Ion acceleration in plasmas with Alfvén waves

Effects of elliptically polarized Alfvén waves on thermal ions are investigated. Both regular oscillations and stochastic motion of the particles are observed. It is found that during regular oscillations the energy of the thermal ions can reach magnitudes well exceeding the plasma temperature, the effect being largest in low-$β$ plasmas (⁠$β$ is the ratio of the plasma pressure to the magnetic-field pressure). Conditions of low stochasticity threshold are obtained. It is shown that stochasticity can arise even for waves propagating along the magnetic field provided that the frequency spectrum is nonmonochromatic. The analysis carried out is based on equations derived from using a Lagrangian formalism. A code solving these equations is developed. Steady-state perturbations and perturbations with the amplitude slowly varying in time are considered.