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Theoretical Principles of the Plasma-Equilibrium Control in Stellarators

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Reviews of Plasma Physics

Part of the book series: Reviews of Plasma Physics ((ROPP,volume 21))

Abstract

This review is devoted to the theory of plasma equilibrium in conventional stellarators with a plane circular axis and helical magnetic fields. Its primary objectives are the analysis of the conditions of finite-pressure plasma equilibrium in stellarators and the search for ways of increasing the achievable β (ratio of kinetic to magnetic pressures).

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References

  1. L.A. Artsimovich and K.B. Kartashev, Dokl. Akad. Nauk SSSR, 146, 1305–1308 (1962). English translation: Sov. Phys. Dokl., 5 (1962).

    Google Scholar 

  2. V.D. Shafranov, At. Energ., 13, 521–529 (1962).

    Google Scholar 

  3. V.D. Shafranov, in: Reviews of Plasma Physics (edited by M.A. Leontovich), Vol. 2, Gosatomizdat, Moscow (1963), pp. 92–131. English translation: Consultants Bureau, New York (1966), pp. 103-151.

    Google Scholar 

  4. V.S. Mukhovatov and V.D. Shafranov, Nucl. Fusion, 11, 605–633 (1971).

    Article  Google Scholar 

  5. L.A. Artsimovich, Closed Plasma Configurations [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  6. L.A. Artsimovich, Nucl. Fusion, 12, 215–252 (1972).

    Article  Google Scholar 

  7. V.S. Mukhovatov, in: Itogi Nauki i Tekhniki: Fizika Plazmy (Advances in Science and Technology: Plasma Physics) [in Russian, edited by V.D. Shafranov], Vol. 1, Part 1, VINITI, Moscow (1980), pp. 6–118.

    Google Scholar 

  8. L.I. Artemenkov, I.N. Golovin, P.I. Kozlov, et al., in: Proc. 4th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Madison, 1971, Vol. 1, IAEA, Vienna (1971), pp. 359–367

    Google Scholar 

  9. L. Spitzer, Phys. Fluids, 1, 253–264 (1958).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. A.S. Bishop, Project Sherwood, Addison-Wesley, Massachusetts (1958).

    Google Scholar 

  11. L.M. Kovrizhnykh, Zh. Tekh. Fiz., 31, 888–890 (1961). English translation: Sov. Phys. Tech. Phys., 6, 643 (1962).

    Google Scholar 

  12. L.V. Korablev, A.I. Morozov, and L.S. Solov’ev, Zh. Tekh. Fiz., 31, 1153–1163 (1961). English translation: Sov. Phys. Tech. Phys., 6, 845-851 (1962).

    Google Scholar 

  13. I.M. Gel’fand, M.I. Graev, N.M. Zueva, A.I. Morozov, and L.S. Solov’ev, Zh. Tekh. Fiz., 31, 1164–1168 (1961). English translation: Sov. Phys. Tech. Phys., 6, 852 (1962).

    Google Scholar 

  14. L.M. Kovrizhnykh, Zh. Tekh. Fiz., 32, 526–535 (1962). English translation: Sov. Phys. Tech. Phys., 7, 383 (1962).

    Google Scholar 

  15. D.W. Kerst, Plasma Phys. C, 4, 253–262 (1962).

    Google Scholar 

  16. V.F. Aleksin, in: Plasma Physics and Problems of Controlled Thermonuclear Fusion [in Russian], Vol. 3, the Ukrainian Academy of Sciences, Kiev (1963), pp. 216–224.

    Google Scholar 

  17. L.M. Kovrizhnykh, Zh. Tekh. Fiz., 33, 377–381 (1963). English translation: Sov. Phys. Tech. Phys., 8, 281 (1963).

    Google Scholar 

  18. V.K. Mel’nikov, Dokl. Akad. Nauk SSSR, 149, 1056–1059 (1963). English translation: Sov. Phys. Dokl., 8, 176 (1963).

    Google Scholar 

  19. A.P. Popryadukhin, Zh. Tekh. Fiz., 34, 658–665 (1964). English translation: Sov. Phys. Tech. Phys., 9 (1964).

    Google Scholar 

  20. A.I. Morozov and L.S. Solov’ev, in: Reviews of Plasma Physics (edited by M.A. Leontovich), Vol. 2, Gosatomizdat, Moscow (1963), pp. 3–91. English translation: Consultants Bureau, New York (1966), pp. 1-101.

    Google Scholar 

  21. L.S. Solov’ev and V.D. Shafranov, in: Reviews of Plasma Physics (edited by M.A. Leontovich), Vol. 5, Atomizdat, Moscow (1967), pp. 3–208. English translation: Consultants Bureau, New York (1970), pp. 1-247.

    Google Scholar 

  22. E.D. Volkov, V.A. Suprunenko, and A.A. Shishkin, The Stellarator [in Russian], Naukova Dumka, Kiev (1983).

    Google Scholar 

  23. M.S. Berezhetskii, S.E. Grebenshchikov, A.P. Popryadukhin, and I.S. Shpigel’, Zh. Tekh. Fiz., 35, 2167–2175 (1965). English translation: Sov. Phys. Tech. Phys., 10, 1662, (1966).

    Google Scholar 

  24. A. Gibson and J. Hugill, Phys. Rev. Lett., 21, 1052–1055 (1968).

    Article  ADS  Google Scholar 

  25. M.A. Ivanovskii, S.N. Popov, A.P. Popryadukhin, and M.S. Rabinovich, in: Proc. 4th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Madison, 1971, Vol. 3, IAEA, Vienna (1971), pp. 63–77.

    Google Scholar 

  26. O.I. Fedyanin, “Studies of the magnetic configuration of an l = 2 stellarator,” Preprint CLM-R 142, Culham (1975).

    Google Scholar 

  27. D.K. Akulina, Eh. D. Andryukhina, M.S. Berezhetskij, et al., in: Proc. 6th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Berchtesgaden, 1976, Vol. 2, IAEA, Vienna (1977), pp. 115–126.

    Google Scholar 

  28. T. Mizuuchi, S. Morimoto, A. Iiyoshi, and K. Uo, Nucl. Fusion, 22, 247–253 (1982).

    Article  Google Scholar 

  29. R.P. Doerner, D.T. Anderson, F.S.B. Anderson, et al., Phys. Fluids, 29, 3807–3812 (1986).

    Article  ADS  Google Scholar 

  30. R. Takahashi, H. Matuura, T. Mizuuchi, et al., in: Proc. Int. Stellarator/Heliotron Workshop, Kyoto University, 1986, Vol. 1, Kyoto (1986), pp. 220–232.

