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Relaxation and magnetic reconnection in plasmas

J. B. Taylor

J. B. Taylor

  • Culham Laboratory, Abingdon, Oxfordshire, OX14 3DB, England

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Rev. Mod. Phys. 58, 741 – Published 1 July, 1986

DOI: https://doi.org/10.1103/RevModPhys.58.741

Abstract

The theory of plasma relaxation is described and developed. Turbulence, allied with a small resistivity, allows the plasma rapid access to a particular minimum-energy state. This process involves reconnection of magnetic field lines in a manner that destroys all the topological invariants of ideal plasma so that only total magnetic helicity survives. Although this mechanism, and the equations describing the relaxed state, are similar in all systems, the properties of the relaxed state depend crucially on the topology—toroidal or spherical—of the container and on the boundary conditions. Consequently there are several different types of relaxed state, each with its own special characteristics, which are derived and discussed. The measurements made on many experiments, including toroidal pinches, OHTE, multipinch, and spheromaks, are reviewed and shown to be in striking agreement with the theoretical predictions.

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References (105)

  1. Antoni, V., S. Martini, S. Ortolani, and R. Paccagnella, 1983, in Mirror Based and Field Reversed Approaches to Magnetic Fusion, proceedings of the International School of Physics Workshop, edited by R. Post, D. E. Baldwin, and D. D. Ryutov [International School of Plasma Physics, Varenna (Como), Italy], p. 107
  2. Aydemir, A. Y., and D. C. Barnes, 1984, Phys. Rev. Lett. 52, 930
  3. Aydemir, A. Y., D. C. Barnes, E. J. Caramana, A. A. Mirin, R. A. Nebel, D. D. Schnack, and A. G. Sgro, 1985, Phys. Fluids 28, 898
  4. Barnes, C. W., H. W. Hoida, I. Henins, J. C. Fernandez, T. R. Jarboe, S. O. Knox, G. J. Marklin, and R. M. Mayo, 1985, Bull. Am. Phys. Soc. 30, 1453
  5. Berger, M. A., and G. B. Field, 1984, J. Fluid Mech. 147, 133
  6. Bevir, M., and J. Gray, 1980, in Proceedings of the Reverse Field Pinch Theory Workshop, edited by H. R. Lewis and R. A. Gerwin (Los Alamos National Laboratory, Los Alamos, New Mexico), Session III, paper A-3
  7. Bhattacharjee, A., and R. L. Dewar, 1982, Phys. Fluids 25, 887
  8. Bhattacharjee, A., R. L. Dewar, and D. Monticello, 1980, Phys. Rev. Lett. 45, 347
  9. Bodin, H. A. B., 1984, in Proceedings of the International Conference on Plasma Physics, Lausanne, edited by M. Q. Tran and R. J. Verbeek (EEC, Brussels), Vol. I, p. 417
  10. Bodin, H. A. B., and A. A. Newton, 1980, Nucl. Fusion 20, 1255
  11. Bondeson, A., G. Marklin, Z. G. An, H. H. Chen, Y. C. Lee, and C. S. Liu, 1981, Phys. Fluids 24, 1682
  12. Bruhns, H., C. Chin-Fatt, Y. P. Chong, A. W. DeSilva, G. C. Goldenbaum, H. R. Griem, G. W. Hart, R. A. Hess, J. H. Irby, and R. S. Shaw, 1983, Phys. Fluids 26, 1616
  13. Bruhns, H., G. Raupp, K. Sobel, J. Steiger, and A. Weichelt, 1984, in Proceedings of the 6th U.S. Symposium on Compact Toroid Research, edited by M. Yamada and R. Ellis, Jr. (Princeton Plasma Physics Laboratory, Princeton, N.J.), p. 25
