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 degrees, 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.