Nonlinear neoclassical two-fluid theory of response of tokamak plasma to resonant error-field

Abstract

A nonlinear, neoclassical, two-fluid theory of the interaction of a single-helicity magnetic island chain with a resonant error-field in a quasi-cylindrical, low-β, tokamak plasma is presented. In particular, the analysis of Fitzpatrick [Phys. Plasmas 25, 042503 (2018)] is generalized to take explicit time dependence into account. Aside from the ability to more accurately treat time-varying problems, the main physical effect that is introduced into the theory by the incorporation of explicit time dependence is ion inertia. The formalism developed in the paper is used to analyze two time-varying problems. First, the interaction of a pre-existing magnetic island chain with a resonant error-field. Second, an error-field-maintained magnetic island chain. The latter problem is of direct relevance to experiments in which deliberately applied, multi-harmonic, resonant magnetic perturbations are used to suppress edge localized modes (ELMs) in tokamak plasmas. Indeed, the predictions of the theory are strikingly similar to data recently obtained from ELM suppression experiments in the DIII-D tokamak [R. Nazikian et al., Nucl. Fusion 58, 106010 (2018)].