Stability of an ion-ring distribution in a multi-ion component plasma

The stability of a cold ion-ring velocity distribution in a thermal plasma is analyzed. In particular, the effect of plasma temperature and density on the instability is considered. A high ring density (compared to the background plasma) neutralizes the stabilizing effect of the warm background plasma and the ring is unstable to the generation of waves below the lower-hybrid frequency even for a very high temperature plasma. For ring densities lower than the background plasma density, there is a slow instability where the growth rate is less than the background-ion cyclotron frequency and, consequently, the background-ion response is magnetized. This is in addition to the widely discussed fast instability where the wave growth rate exceeds the background-ion cyclotron frequency and hence the background ions are effectively unmagnetized. Thus, even a low density ring is unstable to waves around the lower-hybrid frequency range for any ring speed. This implies that effectively there is no velocity threshold for a sufficiently cold ring.