Statistical description and transport in stochastic magnetic fields

Physics of Plasmas

Volumn 3, Issue 3, 1996, Pages 874-888

  Vanden Eijnden, E ^a   Balescu, R ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0008439980     PISSN: 1070664X     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.871791     Document Type: Article

References (45)

1. P. Liewer, Nucl. Fusion 22, 543 (1985).
2. R. Balescu, Transport Process in Plasmas (North-Holland, Amsterdam, 1988), Vol. 2.
3. M. N. Rosenbluth, R. Z. Sagdeev, J. B. Tylor, and G. M. Zaslavsky, Nucl. Fusion 6, 297 (1966).
4. A. A. Galeev and L. M. Zelenyi, Comments Plasmas Phys. Controlled Fusion 14, 249 (1971).
5. T. H. Stix, Phys. Rev. Lett. 30, 833 (1973).
6. A. B. Rechester and M. N. Rosenbluth, Phys. Rev. Lett. 40, 38 (1978).
7. J. H. Krommes, Progr. Theor. Phys. Suppl. 64, 137 (1978).
8. B. B. Kadomtsev and O. P. Pogutse, in Plasma Physics and Controlled Nuclear Fusion Research, Proceedings of the 7th International Conference, Innsbruck, 1978 (Internatinoal Atomic Energy Agency, Vienna, 1979), Vol. 1, p. 649.
9. P. H. Diamond, T. H. Dupree, and D. J. Tetreault, Phys. Rev. Lett. 45, 562 (1980).
10. F. A. Haas, A. Thyagaraja, and I. Cook, Plasma Phys. 23, 1027 (1981).
11. H. A. Rose, Phys. Rev. Lett. 48, 260 (1982).
12. J. A. Krommes, C. Oberman, and R. G. Kleva, J. Plasma Phys. 30, 11 (1983).
13. G. Zimbardo, P. Veltri and F. Malara, J. Plasma Phys. 32, 141 (1984).
14. A. Thyagaraja and F. Haas, Phys. Scr. 31, 83 (1985).
15. M. B. Isichenko, Plasma Phys. Controlled Fusion 33, 795 (1991).
16. M. B. Isichenko, Plasma Phys. Controlled Fusion 33, 809 (1991).
17. J. M. Rax and R. B. White, Phys. Rev. Lett. 68, 1523 (1992).
18. M. Coronado, E. J. Vitela, and A. Akcasu, Phys. Fluids B 4, 3935 (1992).
19. J. R. Myra, P. J. Catto, H. E. Mynick, and R. E. Duvall, Phys. Fluids B 5, 1160 (1993).
20. G. Laval, Phys. Fluids B 5, 711 (1993).
21. R. B. White and Y. Wu, Phys. Controlled Fusion 35, 595 (1993).
22. L. Hannibal, Phys. Fluids B 5, 3551 (1993).
23. R. Balescu, H.-D. Wang and J. H. Misguich, Phys. Plasmas 1, 3826 (1994).
24. H. Sugimoto, T. Kurasawa, and H. Ashida, Plasma Phys. Controlled Fusion 36, 383 (1994).
25. H.-D. Wang, M. Vlad, E. Vanden Eijnden, F. Spineanu, J. H. Misguich, and R. Balescu, Phys. Rev. E 51, 4844 (1995).
26. E. Vanden Eijnden and R. Balescu, J. Plasma Phys. 54, 185 (1995).
27. E. Vanden Eijnden and R. Balescu, Phys. Plasma 3, 815 (1996).
28. N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1992).
29. C. W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, Berlin, 1985).
30. R. Balescu, Equilibrium and Non Equilibrium Statistical Mechanics (North-Holland, Amsterdam, 1975).
31. It should be noted that the hybrid kinetic equation (3) can be coupled with the Maxwell equations, and, hence, allows a self-consistent treatment of the magnetic field. In contrast, the Langevin equations (2) are necessarily non-self-consistent. The self-consistency problem will not be considered here and the magnetic field properties will be specified a priori.
32. R. Balescu, Phys. Rev. E 51, 4807 (1995).
33. R.H. Kraichnan, Phys. Rev. 108, 1407 (1958).
34. R. H. Kraichnan, J. Math. Phys. 2, 124 (1961).
35. P. C. Martin, E. D. Siggia, and H. A. Rose, Phys. Rev. A 8, 423 (1973).
36. A. Brissaud and U. Frisch, J. Math. Phys. 15, 524 (1974).
37. U. Deker and F. Haake, Phys. Rev. A 11, 2043 (1975).
38. R. J. Jensen, J. Stat. Mech. 25, 183 (1981).
39. J. A. Krommes, Handbook of Plasma Physics, edited by M. N. Rosenbluth and R. Z. Sagdeev (North-Holland, Amsterdam, 1984), Vol. 2, p. 183.
40. T. H. Dupree, Phys. Rev. Lett. 25, 789 (1970).
41. T. H. Dupree, Phys. Fluids 15, 334 (1972).
42. B. B. Kadomtsev and O. P. Pogutse, Phys. Rev. Lett. 25, 1155 (1970).
43. B. B. Kadomtsev and O. P. Pogutse, Proceedings of the European Conference Controlled Fusion and Plasma Physics (European Physical Society Petit-Lancy, 1970), p. 74.
44. J. H. Misguich and R. Balcscu, Plasma Phys. 20, 781 (1978).
45. Two comments about this result: The distribution function F depends on z, contrary to the density profile n(x;t) introduced in Ref. 33. The density profile n(x;t) of Ref. 33, defined with a different choice of normalization, must thus be identified with our reduced distribution function (32).