  14. Butt, E. P., C. W. Gowers, A. Mohri, A. A. Newton, D. C. Robinson, A. J. L. Verhage, M. R. C. Watts, Li Yin-An, and H. A. B. Bodin, 1975, Proceedings of the 7th European Conference on Controlled Fusion and Plasma Physics, Lausanne (Centre de Recherches en Physique des Plasmas, Lausanne), Vol. I, p. 39
  15. Caramana, E. J., R. A. Nebel, and D. D. Schnack, 1983, Phys. Fluids 26, 1305
  16. Chandrasekhar, S., and P. C. Kendall, 1957, Astrophys. J. 126, 457
  17. DiMarco, J. N., 1983, in Mirror Based and Field Reversed Approaches to Magnetic Fusion, proceedings of the International School of Plasma Physics Course, edited by R. F. Post, D. E. Baldwin, and D. D. Ryutov [International School of Plasma Physics, Varenna (Como), Italy], Vol. II, p. 681
  18. Edenstrasse, J. W., and W. Schuurman, 1983, Phys. Fluids 26, 500
  19. Faber, V., A. B. White, and G. M. Wing, 1982, J. Math. Phys. 23, 1524
  20. Faber, V., A. B. White, and G. M. Wing, 1985, Plasma Phys. Cont. Fusion 27, 509
  21. Finn, J. M., W. M. Mannheimer, and E. Ott, 1981, Phys. Fluids 24, 1336
  22. Frisch, U., A. Pouquet, J. Léorat, and A. Mazure, 1975, J. Fluid Mechn. 68, 769
  23. Furth, H., 1981, J. Vac. Sci. Technol. 18, 1073
  24. Furth, H., 1985, Phys. Fluids 28, 1595
  25. Furth, H., J. Killeen, and M. N. Rosenbluth, 1963, Phys. Fluids 6, 459
  26. Gibson, R. D., and K. Whiteman, 1968, Plasma Phys. 10, 1101
  27. Goldenbaum, G. C., 1982, Phys. Scr. T2/2, 359
  28. Goldenbaum, G. C., J. H. Irby, Y. P. Chong, and G. W. Hart, 1980, Phys. Rev. Lett. 44, 393
  29. Hameiri, E., and J. H. Hammer, 1982, Phys. Fluids 25, 1855
  30. Hart, G. W., A. Janos, D. D. Meyerhofer, and M. Yamada, 1985, Phys. Fluids (in press)
  31. Hasegawa, A., 1985, Adv. Phys. 34, 1
  32. Heyvaerts, J., and E. R. Priest, 1984, Astron. Astrophys. 137, 63
  33. Janos, A., G. W. Hart, C. H. Nam, and M. Yamada, 1985b, Phys. Fluids 28, 3667
  34. Janos, A., G. W. Hart, and M. Yamada, 1985a, Phys. Rev. Lett. 55, 2868
  35. Jarboe, T. R., 1985a, Comments Plasma Phys. 9, 161
  36. Jarboe, T. R., 1985b, Bull. Am. Phys. Soc. 30, 1408
  37. Jarboe, T. R., Cris W. Barnes, I. Henins, H. W. Hoida, S. O. Knox, R. K. Linford, and A. R. Sherwood, 1984, Phys. Fluids 27, 13
  38. Jarboe, T. R., I. Henins, H. W. Hoida, R. K. Linford, J. Marshall, D. A. Platts, and A. R. Sherwood, 1980, Phys. Rev. Lett. 45, 1264
  39. Jarboe, T. R., I. Henins, A. R. Sherwood, Cris W. Barnes, and H. W. Hoida, 1983, Phys. Rev. Lett. 51, 39
  40. Jensen, T., and M. S. Chu, 1981, J. Plasma Phys. 25, 459
  41. Jensen, T., and M. S. Chu, 1983, in Proceedings of the 5th Symposium on Physics and Technology of Compact Toroids, edited by A. L. Hoffman and R. D. Milroy (Mathematical Sciences Northwest Inc.), pp. 174-177
  42. Jensen, T., and M. S. Chu, 1984, Phys. Fluids 27, 2881
  43. Kadomtsev, B. B., 1975, Fiz. Plazmy 1, 710 [Sov. J. Plasma Phys. 1, 389 (1975)]
  44. Kadomtsev, B. B., 1977, Plasma Physics and Controlled Nuclear Fusion Research 1976, Proceedings of the 6th International Conference, Berchtesgaden, 1976 (IAEA, Vienna), Vol. I, p. 555
  45. Katsurai et al., 1984, Proceedings of the 6th US-Japan Compact Toroid Symposium (Hiroshima University, Hiroshima, Japan)
  46. Kawai, K., and A. A. Pietrzyk, 1981, Bull. Am. Phys. Soc. 26, 905
  47. Kondoh, Y., 1981, Nucl. Fusion 21, 1607
  48. Konigl, A., and A. R. Choudhuri, 1985, Astrophys. J. 289, 173
  49. Krüger, J., 1976a, J. Plasma Phys. 15, 15
  50. Krüger, J., 1976b, J. Plasma Phys. 15, 31
  51. Kruskal, M. D., and R. M. Kulsrud, 1958, Phys. Fluids 1, 265
