The zero-frequency ion ring instability

The electrostatic zero-frequency ion ring instability with wave vector perpendicular to a uniform magnetic field B is examined through linear and second-order theory as well as by computer simulation. In the simulation ions are taken as magnetized particles; the electrons are described as a massless fluid subject to E x B motion. Saturation of the instability is primarily due to broadening of the ion ring distribution. A second-order theory provides an approximate criterion for the saturation amplitude, as does a simple trapping argument. Thus, for the simulation presented here, both quasi-linear and trapping effects contribute to saturation.