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Plasma Transport in Toroidal Confinement Systems

### Abstract

The neoclassical theory of plasma transport in axisymmetric, toroidal confinement systems, is developed by means of a variational principle for the rate of irreversible entropy production. The variational principle derived here employs the full Fokker‐Planck collision operator, including both like and unlike species collisions. Using the variational principle, all the relevant neoclassical transport coefficients are systematically evaluated in the “banana” regime of small collisional frequency, to lowest order in the inverse aspect ratio. These results include both the “diagonal” and “cross” coefficients for the particle fluxes, ion and electron heat flux, and electric current. By combining the transport coefficients with appropriate moments of the drift equation, a closed set of equations which accurately summarize the predictions of neoclassical theory in the banana regime is obtained. The significance of these equations, in particular with regard to recent tokamak experiments, is discussed briefly.

© 1972 American Institute of Physics

Received 25 August 1971
Published online 31 July 2003

/content/aip/journal/pof1/15/1/10.1063/1.1693728

1.

1.L. A. Artsimovich, G. A. Bobrovskii, E. P. Gorbunov, D. P. Ianov, V. D. Kirilov, E. I. Kuznetsov, S. V. Mirnov, M. P. Petrov, K. A. Razumova, V. S. Strelkov, and D. A. Scheglov, in Plasma Physics and Controlled Nuclear Fusion Research (International Atomic Energy Agency, Vienna, 1969), Vol. I. p. 157

1.[Nucl. Fusion Suppl., p. 17 (1969)].

2.

2.L. A. Artsimovich, A. M. Anashin, E. P. Gorbunov, D. P. Ianov, M. P. Petrov, and V. S. Strelkov, ZhETF Pis. Red. 10, 130 (1969)

2.[L. A. Artsimovich, A. M. Anashin, E. P. Gorbunov, D. P. Ianov, M. P. Petrov, and V. S. Strelkov, JETP Letters 10, 82 (1969)].

3.

3.N. J. Peacock, D. C. Robinson, M. J. Forrest, P. D. Wilcock, and V. V. Sannikov, Nature 224, 488 (1969).

4.

4.A. A. Galeev and R. Z. Sagdeev, Zh. Eksp. Teor. Fiz. 53, 348 (1967)

4.[A. A. Galeev and R. Z. Sagdeev, Sov. Phys. JETP 26, 233 (1968)].

5.

5.P. H. Rutherford, Phys. Fluids 13, 482 (1970).

6.

6.E. A. Frieman, Phys. Fluids 13, 490 (1970).

7.

7.L. M. Kovrizhnikh, Zh. Eksp. Teor. Fiz. 56, 877 (1969)

7.[L. M. Kovrizhnikh, Sov. Phys. JETP 29, 475 (1969)].

8.

8.A. A. Ware, Phys. Rev. Letters 25, 916 (1970).

9.

9.An analysis of this point, which however includes the effects of like species collisions only through a model collision operator, has been presented by P. H. Rutherford, L. M. Kovrizhnikh, M. N. Rosenbluth, and F. L. Hinton [Phys. Rev. Letters. 25, 1090 (1970)].

10.

10.B. B. Robinson and I. B. Bernstein, Ann. Phys. (N.Y.) 18, 110 (1962).

11.

11.S. R. de Groot and P. Mazur, Non‐Equilibrium Thermodynamics (North‐Holland, Amsterdam, 1962), Chap. 4.

12.

12.H. P. Furth, M. N. Rosenbluth, P. H. Rutherford, and W. Stodiek, Phys. Fluids 13, 3020 (1970).

13.

13.L. Spitzer and R. Härm, Phys. Rev. 89, 977 (1953).

14.

14.M. N. Rosenbluth, W. MacDonald, and D. Judd, Phys. Rev. 107, 1 (1957).

15.

15.S. I. Braginskii, in Reviews of Plasma Physics, edited by M. A. Leontovich (Consultants Bureau, New York, 1965), Vol. I, p. 205.

16.

16.M. N. Rosenbluth, P. H. Rutherford, J. B. Taylor, E. A. Frieman, and L. M. Kovrizhnikh, presented at the Fourth Conference on Plasma Physics and Controlled Nuclear Fusion Research, Madison, Wisconsin, (1971).

17.

17.Some terms in which relate that flux to the forces n′, and have been neglected in Eq. (173). (In this approximation, ) These terms may be significant, however, in the substitution of Eq. (173) into the ion heat balance Eq. (172). We therefore remark that the corrections to which can be calculated with some refinement of our procedures of Secs. III and IV, are proportional to г, and that results correct to may be obtained simply by replacing the left‐hand side of Eq. (173) by

18.

18.Compare Ref. 9. The coefficient 1.6 in Eq. (9) of this reference results from a numerical error, and should be 1.46, as given in our Eq. (182).

19.

19.F. L. Hinton and C. R. Oberman, Nucl. Fusion 9, 319 (1969).

20.

20.We are indebted to A. A. Ware (private communication) for pointing out this relation.

21.

21.R. J. Bickerton, J. W. Connor, and J. B. Taylor, (to be published).

22.

22.A. A. Galeev, Zh. Eksp. Teor. Fiz. 59, 1378 (1970)

22.[A. A. Galeev, Sov. Phys. JETP 32, 752 (1971)].

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