Rapid Particle Acceleration by Large-Amplitude Magnetohydrodynamic Waves

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We have studied nonlinear structure of magnetosonic waves, current driven instabilities, and particle acceleration, with special attention to effects of multi-species ions. These results have been applied to the investigation of solar energetic particles.In a plasma with two ion-species, a magnetosonic wave splits into two modes ; low- and high- frequency modes. The frequency of the low-frequency mode tends to zero as the wave number k approaches zero. On the other hand, the high-frequency mode has a finite cut-off frequency of the order of the ion cyclotron frequency. These two modes, however, are found to be described by KdV equations. This shows that KdV equations are not limited to the waves whose frequencies tend to zero as k->0. The characteristic solition widths are the ion inertal length for the low-frequency mode and the electron inertial length for the high-frequency mode.In ^3He-rich events occuring in some solar flares, the waves having frequencies close to the ^3He cyclotron frequency are expected to play an important role. Thus, we invesutigated current driven, electrostatic instabilities in a plasma whose main components are hydrogen and helium (^4He) cyclotron waves can be driven unstable with frequencies close to the ^3He cyclotron frequency.On the basis of these studies we proposed a unified theory for solar energetic particles that accounts for the mean chemical composition, ^3He-rich events, and prompt ion acceleration to relativistic energies.