Abstract
In a Tokamak the plasma is confined inside a toroidal vacuum vessel by the magnetic field. In the present Tokamak modeling the plasma boundary is a flux line, which is a free boundary and in contact with a given limiter. We give a model for the plasma equilibrium in a Tokamak with a limiter and a nonlinear plasma current. And we prove, under suitable conditions on the nonlinearity of the plasma current, the existence of such an equilibrium for given external current.
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References
H. Berestycki and H. Brezis, Sur certains problèmes de frontière libre. C. R. Acad. Sci. Paris,283 (1976), 1091–1094.
H. Berestycki and H. Brezis, On a free boundary problem arising in plasma physics. Nonlinear Anal.,4 (1980), 415–436.
J. Blum, T. Gallouet and J. Simon, Existence and control of plasma equilibrium. SIAM. J. Math. Anal.,17 (1986), 1158–1177.
T. Gallouet, Contribution à l’étude d’une équation apparaissant en physique des plasma. Thèse 3ème cycle, Université Paris VI, 1978.
J. Leray and J. Schaudr, Topologie et Équation Fonctionnelles. Ann. Sci. École. Norm. Sup.,51 (1934), 45–78.
J.P. Puel, Un problème de valeur propre non linéaire et de frontièr libre. Journées d’Analyse Non Linéaire, Lecture Notes in Math. No. 665, Springer Verlag, Berlin, 1977, 188–204.
R. Temam, Remarks on a free boundary problems arising in plasma physics. Comm. Partial Differential Equations,2 (1977), 563–585.
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Nakamura, M.A. On an equilibrium of the plasma in a Tokamak with a limiter. Japan J. Indust. Appl. Math. 8, 431–444 (1991). https://doi.org/10.1007/BF03167145
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DOI: https://doi.org/10.1007/BF03167145