A Computational Method in Plasma Physics: Scientific Computation

1. Introduction.- 1.1 Formulation of the Problem.- 1.2 Discussion of Results.- 2. The Variational Principle.- 2.1 The Magnetostatic Equations.- 2.2 Flux Constraints in the Plasma.- 2.3 The Ergodic Constraint.- 2.4 Coordinate System in the Plasma.- 2.5 First Variation of the Potential Energy.- 2.6 Vacuum Region and Force-Free Fields.- 2.7 Variation of the Vacuum Field.- 2.8 Variation of the Free Boundary.- 2.9 Coordinate System in the Vacuum.- 2.10 Accelerated Paths of Steepest Descent.- 2.11 Determination of the Acceleration Coefficients.- 3. The Discrete Equations.- 3.1 The Numerical Method.- 3.2 Difference Equations for the Plasma Region.- 3.3 Difference Equations for the Vacuum Region.- 3.4 Iterative Scheme for the Plasma Region.- 3.5 Iterative Scheme for the Vacuum Region.- 3.6 Iterative Scheme for the Free Boundary.- 3.7 Remarks about the Method.- 3.8 Iterative Schemes for Elliptic Equations.- 4. Description of the Computer Code.- 4.1 Introduction.- 4.2 Input Data.- 4.3 Printed Output.- 4.4 Glossary.- 5. Applications.- 5.1 Historical Development of the Code.- 5.2 Comparison with Exact Solutions.- 5.3 Unstable High ? Stellarator Equilibria.- 5.4 Triangular Cross Sections.- 5.5 High ? Tokamaks.- 5.6 Discussion.- References.- Listing of the Code with Comment Cards.- 1. Output from a Sample Run.- 2. Fortran Listing.