Collisional broadening of nonlinear resonant wave–particle interactions

Abstract

A general procedure for understanding plasma behaviour when resonant wave–particle interactions are the sole destabilizing and transport mechanism or only heating and/or current drive source is highlighted without recourse to involved numerical or analytical treatments. These phenomena are characterized by transport that appears to be collisionless even though collisions play a central role in narrow collisional boundary layers. The order of magnitude estimates, which include nonlinear effects, are shown to provide expressions in agreement with the principal results of recent toroidal Alfvén eigenmode (TAE), toroidal magnetic field ripple, and heating and current drive treatments. More importantly, the retention of nonlinearities leads to new estimates of the alpha particle energy diffusivity at saturation for TAE modes, and the ripple threshold at which superbanana plateau evaluations of alpha particle transport are modified by nonlinear radial drift effects. In addition, the estimates indicate when quasilinear descriptions for heating and current drive will begin to fail. The phenomenological procedure demonstrates that in magnetic fusion relevant plasmas, narrow collisional boundary layers must be retained for resonant wave–particle interactions as they enhance the role of collisions, and make stochastic particle motion unlikely to be more important than other nonlinear processes.

Merging of the superbanana plateau and transport regimes in nearly quasisymmetric stellarators

“…Inserting with , (8.3) becomes The delta function behaviour of occurs upon integration over pitch angle (Catto & Tolman 2021). Using with and gives due to the superbanana or resonant plateau contribution.…”

“…A resonance occurs because the tangential drift vanishes at some pitch angle with collisions resulting in a spread out drift resonance with an effective width given by . Balancing the effective drift and collisions gives the dimensionless width (Catto & Tolman 2021) to be , and thereby an enhanced collision frequency of , where is the pitch angle scattering frequency of the alphas by the background ions. The resulting radial step size is then .…”

Helicon and lower hybrid current drive comparisons in tokamak geometry

“…This like particle operator is the usual non-momentum conserving, high speed expansion of the Rosenbluth potentials for collisions with a Maxwellian used by Karney & Fisch (1979, 1985). Recent estimates (Catto 2021; Catto & Tolman 2021 a , b ) indicate must be nearly Maxwellian for QL theory to remain valid.…”