    Google Scholar 

  31. K. Nishimura, K. Matsuoka, M. Pujiwara, et al., in: Proc. 15th Symposium on Fusion Technology, Utrecht, 1988, Vol. 1, Else-vier, North-Holland (1989), pp. 398–401.

    Google Scholar 

  32. R. Jaenicke, K. Schworer, E. Ascasibar, et al., in: Proc. 16th Europ. Conf. on Controlled Fusion and Plasma Physics, Vol. 13B, Part II, Venice (1989), pp. 627–630.

    Google Scholar 

  33. R.J. Colchin, F.S.B. Anderson, A.C. England, et al., Rev. Sci. Instrum., 60, 2680–2689 (1989).

    Article  ADS  Google Scholar 

  34. J.H. Harris, T.C. Jernigan, F.S.B. Anderson, et al., Fusion Technol., 17, 51–61 (1990).

    Google Scholar 

  35. H. Yamada, K. Matsuoka, S. Okamura, K. Ida, and K. Nishimura, Rev. Sci. Instrum., 61, 686–692 (1990).

    Article  ADS  Google Scholar 

  36. M. Murakami, S.C. Aceto, E. Anabitarte, et al., Phys. Fluids, B3, 2261–2269 (1991).

    ADS  Google Scholar 

  37. G.G. Lesnyakov, E.D. Volkov, A.V. Georgievskij, et al., Nucl. Fusion, 32, 2157–2176 (1992).

    Article  ADS  Google Scholar 

  38. U. Brossman, W. Dommaschk, F. Herrnegger, et al., in: Proc. 9th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Baltimore, 1982, Vol. 3, IAEA, Vienna (1983), pp. 141–156.

    Google Scholar 

  39. B.A. Carreras, H.R. Hicks, J.A. Holmes, et al., Phys. Fluids, 26, 3569–3579 (1983).

    Article  ADS  MATH  Google Scholar 

  40. J.R. Cary, Phys. Fluids, 27, 119–128 (1984).

    Article  ADS  MATH  Google Scholar 

  41. L. Garcia, B.A. Carreras, J.H. Harris, H.R. Hicks, and V.E. Lynch, Nucl. Fusion, 24, 115–129 (1984).

    Article  Google Scholar 

  42. T.C. Hender, B.A. Carreras, L.A. Charlton, et al., Nucl. Fusion, 25, 1463–1473 (1985).

    Article  Google Scholar 

  43. J.R. Cary and J.D. Hanson, Phys. Fluids, 29, 2464–2473 (1986).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  44. P. Merkel, J. Comput. Phys., 66, 83–98 (1986).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  45. J.F. Lyon, B.A. Carreras, K.K. Chipley, et al., Fusion Technol., 10, 179–226 (1986).

    Google Scholar 

  46. N.T. Besedin, Yu. K. Kuznetsov, and I.M. Pankratov, in: Voprosy Atomnoi Nauki i Tekhniki: Termoyaderny Sintez (Atomic Science and Technology: Thermonuclear Fusion) [in Russian], No. 3, Kurchatov Institute, Moscow (1987), pp. 18–20.

    Google Scholar 

  47. P. Merkel, Nucl Fusion, 27, 867–871 (1987).

    Article  Google Scholar 

  48. I.S. Danilikin and O.E. Khadin, in: Voprosy Atomnoi Nauki i Tekhniki: Termoyaderny Sintez (Atomic Science and Technology: Thermonuclear Fusion) [in Russian], No. 1, Kurchatov Institute, Moscow (1988), pp. 41–45.

    Google Scholar 

  49. V.E. Bykov, A.V. Georgievskii, V.V. Demchenko, et al., in: Voprosy Atomnoi Nauki i Tekhniki: Termoyaderny Sintez (Atomic Science and Technology: Thermonuclear Fusion) [in Russian], No. 1, Kurchatov Institute, Moscow (1988), pp. 46–50.

    Google Scholar 

  50. M.A. Henderson, R.F. Gandy, J.D. Hanson, G.J. Hartwell, and D.G. Swanson, Nucl. Fusion, 28, 1099–1104 (1988).

    Article  Google Scholar 

  51. B.A. Carreras, N. Dominguez, L. Garcia, et al., Nucl. Fusion, 28, 1195–1207 (1988).

    Article  Google Scholar 

  52. G. Grieger, C. Beidler, E. Harmeyer, et al., in: Proc. 12th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Nice, 1982, Vol. 2, IAEA, Vienna (1989), pp. 369–387.

    Google Scholar 

  53. Y. Nakamura, K. Ichiguchi, M. Wakatani, and J.L. Johnson, J. Phys. Soc. Jpn., 58, 3157–3174 (1989).

    Article  ADS  Google Scholar 

  54. V.E. Bykov, A.A. Shishkin, J. Kisslinger, and F. Rau, “On vacuum field properties of the Uragan-2M torsatron standard configuration,” Preprint IPP 2/301, Garching (1989).

    Google Scholar 

  55. S.M. Hamberger, B.D. Blackwell, L.E. Sharp, and D.B. Shenton, Fusion Technol., 17, 123–130 (1990).

    Google Scholar 

  56. C. Alejaldre, J.J.A. Gozalo, J.B. Perez, et al., Fusion Technol., 17, 131–139 (1990).

    Google Scholar 

  57. C. Beidler, G. Grieger, F. Herrnegger, et al., Fusion Technol., 17, 148–168 (1990).

    Google Scholar 

  58. A. Iiyoshi, M. Fujiwara, O. Motojima, N. Ohyabu, and K. Yamaaaki, Fusion Technol, 17, 169–187 (1990).

    Google Scholar 

  59. Y. Nakamura, M. Wakatani, J.N. Leboeuf, et al., Fusion Technol., 19, 217–233 (1991).

    Google Scholar 

  60. K. Harafuji, T. Hayashi, and T. Sato, J. Comput. Phys., 81, 169–192 (1989).

    Article  ADS  MATH  Google Scholar 

  61. T. Hayashi, T. Sato, and A. Takei, Phys. Fluids, B2, 329–337 (1990).

    ADS  Google Scholar 

  62. T. Hayashi, A. Takei, N. Ohyabu, et al., in: Proc. 13th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Washington, 1990, Vol. 2, IAEA, Vienna (1991), pp. 143–150.

