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On the non-uniqueness of ideal MHD equilibria, with implications for tokamak calculations

Published online by Cambridge University Press:  13 March 2009

J. J. Field  and
J. C. B. Papaloizou
J. J. Field
Affiliation:
Culham Laboratory, Abingdon, Oxon, UK (Euratom/UKAEA Fusion Association)
J. C. B. Papaloizou
Affiliation:
Culham Laboratory, Abingdon, Oxon, UK (Euratom/UKAEA Fusion Association)
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Abstract

Non-linear ideal MHD equilibria in axisymmetric systems are examined, both in diffuse and free boundary cases. Attention is restricted to the situation in present low-β tokamak experiments, in which there are no current reversals. Both general qualitative results on the uniqueness and bifurcation of solutions are provided and exact solutions of several problems in a circular cylinder are given, exhibiting bifurcation phenomena. In particular sufficient conditions for bifurcation behaviour are conjectured, for both diffuse and free boundary equilibria.

Type
Research Article
Information
Journal of Plasma Physics , Volume 18 , Issue 2 , October 1977 , pp. 347 - 361
Copyright
Copyright © Cambridge University Press 1977

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References

REFERENCES

Courant, R. & Hilbert, D. 1953 Methods of Mathematical Physics, vol. 1. Interscience.Google Scholar
Dory, R. A. & Peng, Y. K. M. 1977 Nucl. Fusion, 17, 21.CrossRefGoogle Scholar
Haas, F. A. & Thomas, C. Ll. 1973 Phys. Fluids, 16, 152.CrossRefGoogle Scholar
Hammerstein, A. 1930 Acta Math. 54, 117.CrossRefGoogle Scholar
Marder, B. & Weitzner, H. 1970 Plasma Phys. 12, 435.CrossRefGoogle Scholar
Pao, Y. P. 1976 Phys. Fluids, 19, 1177.CrossRefGoogle Scholar
Papaloizou, J. C. B., Rebelo, I., Field, J. J., Thomas, C. Ll. & Haas, F. A. 1977 Nucl. Fusion, 17, 33.CrossRefGoogle Scholar
Strauss, H. R. 1974 Phys. Fluids, 17, 1040.CrossRefGoogle Scholar
Thomas, C. Ll. & Haas, F. A. 1974 Culham Report CLM-R 133.Google Scholar