Abstract
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 Lp is examined. The mode conversion points are located a distance Δ0 from the peak of the profile, where the electron plasma frequency ωp(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., (cLp/ω)1/2≪Δ0<Lp, the appropriately scaled result [D. E. Hinkel-Lipsker et al., Phys. Fluids B 4, 559 (1992)] for a linear density profile is recovered as the parabolic cylinder functions asymptotically become Airy functions. When Δ0→0, the special case of conversion at the peak of the profile [D. E. Hinkel-Lipsker et al., Phys. Fluids B 4, 1772 (1992)] is obtained.
Published Version
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