    Google Scholar 

  63. T. Hayashi, A. Takei, N. Ohyabu, and T. Sato, Nucl. Fusion, 31, 1767–1770 (1991).

    Article  Google Scholar 

  64. T. Hayashi, A. Takei, and T. Sato, Phys. Fluids, B4, 1539–1546 (1992).

    ADS  Google Scholar 

  65. T. Hayashi, T. Sato, W. Lotz, et al., in: Proc. 14th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Würzburg, 1992, Vol. 2, IAEA, Vienna (1993), pp. 29–34.

    Google Scholar 

  66. T. Hayashi, T. Sato, P. Merkel, J. Nuhrenberg, and U. Schwenn, Phys. Plasmas, 1, 3262–3268 (1994).

    Article  ADS  Google Scholar 

  67. T. Hayashi, T. Sato, N. Nakajima, et al., in: Proc. 15th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Seville, 1994, Vol. 3, IAEA, Vienna (1996), pp. 309–312.

    Google Scholar 

  68. H. Grad, Phys. Fluids, 10, 137–154 (1967).

    Article  ADS  Google Scholar 

  69. J.R. Cary and M. Kotschenreuther, Phys. Fluids, 28, 1392–1401 (1985).

    Article  ADS  MATH  Google Scholar 

  70. G. Grieger, H. Renner, and H. Wobig, Nucl. Fusion, 25, 1231–1242 (1985).

    Article  Google Scholar 

  71. K. Uo, Nucl. Fusion, 25, 1243–1248 (1985).

    Article  Google Scholar 

  72. J. Fujita and K. Matsuoka, Nucl. Fusion, 25, 1253–1257 (1985).

    Article  Google Scholar 

  73. D.J. Lees, Nucl. Fusion, 25, 1259–1265 (1985).

    Article  Google Scholar 

  74. S. Yoshikawa and T.H. Stix, Nucl. Fusion, 25, 1275–1279 (1985).

    Article  Google Scholar 

  75. UW/TSL Group, Nucl. Fusion, 25, 1281–1284 (1985).

    Article  Google Scholar 

  76. L.M. Kovrizhnykh and I.S. Shpigel’, Nucl. Fusion, 25, 1285–1288 (1985).

    Article  Google Scholar 

  77. B.A. Carreras, G. Grieger, J.H. Harris, et al., Nucl. Fusion, 28, 1613–1694 (1988).

    Article  Google Scholar 

  78. J.L. Johnson, C.R. Oberman, R.M. Kulsrud, and E.A. Prieman, Phys. Fluids, 1, 281–296 (1958).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  79. A. Lenard, Phys. Fluids, 7, 1875–1877 (1964).

    Article  ADS  Google Scholar 

  80. J.L. Johnson, Phys. Fluids, 7, 2015–2016 (1964).

    Article  ADS  Google Scholar 

  81. J.B. Taylor, Phys. Fluids, 8, 1203–1205 (1965).

    Article  ADS  Google Scholar 

  82. H.P. Fürth, in: Plasma Physics, Trieste, 1964, IAEA, Vienna (1965), pp. 391–409.

    Google Scholar 

  83. H.P. Fürth, J. Killen, M.N. Rosenbluth, and B. Coppi, in: Proc. 2nd Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Culham, 1965, Vol. 1, IAEA, Vienna (1966), pp. 103-125.

    Google Scholar 

  84. R.M. Kulsrud, in: Proc. 2nd Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Culham, 1965, Vol. 1, IAEA, Vienna (1966), pp. 127–143.

    Google Scholar 

  85. B. McNamara, K.J. Whiteman, and J.B. Taylor, in: Proc. 2nd Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Culham, 1965, Vol. 1, IAEA, Vienna (1966), pp. 145–167.

    Google Scholar 

  86. L.S. Solov’ev and V.D. Shafranov, in: Proc. 2nd Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Culham, 1965, Vol. 1, IAEA, Vienna (1966), pp. 169–190.

    Google Scholar 

  87. V.D. Shafranov, Plasma Phys., 13, 349–352 (1971).

    Article  ADS  Google Scholar 

  88. T. Coor, S.P. Cunningham, R.A. Ellis, M.A. Heald, and A.Z. Kranz, Phys. Fluids, 1, 411–420 (1958).

    Article  ADS  Google Scholar 

  89. W. Stodiek, R.A. Ellis, Jr., and J.G. Gorman, Nucl. Fusion, Supplement, Part 1, 193–198 (1962).

    Google Scholar 

  90. R.M. Sinclair, S. Yoshikawa, W.L. Harries, and J.O. Kessler, Phys. Fluids, 6, 937–945 (1963).

    Article  ADS  Google Scholar 

  91. K. Bol, Phys. Fluids, 7, 1855–1863 (1964).

    Article  ADS  Google Scholar 

  92. K.M. Young, Plasma Phys., 16, 119–152 (1974).

    Article  ADS  Google Scholar 

  93. J.M. Greene and J.L. Johnson, Phys. Fluids, 4, 875–890 (1961).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  94. M.D. Kruskal and R.M. Kulsrud, Phys. Fluids, 1, 265–274 (1958).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  95. D.V. Bartlett, G. Cannici, G. Cattanei, et al., in: Proc. 8th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Brussels, 1980, Vol. 1, IAEA, Vienna (1981), pp. 185–196.

    Google Scholar 

  96. A. Iiyoshi, M. Sato, O. Motojima, et al., Phys. Rev. Lett., 48, 745–748 (1982).

    Article  ADS  Google Scholar 

  97. M. Fujiwara, K. Matsuoka, K. Yamazaki, et al., in: Proc. 14th Europ. Conf. on Controlled Fusion and Plasma Physics, Vol. 11D, Part I, Madrid (1987), pp. 404–404C.

    Google Scholar 

  98. V.E. Bykov, A.V. Georgievskij, V.V. Demchenko, et al., Fusion Technol., 17, 140–147 (1990).

    Google Scholar 

  99. K. Nishimura, K. Matsuoka, M. Fujiwara, et al., Fusion Technol., 17, 86–100 (1990).

    Google Scholar 

  100. O. Motojima, K. Akaishi, M. Asao, et al., in: Proc. 13th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Washington, 1990, Vol. 3, IAEA, Vienna (1991), pp. 513–523.

    Google Scholar 

  101. G. Grieger, W. Lotz, P. Merkel, et al., Phys. Fluids, B4, 2081–2091 (1992).

    ADS  Google Scholar 

  102. I.S. Danilkin, L.M. Kovrizhnykh, and I.S. Shpigel’, in: Voprosy Atomnoi Nauki i Tekhniki: Termoyaderny Sintez (Atomic Science and Technology: Thermonuclear Fusion) [in Russian], No. 3, Kurchatov Institute, Moscow (1990), pp. 31–38.

