Parametric excitation of ion Bernstein waves in a plasma with two ion species

Abstract

The stability of ion Bernstein waves (frequency ω, wave number k⃗) in a plasma with two ion species pumped by a magneto-acoustic wave (ωp, k⃗p) which propagates perpendicularly to the static magnetic field is studied. The background plasma is assumed to be infinite, homogeneous and collision-free. If ωp > |ω| is properly chosen, ion Bernstein waves become unstable (decay instability, non-linear Landau instability) at rather low values of the pump electric field amplitude |E⃗D|. The instability is excited by the relative drift motion of different species induced by the pump wave. Assuming |k⃗⋅(D⃗a−D⃗b)|≪1 (D⃗a = displacement for particles of species a, a = e, 1, 2) the general non-linear dispersion relation is approximately solved in a deuterium-tritium plasma for two different k⃗: In case A (k⃗=k⃗⊥ ∥ k⃗p) only the relative ion motion D⃗d⋅D⃗t comes into play; this gives rise to decay instabilities which are only present in plasmas with two ion species. The instabilities of case B(k⊥ ⊥ kp, kz ≠ 0) caused mainly by the relative electron-ion drift motion are similar to those in plasmas with only one ion species. For given |E⃗p| the growth rates in both cases are equal in order of magnitude (for low values of ωp, case A is slightly more favourable); however, in case A the theory is valid up to considerably higher values of |E⃗p|. Some effects depending substantially on the presence of two ion species are discussed in detail.