Introduction

In Chapter 5 it was shown that a one-dimensional, cylindrically symmetric magnetic geometry accurately describes radial pressure balance in many fusion configurations. The primary goal of Chapter 6 is to address the problem of toroidal force balance in a two-dimensional axisymmetric toroidal geometry. A secondary goal analyzes straight systems with two-dimensional helical symmetry.

The discussion starts with a derivation of the Grad–Shafranov equation, the basic equation describing axisymmetric toroidal equilibrium. For configurations possessing such symmetry, the solutions to this equation provide a complete description of ideal MHD equilibria: radial pressure balance, toroidal force balance, equilibrium β limits, rotational transform, and kink safety factor. A wide number of configurations are well described by the Grad–Shafranov equation. Included among them are all types of tokamaks, the reversed field pinch, the levitated dipole, the spheromak, and the field reversed configuration.