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Beta-limiting MHD phenomena in toroidal systems

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Abstract

Equilibrium effects, neoclassical tearing modes, and resistive wall modes are discussed as phenomena limiting attainable plasma pressure, with emphasis on the current progress in theoretical studies at the Kurchatov Institute. The review is based on the results presented at the 11th International Congress on Plasma Physics (Sydney, 2002).

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References

  1. ITER Physics Basis, Nucl. Fusion 39, 2137 (1999).

    Google Scholar 

  2. L. E. Zakharov and V. D. Shafranov, Reviews of Plasma Physics, Ed. by M. A. Leontovich and B. B. Kadomtsev (Énergoizdat, Moscow, 1982; Consultants Bureau, New York, 1986), Vol. 11.

    Google Scholar 

  3. V. D. Pustovitov, Reviews of Plasma Physics, Ed. by B. B. Kadomtsev and V. D. Shafranov (Consultants Bureau, New York, 2000), Vol. 21, p. 1.

    Google Scholar 

  4. G. Bateman, MHD Instabilities (MIT Press, Cambridge, 1978; Énergoizdat, Moscow, 1982).

    Google Scholar 

  5. J. Wesson, Tokamaks (Clarendon, Oxford, 1987).

    Google Scholar 

  6. B. A. Carreras, L. Garcia, and V. E. Lynch, Phys. Fluids 29, 3356 (1986).

    Article  ADS  Google Scholar 

  7. M. Wakatani, K. Ichiguchi, F. Bauer, et al., Nucl. Fusion 26, 1359 (1986).

    Google Scholar 

  8. T. Matsumoto, Y. Nakamura, and M. Wakatani, Nucl. Fusion 36, 1571 (1996).

    Article  Google Scholar 

  9. Y.-K. M. Peng and D. J. Strickler, Nucl. Fusion 26, 769 (1986).

    Google Scholar 

  10. S. M. Kaye, M. G. Bell, R. E. Bell, et al., Phys. Plasmas 8, 1977 (2001).

    Article  ADS  Google Scholar 

  11. A. Sykes, Plasma Phys. Controlled Fusion 43, A127 (2001).

    Article  ADS  Google Scholar 

  12. S. M. Kaye, M. Bell, R. Bell, et al., in Proceedings of the ITPA Meeting on CDs and Modeling, Princeton, 2002.

  13. S. Okamura, K. Matsuoka, S. Nishimura, et al., Nucl. Fusion 41, 1865 (2001).

    Article  Google Scholar 

  14. M. C. Zarnstorff, L. A. Berry, A. Brooks, et al., Plasma Phys. Controlled Fusion 43, A237 (2001).

    Article  ADS  Google Scholar 

  15. P. R. Garabedian, Phys. Plasmas 9, 137 (2002).

    Article  ADS  Google Scholar 

  16. R. Maingi, M. G. Bell, R. E. Bell, et al., Plasma Phys. Controlled Fusion 45, 657 (2003).

    Article  ADS  Google Scholar 

  17. C. O. Beastly and J. T. Hogan, Nucl. Fusion 28, 1923 (1988).

    Google Scholar 

  18. R. E. Bell, N. Asakura, S. Bernabei, et al., Phys. Fluids B 2, 1271 (1990).

    Article  ADS  Google Scholar 

  19. C. S. Chang and S. M. Kaye, Phys. Fluids B 3, 395 (1991).

    ADS  Google Scholar 

  20. A. Bondeson, M. Benda, M. Persson, and M. S. Chu, Nucl. Fusion 37, 1419 (1997).

    Article  Google Scholar 

  21. A. C. England, R. E. Bell, S. P. Hirshman, et al., Plasma Phys. Controlled Fusion 39, 1373 (1997).

    Article  ADS  Google Scholar 

  22. A. D. Turnbull, T. S. Taylor, M. S. Chu, et al., Nucl. Fusion 38, 1467 (1998).

    Article  Google Scholar 

  23. A. Pochelon, T. P. Goodman, M. Henderson, et al., Nucl. Fusion 39, 1807 (1999).