    Google Scholar 

  103. K. Matsuoka, S. Okamura, K. Nishimura, et al., Fusion Eng. Design, 26, 135–140 (1995).

    Article  Google Scholar 

  104. S. Okamura, K. Matsuoka, K. Nishimura, et al., Nucl. Fusion, 35, 283–296 (1995).

    Article  ADS  Google Scholar 

  105. H. Yamada, K. Ida, H. Iguchi, et al., Nucl. Fusion, 32, 25–32 (1992).

    Article  ADS  Google Scholar 

  106. K. Miyamoto, Nucl. Fusion, 18, 243–284 (1978).

    Article  ADS  Google Scholar 

  107. V.D. Shafranov, Nucl. Fusion, 20, 1075–1083 (1980).

    Article  Google Scholar 

  108. J.L. Shohet, in: Fusion (edited by E. Teller), Vol. 1, part A, Academic Press, New York (1981), pp. 243–289.

    Google Scholar 

  109. D.J. Lees, in: Plasma Physics and Nuclear Fusion Research (edited by R.D. Gill), Academic Press (1981), pp. 385–399.

    Google Scholar 

  110. J.L. Johnson, G. Grieger, D.J. Lees, M.S. Rabinovich, J.L. Shohet, and K. Uo, IEEE Transactions on Plasma Science, PS-9, 142–149 (1981).

    Article  ADS  Google Scholar 

  111. M.S. Rabinovich, in: Itogi Nauki i Tekhniki: Fizika Plazmy (Advances in Science and Technology: Plasma Physics) [in Russian, edited by V.D. Shafranov], Vol. 2, VINITI, Moscow (1981), pp. 6–79.

    Google Scholar 

  112. J.L. Johnson, Nucl. Technology/Fusion, 2, 340–361 (1982).

    Google Scholar 

  113. B.B. Kadomtsev and V.D. Shafranov, Usp. Fiz. Nauk, 139, 399–434 (1983). English translation: Sov. Phys. Uspekhi, 26, 207 (1983).

    Article  Google Scholar 

  114. V.D. Shafranov, in: Itogi Nauki i Tekhniki: Fizika Plazmy (Advances in Science and Technology: Plasma Physics) [in Russian, edited by V.D. Shafranov], Vol. 8, VINITI, Moscow (1988), pp. 131–171.

    Google Scholar 

  115. A. Gibson, in: Proc. Conf. on Nuclear Fusion Reactors, Culham, 1969, UKAEA Culham Laboratory (1970), pp. 233–241.

    Google Scholar 

  116. V.N. Pyatov and A.A. Shishkin, Nucl. Fusion, 6, 937–941 (1976).

    Article  ADS  Google Scholar 

  117. I.S. Danilkin, Fiz. Plazmy, 4, 1033–1043 (1978). English translation: Sov. J. Plasma Phys., 4, 576-581 (1978).

    Google Scholar 

  118. N.S. Gorbachev, Yu. K. Kuznetsov, and I.B. Pinos, Nucl. Fusion, 20, 341–347 (1980).

    Article  ADS  Google Scholar 

  119. P.J. Fielding and W.N.G. Hitchon, “Plasma equilibrium in toroidal l = 3 stellarators,” Preprint CLM-P605, Culham (1980).

    Google Scholar 

  120. P.J. Fielding and W.N.G. Hitchon, J. Plasma Phys., 24, 453–478 (1980).

    Article  ADS  Google Scholar 

  121. P.J. Fielding and W.N.G. Hitchon, Nucl. Fusion, 21, 775–785 (1981).

    Article  ADS  Google Scholar 

  122. The T.F.R. Group, in: Proc. 6th Europ. Conf. on Controlled Fusion and Plasma Physics, Vol. 2, Moscow (1973), pp. 20–36.

    Google Scholar 

  123. J. Hugill and A. Gibson, Nucl. Fusion, 14, 611–619 (1974).

    Article  Google Scholar 

  124. O. Kluber, S. Corti, J. Gernhardt, et al., in: Proc. 6th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Tokyo, 1974, Vol. 1, IAEA, Vienna (1975), pp. 179–189.

    Google Scholar 

  125. M. Fujiwara, S. Itoh, K. Matsuoka, et al., Jpn. J. Appl. Phys., 14, 675–690 (1975).

    Article  ADS  Google Scholar 

  126. J.L. Anderson, R.S. Booth, R.J. Colchin, R.V. Miskell, and J.M. Bailey, Nucl. Fusion, 16, 629–637 (1976).

    Article  ADS  Google Scholar 

  127. D. Grove, V. Arunasalam, K. Bol, et al., in: Proc. 6th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Berchtesgaden, 1976, Vol. 1, IAEA, Vienna (1977), pp. 21–32.

    Google Scholar 

  128. F. Schneider, in: Proc. 10th Symposium on Fusion Technology, Padova, 1978, Vol. 2, Pergamon Press (1979), pp. 1013–1018

    Google Scholar 

  129. V.D. Shafranov, in: Proc. 2nd Int. Conf. Plasma Theory, Kiev, 1974 [in Russian], Naukova Dumka, Kiev (1976), pp. 43–48.

    Google Scholar 

  130. L.E. Zakharov and V.D. Shafranov, in: Reviews of Plasma Physics (edited by M.A. Leontovich and B.B. Kadomtsev), Vol. 11, Energoizdat, Moscow (1982), pp. 118–235. English translation: Consultants Bureau, New York (1986), pp. 153-302.

    Google Scholar 

  131. V.D. Pustovitov and V.D. Shafranov, in: Reviews of Plasma Physics [in Russian], (edited by B.B. Kadomtsev), Vol. 15, Energatomoizdat, Moscow (1987), pp. 146–291. English translation: Consultants Bureau, New York (1990), pp. 163-326.

    Google Scholar 

  132. V.D. Shafranov, Zh. Eksp. Teor. Fiz., 33, 710–722 (1957). English translation: Sov. Phys. JETP, 6, 545 (1958).

    Google Scholar 

  133. H. Grad and H. Rubin, in: Proc. of Second United Nations International Conference on the Peaceful Uses of Atomic Energy, Geneva, 1958, Vol. 31, United Nations, New York (1958), pp. 190–197.

    Google Scholar 

  134. R. Lust and A. Schlüter, Z. Naturforsch., 12a, 850–854 (1957).

    ADS  Google Scholar 

  135. J.M. Greene and J.L. Johnson, Phys. Fluids, 4, 1417–1426 (1961).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  136. J.L. Johnson, J.M. Greene, and K.E. Weimer, Nucl. Fusion, 2, 16–22 (1962).

