Hydromagnetic stability of tokamaks

TLDR

The linear theory of ideal and resistive hydromagnetic stability in tokamaks is well established for large‑aspect‑ratio, low‑β devices, but small‑aspect‑ratio, high‑β configurations remain largely unexplored. The review surveys the stability problem, covering introductory aspects and a comprehensive literature survey. In a perfectly conducting plasma, instabilities appear as kink, internal, and axisymmetric modes, and the introduction of resistivity significantly modifies the kink and internal modes.

Abstract

A summary is given of the linear theory of the ideal and resistive hydromagnetic stability of tokamaks. The first section provides an introductory account of the various aspects of the stability problem, and the subsequent sections provide a survey of the subject and a review of the literature. For aperfectly conducting plasma the modes of instability are of three types: kink, internal, and axisymmetric. When resistivity is introduced the kink and internal modes have significantly modified forms. The analysis of the standard tokamak, having a large aspect ratio, circular cross-section and low β, is almost complete but the study of small aspect ratio, high-β configurations and the optimization of such configurations are at an early stage.