Ion Resonance Instability in Grossly Nonneutral Plasmas

The addition of a certain fraction of ions to an otherwise stable cloud of electrons can, in certain circumstances, result in an instability. The case of a low-density (q = ωp2/ωc2 ≪ 1) electron cloud in which the electron motions can be described by E + ve×B = 0 is considered in detail. The condition for onset of the instability is that the unperturbed ion orbits (which characteristically traverse the entire electron cloud) should involve frequencies close to that of the diocotron wave that can propagate on the electron cloud. This condition is equivalent to having the ratio Zme/miq of the order of unity and is independent of the ion density. When instability is present, the growth rate is of the order of the ion plasma frequency.