    Article  Google Scholar 

  137. J.M. Greene, J.L. Johnson, and K.E. Weimer, Plasma Phys., 8, 145–155 (1966).

    Google Scholar 

  138. J.L. Johnson, “Comments concerning a numerical model for studying MHD properties of stellarators,” Preprint IPP 6/162, Garching (1977).

    Google Scholar 

  139. M.I. Mikhailov, Fiz. Plazmy, 6, 45–54 (1980). English translation: Sov. J. Plasma Phys., 6, 25-30 (1980).

    Google Scholar 

  140. L.M. Kovrizhnykh and S.V. Shchepetov, Fiz. Plazmy, 6, 976–986 (1980). English translation: Sov. J. Plasma Phys., 6, 533-538 (1980).

    Google Scholar 

  141. L.E. Zakharov, M.I. Mikhailov, V.I. Pistunovich, et al., in: Proc. 8th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Brussels, 1980, Vol. 1, IAEA, Vienna (1981), pp. 313–328.

    Google Scholar 

  142. M.I. Mikhailov and V.D. Shafranov, in: Proc. 10th Europ. Conf. on Controlled Fusion and Plasma Physics, Vol. 1, Moscow (1981), pp. 393–396.

    Google Scholar 

  143. M.I. Mikhailov and V.D. Pustovitov, Pis’ma Zh. Eksp. Teor. Fiz., 34, 388–391 (1981). English translation: JETP Lett., 34, 368-370 (1981).

    Google Scholar 

  144. M.I. Mikhailov and V.D. Shafranov, Plasma Phys., 24, 233–242 (1982).

    Article  ADS  Google Scholar 

  145. V.D. Pustovitov, Fiz. Plazmy, 8, 473–483 (1982). English translation: Sov. J. Plasma Phys., 8, 265-271 (1982).

    Google Scholar 

  146. M.I. Mikhailov, V.D. Pustovitov, and V.D. Shafranov, Pis’ma Zh. Eksp. Teor. Fiz., 35, 152–154 (1982). English translation: JETP Lett., 35, 186-188 (1982).

    Google Scholar 

  147. V.D. Pustovitov, Fiz. Plazmy, 9, 575–584 (1983). English translation: Sov. J. Plasma Phys., 9, 335-340 (1983).

    Google Scholar 

  148. Eh. D. Andryukhina, M.S. Berezhetskij, M.A. Blokh, et al., in: Proc. 8th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Brussels, 1980, Vol. 1, IAEA, Vienna (1981), pp. 199–207.

    Google Scholar 

  149. L.M. Kovrizhnykh and S.V. Shchepetov,-Fiz. Plazmy, 7, 419–427 (1981). English translation: Sov. J. Plasma Phys., 7, 229-233 (1981).

    Google Scholar 

  150. L.M. Kovrizhnykh and S.V. Shchepetov, Fiz. Plazmy, 7, 965–967 (1981). English translation: Sov. J. Plasma Phys., 7, 527-528 (1981).

    Google Scholar 

  151. L.M. Kovrizhnykh and S.V. Shchepetov, Pis’ma Zh. Eksp. Teor. Fiz., 33, 441–444 (1981). English translation: JETP Lett., 33, 427-430 (1981).

    Google Scholar 

  152. I.S. Danilkin, L.M. Kovrizhnykh, and S.V. Shchepetov, in: Proc. 10th Europ. Conf. on Controlled Fusion and Plasma Physics, Vol. 1, Moscow (1981), pp. 397–400.

    Google Scholar 

  153. L.M. Kovrizhnykh and S.V. Shchepetov, Nucl. Fusion, 23, 859–867 (1983).

    Article  Google Scholar 

  154. L.M. Kovrizhnykh, Plasma Phys. Contr. Fusion, 26, 195–207 (1984).

    Article  ADS  Google Scholar 

  155. H.R. Strauss, Plasma Phys., 22, 733–745 (1980).

    Article  ADS  Google Scholar 

  156. H.R. Strauss and D.A. Monticello, Phys. Fluids, 24, 1148–1155 (1981).

    Article  ADS  MATH  Google Scholar 

  157. D. Lortz and J. Nuhrenberg, Z. Naturforsch., 37a, 876–878 (1982).

    ADS  Google Scholar 

  158. V.D. Pustovitov, Nucl. Fusion, 23, 1079–1088 (1983).

    Article  Google Scholar 

  159. V.D. Pustovitov, V.D. Shafranov, L.E. Zakharov, et al., in: Proc. 9th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Baltimore, 1982, Vol. 2, IAEA, Vienna (1983), pp. 541–556.

    Google Scholar 

  160. V.D. Shafranov, Phys. Fluids, 26, 357–364 (1983).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  161. L.M. Kovrizhnykh and S.V. Shchepetov, Usp. Fiz. Nauk, 148, 637–670 (1986). English translation: Sov. Phys. Uspekhi, 29, 343 (1986).

    Article  Google Scholar 

  162. V.D. Shafranov and E.I. Yurchenko, Nucl. Fusion, 8, 329–339 (1968).

    Article  Google Scholar 

  163. C. Mercier, Suppl. Nucl. Fusion, Part 2, 801-808 (1962).

    Google Scholar 

  164. C. Mercier and H. Luc, “The MHD approach to the problem of plasma confinement in closed magnetic configurations,” in: Lectures in Plasma Physics, EUR 5127e, Commission of European Communities, Luxembourg (1974).

    Google Scholar 

  165. J.M. Greene and J.L. Johnson, Phys. Fluids, 5, 510–517 (1962).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  166. L.S. Solov’ev, Zh. Eksp. Teor. Fiz., 53, 626–643 (1967). English translation: Sov. Phys. JETP, 26, 400 (1968).

    Google Scholar 

  167. G. Bateman, MHD Instabilities, MIT Press, Cambridge, MA (1978).

    Google Scholar 

  168. L.S. Solov’ev, Zh. Eksp. Teor. Fiz., 53, 2063–2069 (1967). English translation: Sov. Phys. JETP, 26, 1167 (1968).

    Google Scholar 

  169. L.S. Solov’ev, in: Reviews of Plasma Physics (edited by M.A. Leontovich), Vol. 6, Atomizdat, Moscow (1972), pp. 210–290. English translation: Consultants Bureau, New York (1975), pp. 239-331.

