Second harmonic generation using spatially varying static electron number density in a magnetoplasma

Abstract

The Boltzmann transfer equation for electrons in an r.f. discharge plasma immersed in a stationary magnetic field is solved for the various coefficients of the expansion of the distribution function, expanded in a Taylor series in velocity space. Assuming a spatial variation of static electron number density as the mechanism of harmonic generation, explicit expressions for the inner field and the second harmonic current density are derived. The r.f. electric field is assumed to be spatially uniform. The geometry of the plasma considered is that of a rectangular waveguide, but with the parallel plates of one of the two pairs of the metal plate boundaries of the plasma much more closely spaced than those of the other pair. Cyclotron resonance is studied in a situation where the frequency of electron-neutral particle collisions v is much less than the frequency of the r.f. field ω/2π. The resonance effect is obtained, and is found to be more pronounced at the cyclotron frequency ω = ωc than at 2ω = ωc. For v≫ω/2π, the result is not sensitive to the value of the stationary magnetic field, and the resonance effects are absent. The effect of collisions on the process of harmonic generation is also studied.