    Article  Google Scholar 

  24. O. Gruber, R. Wolf, H.-S. Bosch, et al., Nucl. Fusion 40, 1145 (2000).

    Article  Google Scholar 

  25. L. L. Lao, Y. Kamada, T. Oikawa, et al., Nucl. Fusion 41, 295 (2001).

    Article  Google Scholar 

  26. F. Hofmann, R. Behn, S. Coda, et al., Plasma Phys. Controlled Fusion 43, A161 (2001).

    Article  ADS  Google Scholar 

  27. V. D. Pustovitov, J. Plasma Fusion Res. 70, 943 (1994).

    Google Scholar 

  28. V. D. Pustovitov, J. Plasma Fusion Res. SERIES 3, 571 (2000).

    Google Scholar 

  29. M. Keilhacker, A. Gibson, C. Gormezano, and P. H. Rebut, Nucl. Fusion 41, 1925 (2001).

    Article  Google Scholar 

  30. O. Gruber, R. Arslanbekov, C. Atanasiu, et al., Nucl. Fusion 41, 1369 (2001).

    Article  Google Scholar 

  31. Y. Kamada and JT-60 Team, Nucl. Fusion 41, 1311 (2001).

    Article  Google Scholar 

  32. B. W. Rice, K. H. Burrel, J. R. Ferron, et al., Nucl. Fusion 39, 1855 (1999).

    Google Scholar 

  33. Y. Shimomura, Y. Murakami, A. R. Polevoi, et al., Plasma Phys. Controlled Fusion 43, A385 (2001).

    Article  ADS  Google Scholar 

  34. S. Okamura, K. Matsuoka, R. Akiyama, et al., Nucl. Fusion 39, 1337 (1999).

    Article  Google Scholar 

  35. A. Iiyoshi, A. Komori, A. Ejiri, et al., Nucl. Fusion 39, 1245 (1999).

    Article  Google Scholar 

  36. J. F. Lyon, B. A. Carreras, K. K. Chipley, et al., Fusion Technol. 10, 179 (1986).

    Google Scholar 

  37. B. A. Carreras, H. R. Hicks, J. A. Holmes, et al., Nucl. Fusion 24, 1347 (1984).

    Google Scholar 

  38. R. J. Colchin, M. Murakami, E. Anabitarte, et al., Phys. Fluids B 2, 1347 (1990).

    Article  ADS  Google Scholar 

  39. K. Miyamoto, Fundamentals of Plasma Physics for Controlled Fusion (Iwanami, Tokyo, 1997).

    Google Scholar 

  40. V. D. Pustovitov, Nucl. Fusion 36, 583 (1996).

    Google Scholar 

  41. V. D. Pustovitov, Nucl. Fusion 36, 1281 (1996).

    Google Scholar 

  42. J. M. Greene and J. L. Johnson, Phys. Fluids 4, 875 (1961).

    Article  MathSciNet  Google Scholar 

  43. J. M. Greene, J. L. Johnson, and K. E. Weimer, Plasma Phys. 8, 145 (1966).

    Google Scholar 

  44. S. Besshou, K. Ogata, K. Kondo, et al., Nucl. Fusion 35, 173 (1995).

    Article  Google Scholar 

  45. S. Besshou, K. Ogata, K. Kondo, et al., Trans. Fusion Technol. 27, 219 (1995).

    Google Scholar 

  46. S. Besshou, V. D. Pustovitov, N. Fujita, et al., Phys. Plasmas 5, 481 (1998).

    Article  ADS  Google Scholar 

  47. Y. Sato, M. Yokoyama, M. Wakatani, and V. D. Pustovitov, Nucl. Fusion 40, 1627 (2000).

    Article  Google Scholar 

  48. M. Yokoyama, K. Itoh, K. Nagasaki, et al., Nucl. Fusion 40, 1909 (2000).

    Google Scholar 

  49. N. Yanagi, S. Morimoto, K. Ichiguchi, et al., Nucl. Fusion 32, 1264 (1992).

    Article  Google Scholar 

  50. K. Ichiguchi, N. Nakajima, M. Okamoto, et al., Nucl. Fusion 33, 481 (1993).

    Article  Google Scholar 

  51. S. Sakakibara, H. Yamada, K. Y. Watanabe, et al., Nucl. Fusion 41, 1177 (2001).

    Article  Google Scholar 

  52. H. Yamada, A. Komori, N. Ohyabu, et al., Plasma Phys. Controlled Fusion 43, A55 (2001).

    Article  ADS  Google Scholar 