    Google Scholar 

  170. V.D. Shafranov and E.I. Yurchenko, Nucl. Fusion, 9, 285–289 (1969).

    Article  Google Scholar 

  171. D. Lortz and J. Nuhrenberg, Nucl. Fusion, 17, 125–133 (1977).

    Article  ADS  Google Scholar 

  172. A.B. Mikhailovskii and V.D. Shafranov, Zh. Eksp. Teor. Fiz., 66, 190–199 (1974). English translation: Sov. Phys. JETP, 39, 88-92 (1974).

    ADS  Google Scholar 

  173. B.A. Carreras, Sov. J. Plasma Phys., 16, 722–729 (1990).

    Google Scholar 

  174. L.A. Charlton and J.-N. Leboeuf, Phys. Fluids, B5, 2989–2998 (1993).

    ADS  Google Scholar 

  175. G.H. Neilson, F.S.B. Anderson, D.B. Batchelor, et al., in: Proc. 15th Europ. Conf. on Controlled Fusion and Plasma Heating, Vol. 12B, Part II, Dubrovnik (1988), pp. 486–489.

    Google Scholar 

  176. J.H. Harris, M. Murakami, B.A. Carreras, et al., Phys. Rev. Let. 63, 1249–1252 (1989).

    Article  ADS  Google Scholar 

  177. M. Murakami, B.A. Carreras, J.H. Harris, et al., in: Proc. 16th Europ. Conf. on Controlled Fusion and Plasma Physics, Vol. 13B, Part II, Venice (1988), pp. 575–579.

    Google Scholar 

  178. J.H. Harris, E. Anabitarte, G.L. Bell, et al., Phys. Fluids, B2, 1353–1358 (1990).

    ADS  Google Scholar 

  179. J.H. Harris, L.A. Charlton., G.L. Bell, et al., in: Proc. 13th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Washington, 1990, Vol. 2, IAEA, Vienna (1991), pp. 677–684.

    Google Scholar 

  180. N. Domínguez and V.E. Lynch, “Absence of second stability in ATF”, Report ORNL/TM-13040, Oak Ridge National Laboratory, Oak Ridge, USA (1995).

    Google Scholar 

  181. G. Rewoldt and J.L. Johnson, Nucl. Fusion, 24, 733–738 (1984).

    Article  Google Scholar 

  182. J.L. Johnson, Comput. Phys. Rep., 4, 37–70 (1986).

    Article  ADS  Google Scholar 

  183. B.A. Carreras, H.R. Hicks, J.A. Holmes, et al., Nucl. Fusion, 24, 1347–1355 (1984).

    Article  Google Scholar 

  184. Yu. K. Kuznetsov, M.I. Mikhailov, V.K. Pashnev, and V.M. Tonkopryad, Nucl. Fusion, 23, 15–23 (1983).

    Article  Google Scholar 

  185. J.P. Friedberg, P.A. Politzer, and Ph. Rosenau, Phys. Fluids, 27, 2093–2100 (1984).

    Article  ADS  Google Scholar 

  186. D.K. Akulina, Eh. D. Andryukhina, G.S. Voronov, et al., in: Proc. 7th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Innsbruck, 1978, Vol. 2, IAEA, Vienna (1979), pp. 287–301.

    Google Scholar 

  187. P.H. Rebut, D.V. Bartlett, G. Baumel, et al., in: Proc. 10th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, London, 1984, Vol. 1, IAEA, Vienna (1985), pp. 11–27.

    Google Scholar 

  188. L.A. Artsimovich and V.D. Shafranov, Pis’ma Zh. Eksp. Teor. Fiz., 15, 72–76 (1972). English translation: JETP Lett., 15, 51-54 (1972).

    Google Scholar 

  189. A.V. Bortnikov, Yu. T. Baiborodov, N.N. Brevnov, et al., in: Proc. 6th Europ. Conf. on Controlled Fusion and Plasma Physics, Vol. 1, Moscow (1973), pp. 165–168.

    Google Scholar 

  190. W. Feneberg and K. Lackner, in: Proc. 6th Europ. Conf. on Controlled Fusion and Plasma Physics, Vol. 1, Moscow (1973), pp. 209–212.

    Google Scholar 

  191. G. Laval and R. Pellat, in: Proc. 6th Europ. Conf. on Controlled Fusion and Plasma Physics, Vol. 2, Moscow (1973), pp. 64–74.

    Google Scholar 

  192. A.V. Bortnikov, N.N. Brevnov, S.N. Gerasimov, et al., in: Proc. 6th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Tokyo, 1974, Vol. 1, IAEA, Vienna (1975), pp. 147–159.

    Google Scholar 

  193. M. Okabayashi and G. Sheffild, Nucl. Fusion, 14, 263–265 (1974).

    Article  Google Scholar 

  194. G. Laval, R. Pellat, and J.S. Soule, Phys. Fluids, 17, 835–845 (1974).

    Article  ADS  Google Scholar 

  195. P. Noll, in: Proc. 7th Europ. Conf. on Controlled Fusion and Plasma Physics, Vol. 2, Lausanne (1973), pp. 91–101.

    Google Scholar 

  196. H. Toyama, S. Inoue, K. Itoh, et al., in: Proc. 6th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Berchtesgaden, 1976, Vol. 1, IAEA, Vienna (1977), pp. 323–334.

    Google Scholar 

  197. G. Cima, D.C. Robinson, C.L. Thomas, and A.J. Wootton, in: Proc. 6th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Berchtesgaden, 1976, Vol. 1, IAEA, Vienna (1977), pp. 335–350.

    Google Scholar 

  198. M.S. Chu, D.R. Dobrott, G.E. Guest, et al., in: Proc. 6th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Berchtesgaden, 1976, Vol. 2, IAEA, Vienna (1977), pp. 387–394.

    Google Scholar 

  199. T. Ohkawa and H.G. Voorhies, Phys. Rev. Lett., 22, 1275–1277 (1969).

    Article  ADS  Google Scholar 

  200. T. Ohkawa and T.H. Jensen, Plasma Phys., 12, 789–797 (1970).

    Article  ADS  Google Scholar 

  201. T. Ohkawa, C.C. Baker, N.H. Brooks, et al., in: Proc. 6th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Tokyo, 1974 Vol. 1, IAEA, Vienna (1975), pp. 281–290.

    Google Scholar 

  202. R.L. Freeman, S.J. Adcock, J.F. Baur, et al., in: Proc. 6th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Berchtesgaden, 1976, Vol. 1, IAEA, Vienna (1977), pp. 317–322.

