The ion-ion acoustic instability

This paper considers the linear theory of ion-acoustic-like instabilities in a homogeneous Vlasov plasma with two ion components, a less dense beam and a more dense core, with a relative drift velocity. Numerical solutions of the full electrostatic dispersion equation are presented, and the properties of the ion-ion acoustic instability are studied in detail. The following properties are demonstrated: (i) At relatively cold beam temperatures, the instability is fluid-like, but it becomes a beam resonant kinetic instability as the beam temperature becomes of the order of the core temperature; (ii) if the mode is unstable, its threshold lies well below the threshold of the electron-ion acoustic instability; (iii) an electron temperature anisotropy T/T_e > 1 enhances the instability and (iv) at sufficiently large beam-core relative drift speeds, electron magnetization can either detract from or enhance the instability. If field-aligned ion beams are to drive the ion-acoustic-like enhanced fluctuations observed upstream of the Earth's bow shock, the effective beam temperature must be much smaller than values quoted in the literature.