Parametric instabilities in a magnetic field and possible applications to heating of plasmas

Abstract

The dispersion relation for longitudinal plasma waves in the presence of an external high-frequency electric field is solved in terms of the dielectric function and its derivatives. Particular emphasis is placed on the case of short-wavelength ion acoustic waves (ω <̃ ωpi), electron plasma waves ω <̃ ωce), and cyclotron harmonic waves (ωce <̃ ω). which propagate obliquely to the magnetic field. It is found that these modes are unstable with respect to: (i) the purely growing mode; (ii) the overstable acoustic mode; (iii) the dissipative-kinetic instability. The hot-plasma dispersion relation is solved numerically, and thresholds and growth rates are given for a large range of parameters. It is concluded that both the extraordinary mode and the whistler mode may be used to excite the foregoing instabilities, and thus may provide a means for enhanced heating of plasmas. Possible applications for heating of fusion plasmas are discussed.