Charged Particle Energization by Low-Amplitude Electrostatic Waves at Cyclotron Harmonics

The system made by a charged particle interacting with a single electrostatic wave which propagates perpendicularly to the magnetic field, at a frequency larger than the cyclotron one, has been extensively studied in the literature due to its implications for ion heating in magnetized plasmas. It is known that a threshold in the electrostatic potential must be exceeded in order for stochastic particle motion and heating to occur. Regardless of its amplitude, however, the electrostatic wave induces a periodic oscillation in the particle motion. We show, by analytical and numerical arguments, that this dynamic is non-adiabatic, meaning that the particle does not land back in its initial state when the wave is slowly turned off. This way, particle energization (although not rigorous heating) occurs even under sub-threshold conditions.