  52. La Haye, R. J., T. H. Jensen, P. S. C. Lee, R. W. Moore, and T. Ohkawa, 1986, Nucl. Fusion 26, 255
  53. La Haye, R. J., P. S. C. Lee, R. W. Moore, and T. Ohkawa, 1984, Bull. Am. Phys. Soc. 29, 1331
  54. Mannheimer, W., 1981, Phys. Fluids 24, 986
  55. Martin, T. J., and J. B. Taylor, 1974, "Helically Deformed States in Toroidal Pinches," Culham Laboratory report (unpublished)
  56. Mattheus, W. H., and D. C. Montgomery, 1980a, in Proceedings of the Reverse Field Pinch Theory Workshop, edited by H. R. Lewis and R. A. Gerwin (Los Alamos National Laboratory, Los Alamos, New Mexico), Session V, paper A-5
  57. Mattheus, W. H., and D. C. Montgomery, 1980b, Ann. N.Y. Acad. Sci. 357, 203
  58. Moffatt, H. K., 1978, Magnetic Field Generation in Electrically Conducting Fluids (Cambridge University Press, Cambridge/London/New York)
  59. Montgomery, D., L. Turner, and G. Vahala, 1978, Phys. Fluids 21, 757
  60. Nagata, M., Y. Honda, K. Ikegami, M. Nishikawa, A. Ozaki, N. Satomi, T. Uyama, and K. Watanabe, 1985, Plasma Physics and Controlled Nuclear Fusion Research, 1984, Proceedings of the 10th International Conference, London, 1984 (IAEA, Vienna), Vol. II, p. 655
  61. Newton, A. A., 1985, private communication
  62. Nogi, Y., H. Ogura, Y. Osanai, K. Saito, S. Shiina, and H. Yoshimura, 1980, J. Phys. Soc. Jpn. 49, 710
  63. Ohkawa, T., M. Chu, C. Chu, and M. Schaffer, 1980, Nucl. Fusion 20, 1464
  64. Ortolani, S., 1984, in Twenty Years of Plasma Physics, Proceedings of the ICTP Trieste Meeting, edited by B. McNamara (World Scientific, Philadelphia/Singapore), p. 75
  65. Ortolani, S., and G. Rostagni, 1983, Nucl. Instrum. Methods 207, 35
  66. Parker, E. N., 1957, J. Geophys. Res. 62, 509
  67. Petschek, H. E., 1965, in AAS-NASA Symposium on the Physics of Solar Flares, edited by W. N. Hess (NASA, Washington, D.C.), NASA SP-50, p. 425
  68. Platts, D. A., J. C. Fernandez, T. R. Jarboe, and B. L. Wright, 1985, Bull. Am. Phys. Soc. 30, 1454
  69. Reiman, A., 1980, Phys. Fluids 23, 230
  70. Reiman, A., 1981, Phys. Fluids 24, 956
  71. Riyopoulos, S., A. Bondeson, and D. Montgomery, 1982, Phys. Fluids 25, 107
  72. Rosenbluth, M. N., and M. N. Bussac, 1979, Nucl. Fusion 19, 489
  73. Rusbridge, M. G., 1977, Plasma Phys. 19, 499
  74. Rusbridge, M. G., 1982, Nucl. Fusion 22, 1291
  75. Sato, T., and K. Kusano, 1985, Plasma Physics and Controlled Nuclear Fusion Research 1984, Proceedings of the 10th International Conference, London, 1984 (IAEA, Vienna), Vol. II, p. 461
  76. Schmidt, G., 1966, Physics of High Temperature Plasmas (Academic, New York)
  77. Sweet, P. A., 1958, in Electromagnetic Phenomena in Cosmical Physics, IAU Symposium No. 6, edited by B. Lehnert (Cambridge University Press, Cambridge), p. 123
  78. Sykes, A., and J. A. Wesson, 1977, Proceedings of the 8th European Conference on Controlled Fusion and Plasma Physics, Prague (Czechoslovak Academy of Sciences, Prague), Vol. 1, p. 80
  79. Tamano, T., T. Carlstrom, C. Chu, R. Goforth, G. Jackson, R. La Haye, T. Ohkawa, M. Schaffer, and P. Taylor, 1983, in Mirror Based and Field Reversed Approaches to Magnetic Fusion, proceedings of the International School of Plasma Physics Course, edited by R. F. Post, D. E. Baldwin, and D. D. Ryutov [International School of Plasma Physics, Varenna (Como), Italy], Vol. II, p. 653
