Eigenvalue problems for Beltrami fields arising in a three-dimensional toroidal magnetohydrodynamic equilibrium problem

Physics of Plasmas

Volumn 14, Issue 5, 2007, Pages

  Hudson, S R ^a   Hole, M J ^b   Dewar, R L ^b  

^a PRINCETON PLASMA PHYSICS LABORATORY   (United States)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; CONSTRAINT THEORY; EIGENVALUES AND EIGENFUNCTIONS; GEOMETRY;

BELTRAMI FIELDS; CHAOTIC FIELD LINE TRANSPORT; ENERGY PRINCIPLES; MAGNETIC SURFACES;

MAGNETOHYDRODYNAMICS;

EID: 34249864449     PISSN: 1070664X     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2722721     Document Type: Article

References (57)

1. A. H. Boozer, Phys. Fluids 26, 1288 (1983).
2. J. R. Cary and R. G. Littlejohn, Ann. Phys. (Paris) 151, 1 (1983).
3. W. D. D'haeseleer, W. N. G. Hitchon, J. D. Callen, and J. L. Shohet, Flux Coordinates and Magnetic Field Structure (Springer, Berlin, 1991), p. 170.
4. R. L. Dewar, D. A. Monticello, and W. N.-C. Sy, Phys. Fluids 27, 1723 (1984).
5. H. Goldstein, Classical Mechanics, 2nd ed. (Addison-Wesley, Massachusetts, 1980), Chap. 10.
6. A. H. Boozer, Phys. Plasmas 5, 1647 (1998).
7. D. K. Arrowsmith and C. M. Place, An Introduction to Dynamical Systems (Cambridge University Press, Cambridge, U. K., 1991).
8. A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics, 2nd ed. (Springer-Verlag, New York, 1992).
9. J. D. Meiss, Rev. Mod. Phys. 64, 795 (1992).
10. J. M. Greene, J. Math. Phys. 20, 1183 (1979).
11. S. R. Hudson, D. A. Monticello, A. H. Reiman, A. H. Boozer, D. J. Strickler, S. P. Hirshman, and M. C. Zarnstorff, Phys. Rev. Lett. 89, 275003 (2002).
12. R. S. MacKay and J. Stark, Nonlinearity 5, 867 (1992).
13. I. Niven, Irrational Numbers, Mathematical Association of America (Wiley, New York, 1956).
14. R. S. MacKay, Nonlinearity 5, 161 (1992).
15. J. M. Greene, R. S. MacKay, and J. Stark, Physica D 21, 267 (1986).
16. S. P. Hirshman and Whitson, Phys. Fluids 26, 3553 (1983).
17. H. J. Gardner and D. B. Blackwell, Nucl. Fusion 32, 2009 (1992).
18. A. H. Boozer, Phys. Fluids 24, 1999 (1981).
19. A. Bhattacharjee, T. Hayashi, C. C. Hegna, N. Nakajima, and T. Sato, Phys. Plasmas 2, 883 (1995).
20. H. Grad, Phys. Fluids 10, 137 (1967).
21. A. H. Reiman and H. S. Greenside, J. Comput. Phys. 75, 423 (1988).
22. K. Harafuji, T. Hayashi, and T. Sato, J. Comput. Phys. 81, 169 (1989).
23. M. D. Kruskal and R. M. Kulsrud, Phys. Fluids 1, 265 (1958).
24. J. B. Taylor, Phys. Rev. Lett. 33, 1139 (1974).
25. J. B. Taylor, Rev. Mod. Phys. 58, 741 (1986).
26. J. H. Misguich, Phys. Plasmas 8, 2132 (2001).
27. J. H. Misguich, J.-D. Reuss, D. Constantinescu, G. Steinbrecher, M. Vlad, F. Spineanu, B. Weyssow, and R. Balescu, Ann. Phys. (Paris) 28, 1 (2003).
28. O. P. Bruno and P. Laurence, Commun. Pure Appl. Math. 49, 1717 (1996).
29. H. L. Berk, J. P. Freidberg, X. Llobet, P. J. Morrison, and J. A. Tataronis, Phys. Fluids 29, 3281 (1986).
30. R. Kaiser and A. Salat, Phys. Plasmas 1, 281 (1994).
31. R. Kaiser, Phys. Plasmas 1, 2693 (1994).
32. G. O. Spies and J. Li, Phys. Plasmas 1, 2901 (1994).
33. G. O. Spies, D. Lortz, and R. Kaiser, Phys. Plasmas 8, 3652 (2001).
34. G. O. Spies, Phys. Plasmas 10, 3030 (2003).
35. A. Bhattacharjee and R. L. Dewar, Phys. Fluids 25, 887 (1982).
36. L. Woltjer, Astrophys. J. 128, 384 (1958).
37. P. J. Morrison, Rev. Mod. Phys. 70, 467 (1998), p. 511
38. R. Kress, Z. Angew. Math. Phys. 28, 715 (1977).
39. R. Kress, J. Eng. Math. 15, 29 (1981).
40. R. Kress, J. Eng. Math. 20, 323 (1986).
41. D. Lortz and G. O. Spies, Phys. Plasmas 1, 249 (1994).
42. R. Kaiser and H. Uecker, Q. J. Mech. Appl. Math. 57, 1 (2004).
43. M. J. Hole, S. R. Hudson, and R. L. Dewar, J. Plasma Phys. 72, 1167 (2006).
44. M. J. Hole, S. R. Hudson, and R. L. Dewar, " Equilibria and stability in partially relaxed plasma-vacuum systems., " Nucl. Fusion (to be published).
45. S. Wolfram, The Mathematica Book, 5th ed. (Wolfram Media, Champaign, 2003), pp. 780-781.
46. R. L. Dewar and S. R. Hudson, Physica D 112, 275 (1997).
47. S. R. Hudson, Phys. Plasmas 11, 677 (2004).
48. B. Chirikov, Phys. Rep. 52, 263 (1979).
49. S. R. Hudson, Phys. Rev. E 74, 056203 (2006).
50. H. Kook and J. D. Meiss, Physica D 1-2, 65 (1989).
51. S. Marmi and J. Stark, Nonlinearity 5, 743 (1992).
52. J. W. Belcher and L. Davis, Jr., J. Geophys. Res. 76, 3534 (1971).
53. O. P. Bruno and F. Reitich, J. Fourier Anal. Appl. 7, 169 (2001).
54. S. P. Hirshman, W. I. van Rij, and P. Merkel, Comput. Phys. Commun. 43, 143 (1986).
55. P. Merkel, J. Comput. Phys. 66, 83 (1986).
56. C. C. Hegna and N. Nakajima, Phys. Plasmas 5, 1336 (1998).
57. P. Cuthbert and R. L. Dewar, Phys. Plasmas 7, 2302 (2000).