Modification of a high energy particle distribution by a spectrum of low amplitude modes is investigated using a guiding center code. Only through resonance are modes effective in modifying the distribution. Diagnostics are used to illustrate the mode–particle interaction and to find which effects are relevant in producing significant resonance, including kinetic Poincaré plots and plots showing those orbits with time averaged mode–particle energy transfer. Effects of pitch angle scattering and drag are studied, as well as plasma rotation and time dependence of the equilibrium and mode frequencies. A specific example of changes observed in a DIII-D deuterium beam distribution in the presence of low amplitude experimentally validated Toroidal Alfvèn eigenmodes and reversed shear Alfvèn eigenmodes is examined in detail. Comparison with experimental data shows that multiple low amplitude modes can account for significant modification of high energy beam particle distributions. It is found that there is a stochastic threshold for beam profile modification, and that the experimental amplitudes are only slightly above this threshold.
Collisional dependence of Alfvén mode saturation in tokamaks