  53. S. Sakakibara, H. Yamada, K. Y. Watanabe, et al., Plasma Phys. Controlled Fusion 44, A217 (2002).

    Article  ADS  Google Scholar 

  54. J. Nührenberg and R. Zille, Phys. Lett. A 129, 113 (1988).

    ADS  Google Scholar 

  55. C. Beidler, G. Grieger, F. Herrnegger, et al., Fusion Technol. 17, 148 (1990).

    Google Scholar 

  56. G. Grieger, W. Lotz, P. Merkel, et al., Phys. Fluids B 4, 2081 (1992).

    Article  ADS  Google Scholar 

  57. A. M. Garofalo, M. S. Chu, E. D. Fredrickson, et al., Nucl. Fusion 41, 1171 (2001).

    Article  Google Scholar 

  58. H. P. Zehrfeld and B. J. Green, Nucl. Fusion 13, 750 (1973).

    Google Scholar 

  59. V. D. Shafranov, Reviews of Plasma Physics, Ed. by M. A. Leontovich (Gosatomizdat, Moscow, 1963; Consultants Bureau, New York, 1966), Vol. 2.

    Google Scholar 

  60. V. D. Pustovitov, in Proceedings of the 29th EPS Conference on Controlled Fusion and Plasma Physics, Montreux, 2002, Paper P-2.107.

  61. V. D. Pustovitov, Fiz. Plazmy 29, 124 (2003) [Plasma Phys. Rep. 29, 105 (2003)].

    Google Scholar 

  62. M. Wakatani, Y. Nakamura, and K. Ichiguchi, Nucl. Eng. Des. Fusion 15, 395 (1992).

    Google Scholar 

  63. A. B. Mikhailovskii, Instabilities in a Confined Plasma (Inst. Phys., Bristol, 1998).

    Google Scholar 

  64. O. Sauter, R. J. La Haye, Z. Chang, et al., Phys. Plasmas 4, 1654 (1997).

    Article  ADS  Google Scholar 

  65. R. J. Buttery, S. Günter, G. Giruzzi, et al., Plasma Phys. Controlled Fusion 42, B61 (2000).

    Article  ADS  Google Scholar 

  66. Z. Chang, E. D. Fredrickson, S. H. Batha, et al., Phys. Plasmas 5, 1076 (1998).

    Article  ADS  Google Scholar 

  67. R. J. La Haye, L. L. Lao, E. J. Strait, and T. S. Taylor, Nucl. Fusion 37, 397 (1997).

    Article  Google Scholar 

  68. A. Isayama, Y. Kamada, T. Ozeki, and N. Isei, Plasma Phys. Controlled Fusion 41, 35 (1999).

    Article  ADS  Google Scholar 

  69. M. Maraschek, S. Günter, R. C. Wolf, and ASDEX Upgrade Team, in Proceedings of the 26th EPS Conference on Controlled Fusion and Plasma Physics, Maastricht, 1999; ECA 23J, 1393 (1999).

    Google Scholar 

  70. R. C. Wolf, O. Gruber, M. Maraschek, et al., Plasma Phys. Controlled Fusion 41, B93 (1999).

    Article  Google Scholar 

  71. JET Team, Nucl. Fusion 39, 1965 (1999).

    Google Scholar 

  72. J. D. Galambos, L. J. Perkins, S. W. Haney, and J. Mandrekas, Nucl. Fusion 35, 551 (1995).

    Article  Google Scholar 

  73. S. Günter, A. Gude, M. Maraschek, et al., Nucl. Fusion 38, 1431 (1998).

    Google Scholar 

  74. R. J. Buttery, T. C. Hender, G. T. A. Huysmans, et al., in Proceedings of the 26th EPS Conference on Controlled Fusion and Plasma Physics, Maastricht, 1999; ECA 23J, 121 (1999).

    Google Scholar 

  75. R. J. La Haye, R. J. Buttery, S. Guenter, et al., in Proceedings of the 18th IAEA Fusion Energy Conference, Sorrento, 2000, Paper IAEA-CN-77/EXP3/05.

  76. JET Team, in Proceedings of the 18th IAEA Fusion Energy Conference, Sorrento, 2000, Paper IAEA-CN-77/OV1/2.

  77. A. Isayama, Y. Kamada, T. Ozeki, et al., in Proceedings of the 18th IAEA Fusion Energy Conference, Sorrento, 2000, Paper IAEA-CN-77/EXP3/03.

