5 - Equilibrium: one-dimensional configurations

Summary

Introduction

Although the magnetic configurations of fusion interest are toroidal, one can begin to develop physical intuition by first investigating their one-dimensional cylindrically symmetric analogs: the θ-pinch, the Z-pinch, and the general screw pinch. These can be considered to be the basic building blocks of MHD equilibrium. Focusing on cylindrical systems allows the two basic problems of MHD equilibrium – radial pressure balance and toroidal force balance – to be separated, so that each can be studied individually.

The one-dimensional model focuses entirely on radial pressure balance. The question of toroidal force balance does not enter since by definition the geometry is a linear cylinder. For many configurations, once radial pressure balance is established, toroidicity can be introduced by means of an inverse aspect ratio expansion, from which one can then investigate toroidal force balance.

Chapter 5 provides a description of the basic one-dimensional configurations and how they provide radial pressure balance in a plasma. In particular, it is shown that both toroidal and poloidal fields as well as combinations thereof can easily accomplish this goal.

Included in the analysis are descriptions of two present day fusion concepts: the reversed field pinch, and the ohmic tokamak. These configurations are singled out since both their radial pressure balance and MHD stability are reasonably well described by the one-dimensional cylindrical model. Toroidal effects can be treated perturbatively and make small quantitative, but not qualitative, corrections to the cylindrical equilibrium and stability results.