Invariant imbedding theory of mode conversion in inhomogeneous plasmas: I. Exact calculation of the mode conversion coefficient in cold, unmagnetized plasmas

Abstract

This is the first of a series of papers devoted to the development of the invariant imbedding theory of mode conversion in inhomogeneous plasmas. A new version of the invariant imbedding theory of wave propagation in inhomogeneous media allows one to solve a wide variety of coupled wave equations exactly and efficiently, even in the cases where the material parameters change discontinuously at the boundaries and inside the inhomogeneous medium. In this paper, the invariant imbedding method is applied to the mode conversion of the simplest kind, that is the conversion of $p$-polarized electromagnetic waves into electrostatic modes in cold, unmagnetized plasmas. The mode conversion coefficient and the field distribution are calculated exactly for linear and parabolic plasma density profiles and compared quantitatively with previous results.