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Toroidal Containment of a Plasma
1.H. Grad, Phys. Fluids 9, 225 (1966).
2.H. Grad, in Proceedings of the Symposium on Electromagnetics and Fluids Dynamics of Gaseous Plasma (Polytechnic Press, Brooklyn, New York, 1961).
3.A. S. Bishop and C. G. Smith, Phys. Fluids 9, 1380 (1966).
4.H. Grad, in Proceedings of Symposia in Applied Mathematics (American Mathematical Society, Providence, Rhode Island, 1966), Vol. 18, p. 162.
5.H. Grad, Phys. Fluids 9, 498 (1966).
6.S. Hamada, Nucl. Fusion 2, 23 (1962).
7.For example, see D. W. Kerst, J. Nucl. Energy C4, 253 (1962);
7.A. I. Morozov and L. S. Solov’ev, in Reviews of Plasma Physics (Consultants Bureau, New York, 1966), Vol. II, p. 1.
8.J. Moser, Nachr. Akad. Wiss. Göttingen, II. Math.‐Physik. Kl. I, 1 (1962).
9.R. J. Hastie, J. B. Taylor, and F. A. Haas (to be published).
10.The fact that this class of transitional orbits is not easily contained was first noted by Bishop and Smith, Ref. 3.
11.M. N. Rosenbluth and N. Rostoker, Phys. Fluids 2, 23 (1959).
12.A. Kadish, Phys. Fluids 9, 514 (1966).
13.T. H. Stix, Phys. Fluids 7, 1960 (1964).
14.J. B. Taylor, Phys. Fluids 6, 1529 (1963).
15.H. Grad, in Plasma Physics and Controlled Nuclear Fusion Research (International Atomic Energy Agency, Vienna, 1966), Vol. II, p. 161.
16.H. Grad and H. Rubin, in Proceedings of the Second International Conference on the Peaceful Uses of Atomic Energy (United Nations, Geneva, 1958), Vol. 31, p. 190.
17.H. Grad, Phys. Fluids 7, 1283 (1964).
18.W. Newcomb, Phys. Fluids 2, 362 (1959).
19.B. B. Kadomtsev, in Plasma Physics and the Problem of Controlled Thermonuclear Reactions, M. A. Leontovich, Ed. (Pergamon Press, Inc., New York, 1960), Vol. IV, p. 17.
20.H. P. Furth, Phys. Rev. Letters 11, 308 (1963).
21.J. Andreoletti, Compt. Rend. 257, 1237 (1963).
22.H. Grad, Phys. Rev. Letters 16, 1147 (1966).
23.J. D. Jukes, J. Nucl. Energy C6, 84 (1964).
24.There is some experimental evidence of “anomalous diffusion” wherein both ε and μ may possibly be unaltered in the presence of transverse diffusion [e.g., B. J. Eastlund, Phys. Fluids 9, 594 (1966)]. If this is confirmed, the distribution would take on more importance.
25.D. J. BenDaniel, Phys. Fluids 8, 1567 (1965).
26.The lemma in essentially this form is proved by Moser (Ref. 8). It is also related to a formula given by Newcomb (Ref. 18). The solution of the ordinary differential equation on a torus is standard [e.g., E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations (McGraw‐Hill Book Company, Inc., New York, 1955), Chap. 17], except for the discussion of the dependence on α; see also Hamada (Ref. 6).
27.M. D. Kruskal and R. M. Kulsrud, in Proceedings of the Second International Conference on the Peaceful Uses of Atomic Energy (United Nations, Geneva, 1958), Vol. 31, p. 213.
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