Stability regions and growth rates for a two-ion component plasma, unmagnetized

Abstract

A uniform plasma, with a thermal core and a warm ring, in velocity space, is examined for instabilities. The parameters are the ratio of ring to core densities, the ratio of core thermal velocity to ring peak velocity, and the ring thermal velocity. The boundary between stable and unstable distributions is given, as dependent on these parameters, as obtained from the Penrose criterion. In addition, the upper and lower bounds on the wavenumbers (kmax, kmin) are found for typical distributions, as well as growth rates, ωi(k). For either dense ring or dense core distributions, the distributions are unstable for (vt/vr) ≲0.1, independent of the thermal spread of the ring, where vt is the core thermal spread, and vr is the ring peak speed. For more equal ring and core densities, the stability boundary moves to larger values, dependent on the thermal spread of the ring. Growth rates of ωi≈0.01 to 0.1 ωp are typical. Application of these results to magnetized plasmas is given.