  78. H. R. Wilson, M. Alexander, J. W. Connor, et al., Plasma Phys. Controlled Fusion 38, A149 (1996).

    Article  ADS  Google Scholar 

  79. H. Zohm, Phys. Plasmas 4, 3433 (1997).

    Article  ADS  Google Scholar 

  80. S. Günter, G. Giruzzi, A. Gude, et al., Plasma Phys. Controlled Fusion 41, B231 (1999).

    Google Scholar 

  81. R. J. La Haye, R. J. Buttery, S. Guenter, et al., Phys. Plasmas 7, 3349 (2000).

    ADS  Google Scholar 

  82. A. B. Mikhailovskii, V. D. Pustovitov, and A. I. Smolyakov, Plasma Phys. Controlled Fusion 42, 309 (2000).

    ADS  Google Scholar 

  83. F. L. Waelbroeck and R. Fitzpatrick, Phys. Rev. Lett. 78, 1703 (1997).

    Article  ADS  Google Scholar 

  84. A. B. Mikhailovskii, V. D. Pustovitov, V. S. Tsypin, and A. I. Smolyakov, Phys. Plasmas 7, 1204 (2000).

    MathSciNet  ADS  Google Scholar 

  85. A. B. Mikhailovskii, V. D. Pustovitov, A. I. Smolyakov, and V. S. Tsypin, Phys. Plasmas 7, 1214 (2000).

    MathSciNet  ADS  Google Scholar 

  86. A. B. Mikhailovskii, V. S. Tsypin, I. C. Nascimento, and R. M. Galvão, Phys. Plasmas 7, 3474 (2000).

    MathSciNet  ADS  Google Scholar 

  87. A. I. Smolyakov, E. Lazzaro, R. Coelho, and T. Ozeki, Phys. Plasmas 9, 371 (2002).

    ADS  Google Scholar 

  88. A. B. Mikhailovskii, S. V. Konovalov, V. S. Tsypin, et al., Phys. Plasmas 7, 4763 (2000).

    ADS  Google Scholar 

  89. R. Fitzpatrick and F. L. Waelbroeck, Phys. Plasmas 7, 4983 (2000).

    ADS  Google Scholar 

  90. T. Ozeki, A. I. Smolyakov, A. Isayama, et al., in Proceedings of the 28th EPS Conference on Controlled Fusion and Plasma Physics, Funchal, 2001; ECA 25A, 1345 (2001).

    Google Scholar 

  91. S. V. Konovalov and A. B. Mikhailovskii, Plasma Phys. Controlled Fusion 43, 1149 (2001).

    Article  ADS  Google Scholar 

  92. S. V. Konovalov, A. B. Mikhailovskii, M. S. Shirokov, and V. S. Tsypin, Plasma Phys. Controlled Fusion 44, 579 (2002).

    Article  ADS  Google Scholar 

  93. S. V. Konovalov, A. B. Mikhailovskii, M. S. Shirokov, and V. S. Tsypin, in Proceedings of the 29th EPS Conference on Controlled Fusion and Plasma Physics, Montreux, 2002, Paper P-4.063.

  94. M. Kotschenreuther, R. D. Hazeltine, and P. J. Morrison, Phys. Fluids 19, 249 (1985).

    Google Scholar 

  95. H. Lütjens, J.-F. Luciani, and X. Garbet, Phys. Plasmas 8, 4267 (2001).

    ADS  Google Scholar 

  96. S. E. Kruger, C. C. Hegna, and J. D. Callen, Phys. Plasmas 5, 455 (1998).

    MathSciNet  ADS  Google Scholar 

  97. A. B. Mikhailovskii, B. N. Kuvshinov, V. D. Pustovitov, and S. E. Sharapov, Fiz. Plazmy 26, 403 (2000) [Plasma Phys. Rep. 26, 375 (2000)].

    Google Scholar 

  98. R. J. La Haye, B. W. Rice, and E. J. Strait, Nucl. Fusion 40, 53 (2000).

    Article  Google Scholar 

  99. T. C. Hender, D. N. Borba, R. J. Buttery, et al., in Proceedings of the 18th IAEA Fusion Energy Conference, Sorrento, 2000, Paper IAEA-CN-77/EXP3/02.

