Evidence for topological nonequilibrium in magnetic configurations

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 62, Issue 1 B, 2000, Pages 1245-1251

  Vainshtein, S I ^a   Mikic Z ^b   Rosner, R ^a   Linker, J A ^b  

^a UNIVERSITY OF CHICAGO   (United States)

^b SCIENCE APPLICATIONS INTERNATIONAL CORPORATION   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; MAGNETIZATION;

LAGRANGIAN APPROACH;

TOKAMAK DEVICES;

EID: 0034229833     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.62.1245     Document Type: Article

References (34)

1. M.N. Rosenbluth, R.Y. Dagazian, and P.H. Rutherford, Phys. Fluids 16, 1894 (1973); M.N. Rosenhluth and M.N. Bussac, Nucl. Fusion 19, 489 (1979).
2. M.N. Rosenbluth, R.Y. Dagazian, and P.H. Rutherford, Phys. Fluids 16, 1894 (1973); M.N. Rosenhluth and M.N. Bussac, Nucl. Fusion 19, 489 (1979).
3. E. N. Parker, Spontaneous Current Sheets in Magnetic Fields (Oxford, New York, 1994).
4. L. Golub and J.M. Pasachoff, The Solar Corona (Oxford University Press, Oxford, 1997).
5. E. R. Priest, Solar Magnetohydrodynamics (D. Reidel, Dordrecht, Holland, 1981).
6. S.I. Vainshtein, R.Z. Sagdeev, and R. Rosner, Phys. Rev. E 56, 1605 (1997); S.I. Vainshtein, Phys. Rev. Lett. 80, 4879 (1998).
7. S.I. Vainshtein, R.Z. Sagdeev, and R. Rosner, Phys. Rev. E 56, 1605 (1997); S.I. Vainshtein, Phys. Rev. Lett. 80, 4879 (1998).
8. A.A. Galeev, Space Sci. Rev. 23, 411 (1979).
9. E.N. Parker, Astrophys. J. 174, 499 (1972); Cosmical Magnetic Fields (Clarendon, Oxford, 1979).
10. E.N. Parker, Astrophys. J. 174, 499 (1972); Cosmical Magnetic Fields (Clarendon, Oxford, 1979).
11. H.K. Moffatt, J. Fluid Mech. 159, 359 (1985).
12. H.K. Moffatt, J. Fluid Mech. 166, 359 (1986); in Turbulence and Nonlinear Dynamics in MHD Flows, edited by M. Meneguzzi, A. Pouquet, and P. L. Sulem (Elsevier Science Publishers B. V., Amsterdam, 1989).
13. H.K. Moffatt, J. Fluid Mech. 166, 359 (1986); in Turbulence and Nonlinear Dynamics in MHD Flows, edited by M. Meneguzzi, A. Pouquet, and P. L. Sulem (Elsevier Science Publishers B. V., Amsterdam, 1989).
14. K. Bajer and H.K. Moffatt, J. Fluid Mech. 212, 337 (1990); D. Linardatos, ibid. 246, 569 (1993); A.Y.K. Chui and H.K. Moffatt, Proc. R. Soc. London, Ser. A 451, 609 (1995); A.Y.K. Chui and H.K. Moftatt, J. Plasma Phys. 56, 677 (1996).
15. K. Bajer and H.K. Moffatt, J. Fluid Mech. 212, 337 (1990); D. Linardatos, ibid. 246, 569 (1993); A.Y.K. Chui and H.K. Moffatt, Proc. R. Soc. London, Ser. A 451, 609 (1995); A.Y.K. Chui and H.K. Moftatt, J. Plasma Phys. 56, 677 (1996).
16. K. Bajer and H.K. Moffatt, J. Fluid Mech. 212, 337 (1990); D. Linardatos, ibid. 246, 569 (1993); A.Y.K. Chui and H.K. Moffatt, Proc. R. Soc. London, Ser. A 451, 609 (1995); A.Y.K. Chui and H.K. Moftatt, J. Plasma Phys. 56, 677 (1996).
17. K. Bajer and H.K. Moffatt, J. Fluid Mech. 212, 337 (1990); D. Linardatos, ibid. 246, 569 (1993); A.Y.K. Chui and H.K. Moffatt, Proc. R. Soc. London, Ser. A 451, 609 (1995); A.Y.K. Chui and H.K. Moftatt, J. Plasma Phys. 56, 677 (1996).
18. B.B. Kadomtsev, Plasma Phys. 1, 710 (1975); S.I. Vainshtein, Magn. Gidrodin. 3, 269 (1988).
19. B.B. Kadomtsev, Plasma Phys. 1, 710 (1975); S.I. Vainshtein, Magn. Gidrodin. 3, 269 (1988).
20. S.I. Vainshtein, Zh. Éksp. Teor. Fiz. 86, 451 (1984) [Sov. Phys. JETP 59, 262 (1984)]; S.I. Vainshtein and E.N. Parker, Astrophys. J. 304, 821 (1986); S. I. Vainshtein, A.M. Bykov, and I.N. Toptygin, Turbulence, Current Sheets and Shocks in Cosmic Plasma (Gordon & Breach, Amsterdam, 1993).
