Longitudinal propagation in a layered magneto-ionic medium (Epstein profile)

Summary The longitudinal propagation and reflection of a plane electromagnetic wave in a horizontally stratified magneto-ionic medium is considered. In this case Maxwell's equations reduce to two uncoupled ordinary second-order differential equations, describing the propagation of two elliptically polarized plane waves. The electron density of the medium is assumed to vary with the vertical Cartesian coordinatez according to the Epstein law. Rigorous solutions of the relevant differential equations can be obtained either in the form of hypergeometric functions or in the form of an integral representation. The reflection coefficients of both waves are then expressed in terms of gamma functions. The following quantities are considered in detail in their dependence on the parameters involved: the modulus of the reflection coefficient, the phase delay time and the group delay time. Some numerical results are given.