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 . . . .