  80. Tamaru, T., K. Sugisaki, K. Hayase, T. Shimada, Y. Hirano, Y. Maejima, K. Ogawa, K. Hirano, S. Kitagawa, K. Sato, M. Wakatani, S. Yamada, H. Arimoto, Y. Kita, S. Yamaguchi, A. Nagata, S. Ido, and I. Kawakami, 1979, Plasma Physics and Controlled Nuclear Fusion Research, 1978, Proceedings of the 7th International Conference, Innsbruck, 1978 (IAEA, Vienna), Vol. II, pp. 55-68
  81. Taylor, J. B., 1974a, Phys. Rev. Lett. 33, 1139
  82. Taylor, J. B., 1974b, unpublished
  83. Taylor, J. B., 1975, Plasma Physics and Controlled Nuclear Fusion Research, 1974, Proceedings of the 5th International Conference, Tokyo, 1974 (IAEA, Vienna), Vol. I, p. 161
  84. Taylor, J. B., 1976, in Pulsed High Beta Plasmas, Proceedings of the Third Topical Conference, Abingdon, 1975, edited by D. E. Evans (Pergamon, Oxford/New York), p. 59
  85. Taylor, J. B., 1980, in Proceedings of the Reverse Field Pinch Theory Workshop, edited by H. R. Lewis and R. A. Gerwin (Los Alamos National Laboratory, Los Alamos, New Mexico), Session V, paper A-1
  86. Taylor, J. B., and M. F. Turner, 1985, unpublished
  87. Ting, A. C., W. H. Matthews, and D. Montgomery, 1986, Phys. Fluids (in press)
  88. Toyama, H., N. Asakura, K. Hattori, N. Inoue, S. Ishida, S. Matsuzuka, K. Miyamoto, J. Morikawa, Y. Nagayama, H. Nihei, S. Shinohara, Y. Ueda, K. Yamagishi, and Z. Yoshida, 1985, in Proceedings of the 12th European Conference on Controlled Fusion and Plasma Physics, Budapest, edited by L. Pocs and A. Montvai (European Physical Society, Geneva), Vol. I, p. 602
  89. Turner, L., 1983, Ann. Phys. (N.Y.) 149, 58
  90. Turner, L., 1984, Phys. Fluids 27, 1677
  91. Turner, L., and J. P. Christiansen, 1981, Phys. Fluids 24, 893
  92. Turner, W. C., G. C. Goldenbaum, E. H. A. Granneman, J. H. Hammer, C. W. Hartman, D. S. Prono, and J. Taska, 1983, Phys. Fluids 26, 1965
  93. Turner, W. C., E. H. A. Granneman, C. W. Hartman, D. S. Prono, J. Taska, and A. C. Smith, Jr., 1981, J. Appl. Phys. 52, 175
  94. Vasyliunas, V. M., 1975, Rev. Geophys. Space Phys. 13, 303
  95. Verhage, A. J. L., A. S. Furzer, and D. C. Robinson, 1978, Nucl. Fusion 18, 457
  96. Voslamber, D., and D. K. Callebaut, 1962, Phys. Rev. 128, 2016
  97. Watt, R. G., and R. A. Nebel, 1983, Phys. Fluids 26, 1168
  98. Watt, R. G., J. A. Phillips, and A. A. Newton, 1985, private communication
  99. Wells, D. R., and J. Norwood, 1969, J. Plasma Phys. 3, 21
  100. White, R. B., 1983, Handbook of Plasma Physics (North-Holland, Amsterdam)
  101. Whiteman, K., 1962, Plasma Phys. 7, 293
  102. Woltjer, L., 1958, Proc. Natl. Acad. Sci. U.S.A. 44, 489
  103. Wright, B. L., J. C. Fernandez, T. R. Jarboe, and D. A. Platts, 1985, Bull. Am. Phys. Soc. 30, 1454
  104. Yamada, M., R. Ellis, Jr., H. P. Furth, G. Hart, A. Janos, S. Jardin, F. Levinton, D. Meyerhofer, M. Mimura, C. H. Nam, S. Paul, A. Sperduti, S. Von Goeler, F. Wysocki, and P. Young, 1985, Plasma Physics and Controlled Nuclear Fusion Research, 1984, Proceedings of the 10th International Conference, London, 1984 (IAEA, Vienna), Vol. 2., p. 535
  105. Yamada, M., H. P. Furth, W. Hsu, A. Janos, S. Jardin, M. Okabayashi, J. Sinnis, T. H. Stix, and K. Yamazaki, 1981, Phys. Rev. Lett. 46, 188

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Rev. Mod. Phys. 58, 741– Published 1 July, 1986

    © 1986 American Physical Society

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