Generalized ion ring instability driven by ions with a partial shell distribution

A generalized ion ring instability driven by energetic ions with a shell velocity distribution, which has a central pitch angle at 90°, is studied. We consider waves propagating in both parallel and oblique direction as well as different pitch angle spreads of a partial shell. These unperturbed distributions represent different stages during the time evolution of an ion distribution, that is a ring initially. The evolution is attributed to pitch angle scattering due to wave‐particle interactions. Numerical results obtained by us show that the instability diminishes rapidly, especially for oblique propagation, while the pitch angle spread increase.