Nonlinear Evolution of Multiple-Finite Amplitude Resonant Loss-Cone Modes

The dynamics of hot particles moving in the presence of several finite amplitude longitudinal flute modes with frequencies near a harmonic of the cyclotron frequency are derived. It is found that, in general, such electric fields cause sizable groups of particles to lose or gain a substantial fraction of their kinetic energy. The dynamics are then self-consistently applied to the problem of determining the nonlinear evolution of the resonant hot-cold species loss-cone instabilities. For this model it is shown that nonlinear stabilization takes place through large particle excursions in velocity space and by the nonlinear detuning of the system out of resonance. An estimate of the energy exchange process shows that at any time, only a small fraction of the initial hot particle free energy is in the form of electric field fluctuations; most of the available energy is transformed into heating of the high-energy tail of the ions. The final state of this system is shown to be a stable, completely quiescent extremely hot plasma.