Magnetohydrodynamic Equilibrium and Stability of Stellarators

✍ Scribed by Frances Bauer, Octavio Betancourt, Paul Garabedian (auth.)

• Publisher: Springer-Verlag New York
• Year: 1984
• Tongue: English
• Leaves: 202
• Edition: 1
• Category: Library

✦ Synopsis

In this book, we describe in detail a numerical method to study the equilibrium and stability of a plasma confined by a strong magnetic field in toroidal geometry without two-dimensional symmetry. The principal appli­ cation is to stellarators, which are currently of interest in thermonuclear fusion research. Our mathematical model is based on the partial differential equations of ideal magnetohydrodynamics. The main contribution is a computer code named BETA that is listed in the final chapter. This work is the natural continuation of an investigation that was presented in an early volume of the Springer Series in Computational Physics (cf. [3]). It has been supported over a period of years by the U.S. Department of Energy under Contract DE-AC02-76ER03077 with New York University. We would like to express our gratitude to Dr. Franz Herrnegger for the assistance he has given us with the preparation of the manuscript. We are especially indebted to Connie Engle for the high quality of the final typescript. New York F. BAUER October 1983 O. BETANCOURT P. GARABEDIAN Contents 1. Introduction 1 2. Synopsis of the Method 3 1. Variational principle 3 2. Coordinate system 6 3. Finite Difference Scheme 8 1. Difference equations ....................... " 8 2. Island structure ............................. 10 3. Accelerated iteration procedure .............. . . .. 12 Nonlinear Stability 15 4. 1. Second minimization . . . . . . . . . . . . . . . . .. . . 15 . . . . . 2. Test functions and convergence studies . . . . . . . .. . . 17 . 3. Comparison with exact solutions ................. 19 5. The Mercier Criterion 22 1. Local mode analysis . . . . . . . . . . . . . . . . .. . . 22 . . . . . 2. Computational method . . . . . . . . . . . . . . . .. . . 23 . . . .

✦ Table of Contents

Front Matter....Pages i-x
Introduction....Pages 1-2
Synopsis of the Method....Pages 3-7
Finite Difference Scheme....Pages 8-14
Nonlinear Stability....Pages 15-21
The Mercier Criterion....Pages 22-27
Transport....Pages 28-32
Stellarator Experiments....Pages 33-39
The ATF-1 and the WISTOR-U....Pages 40-47
Heliac....Pages 48-56
References....Pages 57-59
Description of the Computer Code BETA....Pages 60-69
Glossary....Pages 70-77
Sample Run....Pages 78-83
Listing of Code BETA with Comment Cards....Pages 84-191
Back Matter....Pages 193-196

✦ Subjects

Atomic, Molecular, Optical and Plasma Physics;Fluid- and Aerodynamics;Mathematical Methods in Physics;Numerical and Computational Physics