Analytic expression for mode conversion of Langmuir and electromagnetic waves

Abstract

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/${\mathrm{mc}}^2$≪1, agree with earlier numerical calculations.