Analytic expression for mode conversion of Langmuir and electromagnetic waves

We have derived analytic expressions, in terms of Airy functions, for the reflection and mode-conversion coefficients of Langmuir and electromagnetic waves in an inhomogeneous, unmagnetized plasma. The reflection coefficient for the ``direct'' problem (incident electromagnetic wave) is equal in magnitude to that for the ``inverse'' problem (incident electrostatic wave) and the corresponding mode-conversion coefficients satisfy energy conservation. Our results, which are valid in the limit of nonrelativistic electron temperature, T/mc²{}1, agree with earlier numerical calculations.