An Overview of Plasma Confinement in Toroidal Systems

TL;DR

This paper provides a comprehensive tutorial on magnetic plasma confinement in toroidal systems, focusing on equilibrium, stability, and transport phenomena, with applications to the Damavand tokamak.

Contribution

It offers an in-depth overview of theoretical and numerical methods for plasma confinement, emphasizing axisymmetric geometries and recent analytical solutions.

Findings

Analytical solutions to Grad-Shafranov Equation

Application to Damavand tokamak

Insights into plasma stability and transport

Abstract

This overview presents a tutorial introduction to the theory of magnetic plasma confinement in toroidal confinement systems with particular emphasis on axisymmetric equilibrium geometries, and tokamaks. The discussion covers three important aspects of plasma physics: Equilibrium, Stability, and Transport. The section on equilibrium will go through an introduction to ideal magnetohydrodynamics, curvilinear system of coordinates, flux coordinates, extensions to axisymmetric equilibrium, Grad-Shafranov Equation (GSE), Green's function formalism, as well as analytical and numerical solutions to GSE. The section on stability will address topics including Lyapunov Stability in nonlinear systems, energy principle, modal analysis, and simplifications for axisymmetric machines. The final section will consider transport in toroidal systems. We present the flux-surface-averaged system of equations describing classical and non-classical transport phenomena. Applications to the small-sized high-aspect-ratio Damavand tokamak will be described.