Abstract
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 the collision frequency (cold model) or temperature (warm plasma), but a transformation of parameters relates the results for these two limits.
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