Analytic expressions for mode conversion in a plasma with a parabolic density profile: Generalized results

This study provides an analytic solution to the general problem of mode conversion in an unmagnetized plasma. Specifically, an electromagnetic wave of frequency ω propagating through a plasma with a parabolic density profile of scale length L p is examined. The mode conversion points are located a distance Δ0 from the peak of the profile, where the electron plasma frequency ω p (z) matches the wave frequency ω. The corresponding reflection, transmission, and mode conversion coefficients are expressed analytically in terms of parabolic cylinder functions for all values of Δ0. The method of solution is based on a source approximation technique that is valid when the electromagnetic and electrostatic scale lengths are well separated. For large Δ0, i.e., (cL p /ω)1/2≪Δ0