Radiation at the Plasma Frequency and its Harmonic from a Turbulent Plasma

Any mechanism which couples electrostatic waves (plasma oscillations) and electromagnetic waves in a plasma will lead to radiation from plasma oscillations. The most important consequence of nonlinearity of the equations is that two electrostatic waves are coupled to one electromagnetic wave; this process is therefore responsible for radiation at the second harmonic (2ωp). Low-frequency or static inhomogeneities of the plasma couple one electrostatic wave to one electromagnetic wave, and therefore, produce radiation at (or near) the plasma frequency. Two types of inhomogeneity are considered: ``isotropic'' inhomogeneities, which are fluctuations in the plasma density, and ``anisotropic inhomogeneities,'' which comprise an inhomogeneous distribution of currents and magnetic fields. These radiation mechanisms are analyzed by means of a set of fluid equations for the electron component, which should provide an adequate description for plasma oscillations with wavenumbers small compared with the Debye wavenumber. The radiation field is evaluated by a Green function method, ignoring re-absorption, which one expects to be a very weak process. For each radiation mechanism, a formula is obtained for the volume emissivity of a turbulent plasma representing the plasma oscillations and the inhomogeneities each by a correlation function and an energy spectrum. Useful approximate forms of these formulas are given.