  100. A. Bondeson, D.-H. Liu, F. X. Söldner, et al., Nucl. Fusion 39, 1523 (1999).

    Article  Google Scholar 

  101. E. J. Strait, T. S. Taylor, A. D. Turnbull, et al., Phys. Rev. Lett. 74, 2483 (1995).

    Article  ADS  Google Scholar 

  102. T. Taylor, E. J. Strait, L. L. Lao, et al., Phys. Plasmas 2, 2390 (1995).

    Article  ADS  Google Scholar 

  103. T. C. Luce, M. R. Wade, P. A. Politzer, et al., Nucl. Fusion 41, 1585 (2001).

    Article  Google Scholar 

  104. A. M. Garofalo, E. J. Strait, J. M. Bialek, et al., Nucl. Fusion 40, 1491 (2000).

    Article  Google Scholar 

  105. F. Troyon, R. Gruber, H. Saurenmann, et al., Plasma Phys. Controlled Fusion 26, 209 (1984).

    Article  ADS  Google Scholar 

  106. T. S. Taylor, H. St. John, A. D. Turnbull, et al., Plasma Phys. Controlled Fusion 36, B229 (1994).

    Article  ADS  Google Scholar 

  107. C. Gormezano, Plasma Phys. Controlled Fusion 41, B367 (1999).

    Article  Google Scholar 

  108. T. Fujita, Y. Kamada, S. Ishida, et al., Nucl. Fusion 39, 1627 (1999).

    Article  Google Scholar 

  109. N. C. Hawkes, B. C. Stratton, T. Tala, et al., Phys. Rev. Lett. 87, 115001 (2001).

    Google Scholar 

  110. T. Fujita, T. Oikawa, T. Suzuki, et al., Phys. Rev. Lett. 87, 245001 (2001).

  111. G. T. A. Huysmans, T. C. Hender, N. C. Hawkes, and X. Litaudon, Phys. Rev. Lett. 87, 245002 (2001).

    Google Scholar 

  112. Y. R. Lin-Liu, A. D. Turnbull, M. S. Chu, et al., Phys. Plasmas 6, 3934 (1999).

    Article  ADS  Google Scholar 

  113. M. Okabayashi, J. Bialek, M. S. Chance, et al., Phys. Plasmas 8, 2071 (2001).

    Article  ADS  Google Scholar 

  114. L. C. Johnson, M. Okabayashi, A. M. Garofalo, et al., in Proceedings of the 28th EPS Conference on Controlled Fusion and Plasma Physics, Funchal, 2001; ECA 25A, 1361 (2001); http://www.cfn.ist.utl.pt/EPS2001/fin/pdf/P4.008.pdf.

    Google Scholar 

  115. V. D. Pustovitov, Fiz. Plazmy 27, 209 (2001) [Plasma Phys. Rep. 27, 195 (2001)].

    Google Scholar 

  116. A. Bondeson, Yueqiang Liu, D. Gregoratto, et al., Nucl. Fusion 42, 768 (2002).

    Article  Google Scholar 

  117. Y. Q. Liu, A. Bondeson, C. M. Fransson, et al., Phys. Plasmas 7, 3681 (2000).

    ADS  Google Scholar 

  118. A. Bondeson, Y. Q. Liu, C. M. Fransson, et al., Nucl. Fusion 41, 455 (2001).

    Article  Google Scholar 

  119. V. D. Pustovitov, Plasma Phys. Controlled Fusion 44, 295 (2002).

    Article  ADS  Google Scholar 

  120. V. D. Pustovitov, Rep. No. NIFS-723 (Nat. Inst. Fusion Sci., Toki, 2002).

  121. M. S. Chance, M. S. Chu, M. Okabayashi, and A. D. Turnbull, Nucl. Fusion 42, 295 (2002).

    Article  Google Scholar 

  122. V. S. Mukhovatov and V. D. Shafranov, Nucl. Fusion 11, 605 (1971).

    Google Scholar 

  123. B. A. Carreras, G. Grieger, J. H. Harris, et al., Nucl. Fusion 28, 1613 (1988).

    Google Scholar 

  124. C. D. Warrick, R. J. Buttery, G. Cunningham, et al., Phys. Rev. Lett. 85, 574 (2000).

    Article  ADS  Google Scholar 

  125. G. Gantenbein, H. Zohm, G. Giruzzi, et al., Phys. Rev. Lett. 85, 1242 (2000).

    Article  ADS  Google Scholar 

  126. H. Zohm, G. Gantenbein, A. Gude, et al., Nucl. Fusion 41, 197 (2001).

    Article  Google Scholar 

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  1. Nuclear Fusion Institute, Russian Research Centre Kurchatov Institute, pl. Kurchatova 1, Moscow, 123182, Russia

    V. D. Pustovitov

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__________

Translated from Fizika Plazmy, Vol. 29, No. 10, 2003, pp. 880–890.

Original Russian Text Copyright © 2003 by Pustovitov.

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Pustovitov, V.D. Beta-limiting MHD phenomena in toroidal systems. Plasma Phys. Rep. 29, 816–825 (2003). https://doi.org/10.1134/1.1618887

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