Destabilization of energetic particle modes by localized particle sources

In the present paper, in order to delineate the essential physics, analytic dispersion relations for Energetic Particle Modes (EPM) excitation via precessional resonance in toroidal systems are derived in various limiting but still relevant cases. The analytic dispersion relations obtained here can be readily applied to EPM excitations by magnetically trapped energetic ions generated with ion cyclotron frequency heating. It is also demonstrated that "frequency chirping" is what the linear dispersion relation of EPM's predicts when the local properties of either energetic particles or the thermal plasma are changed. A new novel result is that, for sufficiently strong spatial gradients, energetic particles can produce an effective potential well that radially (globally) traps the EPM. This property is a crucial and peculiar one of EPM's, and it could have important implications to the self-consistent nonlinear dynamic evolution of the fast particle distribution. (C) 2000 American Institute of Physics. [S1070-664X(00)02611-2].