Prog. Theor. Phys. Vol. 71 No. 4 (1984) pp. 671-676
On the Quasi-Static Evolution of Two-Dimensional Plasmas
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012
Department of Nuclear Engineering, Faculty of Engineering, University of Tokyo, Tokyo 113
(Received August 20, 1983)
The quasi-statics of current-carrying two-dimensional plasmas have been studied applying operator-theoretic methods in nonlinear functional analysis. A diffusion equation with a singular perturbation has been introduced as a model of the quasi-statics. Roughly speaking, the diffusion coefficient parallel to magnetic surfaces we show must become infinite; this is required by the equilibrium condition. In view of the singular perturbation, we have studied the free-boundary and the bifurcation of solutions. The bifurcation theorem obtained gives theoretical foundations for the argument of neighboring equilibriums.
DOI : 10.1143/PTP.71.671
- R. Temam, Arch. Rational Mech. Anal. 60 (1975), 51.
- H. Berestycki and H. Brezis, CR Acad. Sci. Paris 283A (1976), 1091.
- R. Temam, Comm. in Partial Differential Equations 2 (1977), 563.
- D. G. Schaeffer, Comm. in Partial Differential Equations 2 (1977), 587.
- B. Marder and H. Weitzner, Plasma Phys. 12 (1970), 435.
D. K. Bhadra, Phys. Fluids 16 (1973), 1781[AIP Scitation].
S. Yoshikawa, Phys. Rev. Lett. 27 (1971), 1772[APS].
- A. Sykes and J. A. Wesson, Proc. 8th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Brussels, 1980 (IAEA, Vienna, 1977), vol. 1, p. 237.
H. Grad, Phys. Fluids 10 (1967), 137[AIP Scitation].
- R. B. White et al., Proc. 6th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Berchtesgaden, 1976 (IAEA, Vienna, 1977), vol. 1, p. 569.
A. Sykes and J. A. Wesson, Phys. Rev. Lett. 44 (1980), 1215[APS].
B. V. Waddel et al., Phys. Rev. Lett. 41 (1978), 1386[APS].
- H. Grad and P. N. Hu, Proc. Finite β Workshop, Varenna, 1977 (Office of Fusion Energy, Washington, D.C., 1977) p. 153.
- H. Grad and H. Rubin, Proc. 2nd United Nations International Conference on the Peaceful Uses of Energy 31 (1958), 190.
- Y. Suzuki, Nucl. Fusion 14 (1974), 345.
- J-L. Lions and E. Magenes, Problèms aux limites non homogènes et applications (Dunod, Paris, 1968), chap. I.
- K. Masuda, Evolution Equations (Kinokuniya, Tokyo, 1975), (in Japanese).
- P. H. Rabinowitz, Rocky Mountain Journal 3 (1973), No. 2 (supplement), 161.