Magnetohydrodynamic Equilibrium and Stability of Stellarators

1. Front Matter

   Pages i-x

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2. Introduction

   • Frances Bauer, Octavio Betancourt, Paul Garabedian

   Pages 1-2

3. Synopsis of the Method

   • Frances Bauer, Octavio Betancourt, Paul Garabedian

   Pages 3-7

4. Finite Difference Scheme

   • Frances Bauer, Octavio Betancourt, Paul Garabedian

   Pages 8-14

5. Nonlinear Stability

   • Frances Bauer, Octavio Betancourt, Paul Garabedian

   Pages 15-21

6. The Mercier Criterion

   • Frances Bauer, Octavio Betancourt, Paul Garabedian

   Pages 22-27

7. Transport

   • Frances Bauer, Octavio Betancourt, Paul Garabedian

   Pages 28-32

8. Stellarator Experiments

   • Frances Bauer, Octavio Betancourt, Paul Garabedian

   Pages 33-39

9. The ATF-1 and the WISTOR-U

   • Frances Bauer, Octavio Betancourt, Paul Garabedian

   Pages 40-47

10. Heliac

    • Frances Bauer, Octavio Betancourt, Paul Garabedian

    Pages 48-56

11. References

    • Frances Bauer, Octavio Betancourt, Paul Garabedian

    Pages 57-59

12. Description of the Computer Code BETA

    • Frances Bauer, Octavio Betancourt, Paul Garabedian

    Pages 60-69

13. Glossary

    • Frances Bauer, Octavio Betancourt, Paul Garabedian

    Pages 70-77

14. Sample Run

    • Frances Bauer, Octavio Betancourt, Paul Garabedian

    Pages 78-83

15. Listing of Code BETA with Comment Cards

    • Frances Bauer, Octavio Betancourt, Paul Garabedian

    Pages 84-191

16. Back Matter

    Pages 193-196

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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 . . . .

• BETA
• Magnetohydrodynamik
• Partielle Differentialgleichung
• Plasmaeinschluss
• Stability
• Stellarator
• magnetohydrodynamics
• fluid- and aerodynamics

• Courant Institute of Mathematical Sciences, New York University, New York, USA

  Frances Bauer, Octavio Betancourt, Paul Garabedian

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