Collisional broadening of nonlinear resonant wave-particle interactions.*

A procedure providing insight into plasma behavior when resonant wave-particle interactions are the dominant mechanism will be presented without recourse to involved numerical or analytical treatments. These phenomena are characterized by transport appearing to be collisionless even though collisions play a central role in narrow boundary layers. The order of magnitude estimates, including nonlinear effects, provide expressions in agreement with the principle results of toroidal Alfvén eigenmode (TAE), toroidal magnetic field ripple, and heating and current drive treatments. The retention of nonlinearities for alpha particles leads to estimates of the diffusivity at saturation for TAE modes, and the ripple threshold at which superbanana plateau evaluations of transport are modified by finite radial drift effects. The estimates also place a bound on the applied rf wave amplitude for quasilinear descriptions to remain valid for heating and current drive. The phenomenological procedure indicates that when narrow collisional boundary layers must be retained, any stochastic field line behavior occurring is unlikely to be more important than any other nonlinear process in magnetic fusion plasmas.