The shear Alfv\'en continuum with a magnetic island chain in tokamak plasmas

TL;DR

This paper investigates the shear Alfvén continuum spectrum in tokamaks with magnetic island chains, revealing new frequency gaps, mode structures, and implications for plasma stability using ideal MHD theory.

Contribution

It introduces a detailed analysis of the Alfvén continuum with magnetic islands, highlighting new frequency gaps and mode behaviors due to asymmetry and toroidal effects.

Findings

New frequency gaps such as MAE and HAE are identified within the island.

The TAE/MAE gap narrows with increasing island size, affecting mode stability.

Eigenfunctions become highly localized, indicating a transition from continuous to discrete spectrum.

Abstract

The shear Alfv\'en continuum spectrum is studied for a tokamak with a single island chain using the ideal Magnetohydrodynamics (MHD) theory. We have taken into account the toroidal geometry and toroidal mode coupling with the island considered as a highly-shaped stellarator. Various new frequency gaps open up inside the island due to its asymmetry both poloidally and toroidally, such as the Mirror-induced Alfv\'en Eigenmode (MAE) gap and the Helicity-induced Alfv\'en Eigenmode (HAE) gap. We have shown that the MAE gap acts as the continuation of the outside Toroidal Alfv\'en Eigenmode (TAE) gap into the island. However, the combined TAE/MAE gap is getting narrower as the island grows, leaving only half of its original width with a moderate island size as much as 3.2% of the minor radius. In addition, the two-dimensional eigenfunction of the continuum mode on the lower tip of the MAE gap now has highly localised structures around the island's long axis, contrary to the usual oscillatory global solutions found with no or a low level of toroidal asymmetry - an indication of the continuous spectrum becoming discrete and dense. These results have implications for the frequency, mode structure and continuum damping of global TAEs residing in the gap.