Variational formulation of kinetic-bulk multiple-wave conversion in fusion plasmas

We present a variational formulation of a generic multiple-wave conversion process [1] between a kinetic-ion plasma wave, supported by a non-Maxwellian distribution of energetic particles, and one or two plasma waves supported by bulk-ions with Maxwellian distributions. The variational approach yields important conservation laws (e.g., action), that help us understand how rf power is exchanged between the bulk-ion species and the kinetic-ion species. We also discuss the implications of a kinetic-ion plasma wave with negative energy on the multiple-wave conversion process. [1] A.J. Brizard, A.N. Kaufman, and E.R. Tracy, \textit{Recirculation in multiple wave conversions}, to appear in Physics of Plasmas (2008).