the splitting of the source (incident) wave into new waves whose frequencies are different. Lightning induced effects in the ionosphere cause a temporary enhancement of ionization. Such transient plasmas have a time-varying plasma frequency ωp (t) with a rise time Tr. If the period t0 of a source wave existing before the transient effect begins is much larger than the rise time, the ionization change may be idealized as a sudden switching of the medium. The solution to this initial value problem with a step-change in the electron density profile is known and this profile will be considered as a reference profile. The topic of this paper is the solution of the initial value problem when t0 is comparable to the rise time Tr. The initial motivation for investigating the problem is given below. There is considerable interest in the ionospheric physics community to investigate the recently discovered Sprites phenomenon which are red emissions in the lower D region induced by the lightning discharges from a cloud to the ground. The preliminary indications are that the Sprite is a plasma with electron density enhanced by about 101 to 103/cc in a rise time of about 100 micros