Plasma heating with beating electrostatic waves

The heating of ions in a magnetized plasma with two electrostatic waves whose frequencies differ by the ion cyclotron frequency is analytically, numerically, and experimentally characterized. This process, denoted beating electrostatic wave (BEW) heating, is of particular interest since its ability to non-resonantly accelerate low energy ions suggests that it may be more effective at ion energization than the traditional, resonant heating produced by a single electrostatic wave (SEW). To explore this possibility, the BEW and SEW mechanisms were examined through an analysis of single particle orbits as well as the average power absorbed by an ion ensemble. Using the total input energy density of the waves as a metric, it was found that there are three distinct regimes for comparing the two processes: (I) for low energy density, there is a criterion for the onset of heating that depends on the wave parameters, and this criterion is satisfied for a lower input energy density with BEW; (II) at intermediate energy density, once heating has onset for both processes, SEW heating is superior; and (III) at high energy density above a threshold value that depends both on the wave parameters and background plasma, the BEW heating process is predicted to lead to higher heating levels. These analytical conclusions were tested in a low-temperature experimental setup by examining the increase in ion temperature produced by SEW and BEW as a function of total input energy density and fraction of energy in each wave. The experimental results were found to correspond to within error to the theoretical trends predicted for the first regime (I) and qualitative agreement was found for the second regime (II). Saturation effects combined with a limited available energy density to the experiment precluded a systematic investigation of the third energy density regime.