Ion heating with beating electrostatic waves

The nonlinear interaction of a magnetized ion with two beating electrostatic waves (BEW) whose frequencies differ by a cyclotron harmonic can lead, under some conditions Phys. Rev. E 69, 046402 (2004)], to vigorous acceleration for an ion with arbitrarily low initial velocity. When applied to an ensemble of ions, this mechanism promises enhanced heating over single electrostatic wave (SEW) heating for comparable wave energy densities. The extension of single ion acceleration to heating (SEWH and BEWH) of an ensemble of initially thermalized ions was carried out to compare the processes. Using a numerical solution of the Vlasov equation as a guideline, an analytical expression for the heating level was derived with Lie transforms and was used to show BEWH's superiority over all parameter space.