Conversion of Electrostatic and Electromagnetic Waves in a Plasma at the Peak of a Parabolic Density Profile

Analytic expressions for the reflection, transmission, and mode conversion coefficients for electromagnetic and Langmuir waves in an unmagnetized plasma with a parabolic density profile are found for both the direct problem (incident electromagnetic wave) and the inverse problem (incident Langmuir wave). In contrast to the linear profile problem, the absorption depends explicitly on the value of collision frequency (cold model) or temperature (warm plasma), but a transformation of parameters relates the results for these two limits.