Electrostatic Plasma Instabilities Excited by a High-Frequency Electric Field

Abstract

The electrostatic plasma waves excited by a uniform, alternating electric field of arbitrary intensity are studied on the basis of the Vlasov equation; their dispersion relation, which involves the determinant of either of two infinite matrices, is derived. For ω0 ≫ ωpi (ω0 being the applied frequency and ωpi the ion plasma frequency) the waves may be classified in two groups, each satisfying a simple condition; this allows writing the dispersion relation in closed form. Both groups coalesce (resonance) if (a) ω0 ≈ ωpe/r (r any integer) and (b) the wavenumber k is small. A nonoscillatory instability is found; its distinction from the DuBois-Goldman instability and its physical origin are discussed. Conditions for its excitation (in particular, upper limits to ω0,k, and k·vE, vE being the field-induced electron velocity), and simple equations for the growth rate are given off-resonance and at ω0 ≈ ωpi. The dependence of both threshold and maximum growth rate on various parameters is discussed, and the results are compared with those of Silin and Nishikawa. The threshold at ω0 ≈ ωpi/r,r ≠ 1, is studied.