21. S.I. Vainshtein, Zh. Éksp. Teor. Fiz. 86, 451 (1984) [Sov. Phys. JETP 59, 262 (1984)]; S.I. Vainshtein and E.N. Parker, Astrophys. J. 304, 821 (1986); S. I. Vainshtein, A.M. Bykov, and I.N. Toptygin, Turbulence, Current Sheets and Shocks in Cosmic Plasma (Gordon & Breach, Amsterdam, 1993).
22. S.I. Vainshtein, Zh. Éksp. Teor. Fiz. 86, 451 (1984) [Sov. Phys. JETP 59, 262 (1984)]; S.I. Vainshtein and E.N. Parker, Astrophys. J. 304, 821 (1986); S. I. Vainshtein, A.M. Bykov, and I.N. Toptygin, Turbulence, Current Sheets and Shocks in Cosmic Plasma (Gordon & Breach, Amsterdam, 1993).
23. S.I. Vainshtein, Zh. Éksp. Teor. Fiz. 86, 451 (1984) [Sov. Phys. JETP 59, 262 (1984)]; S.I. Vainshtein and E.N. Parker, Astrophys. J. 304, 821 (1986); S. I. Vainshtein, A.M. Bykov, and I.N. Toptygin, Turbulence, Current Sheets and Shocks in Cosmic Plasma (Gordon & Breach, Amsterdam, 1993).
24. M. Yamada, H. Ji, S. Hsu, T. Carter, R. Kulsrud, Y. Ono, and F. Perkins, Phys. Rev. Lett. 78, 3117 (1997).
25. Z. Mikić and J.A. Linker, Astrophys. J. 430, 898 (1994).
26. Note that Moffatt and collaborators [10] treat the relaxation problem in quasistatic porous media, so that their momentum equation differs from ours.
27. M.B. Isichenko, Rev. Mod. Phys. 64, 961 (1992); M.B. Isichenko and A.V. Gruzinov, Phys. Plasmas 1, 1802 (1994).
28. M.B. Isichenko, Rev. Mod. Phys. 64, 961 (1992); M.B. Isichenko and A.V. Gruzinov, Phys. Plasmas 1, 1802 (1994).
29. S.I. Vainshtein, R.Z. Sagdeev, R. Rosner, and E.-J. Kim, Phys. Rev. E 53, 4729 (1996).
30. In our approach, it is necessary for each Eulerian cell to contain at least several field lines. Therefore, as we increase the spatial resolution of the Eulerian grid, we need to correspondingly increase the number of field lines used for the Lagrangian calculation.
31. In order to resolve the same field with increased N adequately, we have to increase the number of Eulerian cells; see [18].
32. K. Shibata, N. Nitta, R. Matsumoto, T. Tajima, T. Yokoyama, T. Hirayama, and H. Hudson, in X-ray Solar Physics from Yohkoh, edited by Y. Uchida, T. Watanabe, K. Shibata, and H. Hudson (Universal Academic Press, Tokyo, 1993), pp. 29-32.
33. S.I. Vainshtein, Z. Mikić, and J.A. Linker (unpublished). The relatively simple geometry of the configuration makes it possible to study the scaling of the reconnection rate with two decades of scaling in S. Presumably, the reconnection rate substantially exceeds the Sweet-Parker rate because the current sheet is relatively short. Low rates of reconnection observed in coalescing magnetic islands, see, e.g., C. Marliani and H.R. Strauss, Phys. Plasmas 6, 495 (1999), may be attributed to the fact that the configuration is not at topological nonequilibrium, because there is no outermost zero line in the problem, so that the current sheet is instead formed due to instability.
34. S.I. Vainshtein, Z. Mikić, and J.A. Linker (unpublished). The relatively simple geometry of the configuration makes it possible to study the scaling of the reconnection rate with two decades of scaling in S. Presumably, the reconnection rate substantially exceeds the Sweet-Parker rate because the current sheet is relatively short. Low rates of reconnection observed in coalescing magnetic islands, see, e.g., C. Marliani and H.R. Strauss, Phys. Plasmas 6, 495 (1999), may be attributed to the fact that the configuration is not at topological nonequilibrium, because there is no outermost zero line in the problem, so that the current sheet is instead formed due to instability.