    Google Scholar 

  203. S.V. Mirnov, Physical Processes in the Tokamak Plasma [in Russian], Energoatomizdat, Moscow (1983).

    Google Scholar 

  204. J. Wesson, Tokamaks, Clarendon Press, Oxford (1987).

    Google Scholar 

  205. L.M. Degtyarev, Y.V. Drozdov, and S. Yu. Medvedev, Numerical Modeling of Equilibrium and Stability of Toroidal Plasmas [in Russian], Keldysh Institute of Applied Mathematics, the USSR Academy of Sciences, Moscow (1989).

    Google Scholar 

  206. B.B. Kadomtsev, in: Itogi Nauki i Tekhniki: Fizika Plazmy (Advances in Science and Technology: Plasma Physics) [in Russian, edited by V.D. Shafranov], Vol. 10, Part 1, VINITI, Moscow (1991), pp. 5–147.

    Google Scholar 

  207. T. Takeda and S. Tokuda, J. Comput Phys., 93, 1–107 (1991).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  208. E. Bertolimi, P.L. Mondino, and P. Noll, Fusion Technol., 11, 71–119 (1987).

    Google Scholar 

  209. F. Hofmann and S.C. Jardin, Nucl. Fusion, 30, 2013–2022 (1990).

    Article  Google Scholar 

  210. R.E. Bell, N. Asakura, S. Bernabei, et al., Phys. Fluids, B2, 1271–1279 (1990).

    ADS  Google Scholar 

  211. E.A. Lazarus, M.S. Chu, J.R. Ferron, et al., Phys. Fluids, B3, 2220–2229 (1991).

    ADS  Google Scholar 

  212. F. Hofmann, N. Pomphrey, and S.C. Jardin, Nucl. Fusion, 32, 897–902 (1992).

    Article  ADS  Google Scholar 

  213. F. Hofmann, J.B. Lister, M. Anton, et al., Plasma Phys. Contr. Fusion, 36, B277–B287 (1994).

    Article  ADS  Google Scholar 

  214. F.J. Helton and J.M. Greene, J. Comput. Phys., 66, 458–468 (1986).

    Article  ADS  MATH  Google Scholar 

  215. R. Toschi, M. Chazalon, F. Engelmann, J. Nihoul, J. Raeder, and E. Salpietro, Fusion Technol., 14, 19–29 (1988).

    Google Scholar 

  216. F. Najmabadi and R.W. Conn, in: Proc. 14th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Wurzburg, 1992, Vol. 3, IAEA, Vienna (1993), pp. 295–310.

    Google Scholar 

  217. Yu. A. Sokolov, Fusion Eng. Design, 25, 159–167 (1994).

    Article  Google Scholar 

  218. D.A. Humphreys, J.A. Leuer, A.G. Kellman, et al., Fusion Technol, 26, 331–339 (1994).

    Google Scholar 

  219. G.H. Neilson, D.B. Batchelor, D.N. Hill, et al., Fusion Eng. Design, 26, 563–574 (1995).

    Article  Google Scholar 

  220. R.J. Colchin, M. Murakami, E. Anabitarte, et al., Phys. Fluids, B2, 1347–1352 (1990).

    ADS  Google Scholar 

  221. J.F. Lyon, in: Proc. 8th Int. Workshop on Stellarators, Kharkov, 1991, IAEA, Vienna (1991), pp. 7–15.

    Google Scholar 

  222. G. Anania, J.L. Johnson, and K.E. Weimer, Phys. Fluids, 26, 2210–2218 (1983).

    Article  ADS  MATH  Google Scholar 

  223. G. Anania and J.L. Johnson, Phys. Fluids, 26, 3070–3078 (1983).

    Article  ADS  MATH  Google Scholar 

  224. V.E. Lynch, B.A. Carreras, L.A. Charlton, L. Garcia, T.C. Hender, H.R. Hicks, and J.A. Holmes, J. Comput. Phys., 66, 411–444 (1986).

    Article  ADS  MATH  Google Scholar 

  225. M. Wakatani, Y. Nakamura, and K. Ichiguchi, Fusion Eng. Design, 15, 395–413 (1992).

    Article  Google Scholar 

  226. J. Nuhrenberg and R. Zilie, Phys. Lett., A114, 129–132 (1986).

    ADS  Google Scholar 

  227. J. Nuhrenberg and R. Zilie, Phys. Lett., A129, 113–117 (1988).

    ADS  Google Scholar 

  228. G. Grieger, C. Beidler, E. Harmeyer, et al., Fusion Technol., 21, 1767–1778 (1992).

    Google Scholar 

  229. O. Motojima, F. Sano, M. Sato, et al., Nucl. Fusion, 25, 1783–1787 (1985).

    Article  Google Scholar 

  230. V.D. Shafranov and L.E. Zakharov, Nucl. Fusion, 12, 599–601 (1972).

    Article  Google Scholar 

  231. Yu. V. Gutarev, Yu. K. Kuznetsov, V.K. Pashnev, and N.P. Ponomarnenko, Fiz. Plazmy, 14, 286–291 (1988). English translation: Sov. J. Plasma Phys., 14, 164-167 (1988).

    Google Scholar 

  232. V.D. Pustovitov, in: Proc. 15th Europ. Conf. on Controlled Fusion and Plasma Heating, Vol. 12B, Part II, Dubrovnik (1988), pp. 502–505.

    Google Scholar 

  233. V.D. Pustovitov, Fiz. Plazmy, 14, 1436–1443 (1988). English translation: Sov. J. Plasma Phys., 14, 840-844 (1988).

    Google Scholar 

  234. V.D. Pustovitov, Nucl. Fusion, 30, 1523–1531 (1990).

    Article  Google Scholar 

  235. V.D. Pustovitov, in: Proc. 13th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Washington, 1990, Vol. 2, IAEA, Vienna (1991), pp. 301–310.

    Google Scholar 

  236. J.M. Greene, J.L. Johnson, and K.E. Weimer, Phys. Fluids, 14, 671–683 (1971).

    Article  ADS  Google Scholar 

  237. L.E. Zakharov and S.V. Putvinskii, in: Itogi Nauki i Tekhniki: Fizika Plazmy (Advances in Science and Technology: Plasma Physics) [in Russian, edited by V.D. Shafranov], Vol. 7, VINITI, Moscow (1985), pp. 4–79.

    Google Scholar 

  238. V.V. Bakaev, S.P. Bondarenko, V.V. Bronnikov, et al., in: Proc. 10th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, London, 1984, Vol. 2, IAEA, Vienna (1985), pp. 397–407.

