Asymptotic theory of magnetic island saturation in equilibria with a finite current gradient

TL;DR

This paper introduces a new asymptotic matching method to analyze magnetic island saturation in plasmas with finite current gradients, deriving a nonlinear dispersion relation and resolving previous normalization ambiguities.

Contribution

It develops a novel asymptotic matching procedure that fully specifies normalization factors in magnetic island saturation theory with finite current gradients.

Findings

Derived a nonlinear dispersion relation for saturated magnetic islands.

Resolved normalization ambiguities present in earlier theories.

Provided a comprehensive asymptotic framework for magnetic island analysis.

Abstract

A novel asymptotic matching procedure is developed to revisit the problem of magnetic island saturation in case of a finite current gradient at the rational surface. Nonlinear dispersion relation is derived for saturated magnetic island. It is shown that arbitrary normalization factors that were present in previous theories are fully specified with the asymptotic matching.