Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-06-11T06:13:03.986Z Has data issue: false hasContentIssue false

Remarks on the equilibrium shape of a Tokamak plasma

Published online by Cambridge University Press:  14 November 2011

Yang Jianfu
Affiliation:
Department of Mathematics, Nanchang University, Nanchang, Jiangxi 330047, PR China

Synopsis

The equilibrium of a Tokamak plasma not confined inside a conducting shell is governed by a free boundary value problem. The existence of solutions of the free boundary value problem is discussed.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Ambrosetti, A. and Mancini, G.. A free boundary problem and related semilinear equation. Nonlinear Anal. 4 (1980), 909915.CrossRefGoogle Scholar
2Ambrosetti, A. and Rabinowitz, P. H.. Dual variational methods in critical point theory and applications. J. Funct. Anal. 14 (1973), 349381.Google Scholar
3Ambrosetti, A. and Struwe, M.. Existence of steady vortex rings in an ideal fluid. Arch. Rational Mech. Anal. 108 (1989), 97109.CrossRefGoogle Scholar
4Berestycki, H. and Brezis, H.. On a free boundary problem arising in plasma physics. Nonlinear Anal. 4 (1980), 415436.Google Scholar
5Bona, J. L., Bose, D. K. and Turner, R. E. L.. Finite amplitude steady waves in stratified fluids. J. Math. Pure Appl. 62 (1983), 389439.Google Scholar
6Fraenkel, L. E. and Berger, M. S.. A global theory of steady vortex rings in an ideal fluid. Acta Math. 132 (1974), 1351.Google Scholar
7Gilbarg, D. and Trudinger, N. S.. Elliptic partial differential equations of second order, 2nd edn (Berlin: Springer, 1983).Google Scholar
8Grad, H., Kadish, A. and Stevens, D. C.. A free boundary Tokamak equilibrium. Comm. Pure Appl. Math. 27 (1974), 3957.CrossRefGoogle Scholar
9Norbury, J.. Steady planar vortex pairs in an ideal fluid. Comm. Pure Appl. Math. 28 (1975), 679700CrossRefGoogle Scholar
10Teman, R.. A nonlinear eigenvalue problem: The shape at equilibrium of a confined plasma. Arch. Rational Mech. Anal. 60 (1976), 5173.CrossRefGoogle Scholar
11Teman, R.. Remarks on a free boundary value problem arising in plasma physics. Comm. Partial Differential Equations 2 (1977), 563585.Google Scholar
12Jianfu, Yang. Positive solutions of a semilinear elliptic equation and its asymptotic behaviour. Differential and Integral Equations. 4 (1991), 12091216.Google Scholar