Second Harmonic Electromagnetic Wave Emissions from a Turbulent Plasma with Random Density Fluctuations

Abstract In the solar wind, electromagnetic waves at the harmonic plasma frequency 2 ω p can be generated as a result of coalescence between forward- and backward-propagating Langmuir waves. A new approach to calculate their radiation efficiency in plasmas with external background density fluctuations is developed. The evolution of Langmuir wave turbulence is studied by solving numerically the Zakharov equations in a two-dimensional randomly inhomogeneous plasma. Then, the dynamics of the nonlinear electric currents modulated at frequencies close to 2 ω p are calculated, as well as their radiation into harmonic electromagnetic waves. In the frame of this non-self-consistent approach where all transformations of Langmuir waves on density inhomogeneities are taken into account, the electromagnetic wave radiation rate (emissivity) is determined numerically as well as analytically, providing in both cases similar results. Moreover, scaling laws of the harmonic wave emissivity as a function of the ratio of the light velocity to the electron plasma thermal velocity are found. It is also shown how the emissivity depends on the average level of density fluctuations and on the isotropic/anisotropic character of the Langmuir waves’ and density fluctuations’ spectra.