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

The stability of ion Bernstein waves (frequency ω, wave number ) in a plasma with two ion species pumped by a magneto-acoustic wave (ω p , p ) which propagates perpendicularly to the static magnetic field is studied. The background plasma is assumed to be infinite, homogeneous and collision-free. If ω p > |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 | D |. The instability is excited by the relative drift motion of different species induced by the pump wave. Assuming | ⋅( a − b )|≪1 ( a = 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 : In case A ( = ⊥ ∥ p ) only the relative ion motion d ⋅ t 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 ⊥ ⊥ k p , k z ≠ 0) caused mainly by the relative electron-ion drift motion are similar to those in plasmas with only one ion species. For given | p | the growth rates in both cases are equal in order of magnitude (for low values of ω p , case A is slightly more favourable); however, in case A the theory is valid up to considerably higher values of | p |. Some effects depending substantially on the presence of two ion species are discussed in detail.