Harmonics of the Electron Gyro-Frequency in Plasmas

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Abstract
Intense radiation emitted by plasmas at harmonics of the electron gyrofrequency is discussed. The nonrelativistic dispersion relation for propagation vectors nearly perpendicular to the external magnetic field is studied for an unperturbed Maxwellian distribution function. The real and complex wavenumbers of ordinary and extraordinary waves are given when Landau and collisional damping are negligible. Their behavior near the harmonics, the upper hybrid frequency, and cutoffs is considered in detail. When damping is present, the wave propagation undergoes a deep change. In typical experimental conditions no ordinary and no transverse extraordinary waves exist in the very neighborhood of the harmonics with a large index of refraction, while there are sets of short quasi‐electrostatic waves which are of interest in explaining the experiments. Near the hybrid frequency the relatively fast quasi‐electrostatic waves are substituted for elliptically polarized waves (still predominantly longitudinal) which originate from the coupling between the cold‐plasma and the electrostatic modes. The equation for the electrostatic waves is also discussed in plasmas with electron streams and temperature anisotropies.