    Google Scholar 

  239. S. Besshou, K. Ogata, K. Kondo, et al., in: Proc. 21st Europ. Conf. on Controlled Fusion and Plasma Physics, Vol. 18B, Part I, Montpellier (1994), pp. 420–423.

    Google Scholar 

  240. S. Besshou, K. Ogata, K. Kondo, et al., Nucl. Fusion, 35, 173–182 (1995).

    Article  ADS  Google Scholar 

  241. S. Besshou, K. Ogata, K. Kondo, et al., Trans. Fusion Technol., 27, 219–222 (1995).

    Google Scholar 

  242. S.P. Hirshman, W.I. van Rij, and P. Merkel, Comput. Phys. Comm., 43, 143–155 (1986).

    Article  MathSciNet  ADS  Google Scholar 

  243. R.N. Morris, J.C. Glowienka, G.H. Neilson, S.P. Hirshman, and P. Merkel, Nucl. Fusion, 29, 2115–2123 (1989).

    Article  Google Scholar 

  244. H.J. Gardner and K. Ichiguchi, “Free-boundary equilibrium studies for the Large Helical Device,” Preprint NIFS-231, National Institute for Fusion Science, Nagoya, Japan (1993).

    Google Scholar 

  245. I.S. Danilkin and L.M. Kovrizhnykh, Pis’ma Zh. Eksp. Teor. Fiz., 19, 193–197 (1974). English translation: JETP Lett., 19, 119-121 (1974).

    Google Scholar 

  246. I.S. Danilkin and L.M. Kovrizhnykh, in: Proc. 6th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Tokyo, 1974, Vol. 2, IAEA, Vienna (1975), pp. 163–175.

    Google Scholar 

  247. J.L. Shohet, D.T. Anderson, and J.A. Tataronis, Nucl. Fusion, 16, 441–445 (1976).

    Article  ADS  Google Scholar 

  248. T.S. Wang and T.H. Jensen, Nucl. Fusion, 18, 1459–1465 (1978).

    Article  ADS  Google Scholar 

  249. E.A. Matveeva and V.D. Pustovitov, Pis’ma Zh. Eksp. Teor. Fiz., 45, 216–219 (1987). English translation: JETP Lett., 45, 268-271 (1987).

    Google Scholar 

  250. E.A. Matveeva and V.D. Pustovitov, Fiz. Plazmy, 14, 151–160 (1988). English translation: Sov. J. Plasma Phys., 14, 81-87 (1988).

    Google Scholar 

  251. V.D. Pustovitov, Fiz. Plazmy, 14, 522–528 (1988). English translation: Sov. J. Plasma Phys., 14, 305-309 (1988).

    Google Scholar 

  252. A.B. Mikhailovskii, Plasma Instabilities in Magnetic Confinement Systems [in Russian], Atomizdat, Moscow (1978).

    Google Scholar 

  253. O.P. Pogutse and E.I. Yurchenko, in: Reviews of Plasma Physics (edited by M.A. Leontovich and B.B. Kadomtsev), Vol. 11, Energoizdat, Moscow (1982), pp. 56–117. English translation: Consultants Bureau, New York (1986), pp. 65-151.

    Google Scholar 

  254. L.E. Zakharov, V.D. Pustovitov, S.B. Semenov, A.A. Subbotin, and J. Peralto, “Simplified models for plasma equilibrium in a tokamak” [in Russian], Preprint IAE-4115/6, Kurchatov Institute, Moscow (1985).

    Google Scholar 

  255. V.D. Pustovitov, “Unified approach for the description of plasma equilibrium in tokamaks and stellarators” [in Russian], Preprint IAE-4474/6, Kurchatov Institute, Moscow (1987).

    Google Scholar 

  256. V.D. Pustovitov, Fiz. Plazmy, 14, 101–104 (1988). English translation: Sov. J. Plasma Phys., 14, 63-65 (1988).

    Google Scholar 

  257. A. Gibson, Phys. Fluids, 10, 1553–1560 (1967).

    Article  ADS  Google Scholar 

  258. V.N. Kalyuzhnyj, V.V. Nemov, and A.A. Shishkin, Nucl. Fusion, 22, 347–361 (1982).

    Article  Google Scholar 

  259. J.C. Wesley, T. Angel, C.J. Armentrout, et al., in: Proc. 8th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Brussels, 1980, Vol. 1, IAEA, Vienna (1981), pp. 35–42.

    Google Scholar 

  260. R.W. Moore, L.C. Bernanrd, V.S. Chan, et al., in: Proc. 8th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Brussels, 1980, Vol. 1, IAEA, Vienna (1981), pp. 283–290.

    Google Scholar 

  261. V.D. Pustovitov, Fiz. Plazmy, 15, 756–760 (1989). English translation: Sov. J. Plasma Phys., 15, 437-440 (1989).

    Google Scholar 

  262. V.D. Pustovitov, Nucl. Fusion, 30, 1079–1086 (1990).

    Article  Google Scholar 

  263. R. Chodura and A. Schlüter, J. Comput. Phys., 41, 68–88 (1981).

    Article  ADS  MATH  Google Scholar 

  264. T. Ohkawa, Kakuyugo Kenkyu, 20, 557–570 (1968).

    Article  Google Scholar 

  265. T. Ohkawa, Kakuyugo Kenkyu, 22, 395–404 (1969).

    Article  Google Scholar 

  266. D. Yu. Sychugov and S.V. Shchepetov, in: Proc. 8th Int. Workshop on Stellarators, Kharkov, 1991, IAEA, Vienna (1991), pp. 313–316.

    Google Scholar 

  267. I.S. Danilkin and S.V. Shchepetov, Fiz. Plazmy, 13, 392–402 (1987). English translation: Sov. J. Plasma Phys., 13, 220-228 (1987).

    Google Scholar 

  268. V.V. Drozdov and V.D. Pustovitov, in: Voprosy Atomnoi Nauki i Tekhniki: Termoyaderny Sintez (Atomic Science and Technology: Thermonuclear Fusion) [in Russian], No. 2, Kurchatov Institute, Moscow (1989), pp. 16–19.

    Google Scholar 

  269. V.V. Drozdov, M. Yu. Isaev, M.I. Mikhailov, V.D. Pustovitov, and V.D. Shafranov, in: Proc. 12th Int. Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Nice, 1988, Vol. 2, IAEA, Vienna (1989), pp. 611–621.

    Google Scholar 

  270. G.G. Lesnyakov and V.I. Petrenko, in: Proc. 8th Int. Workshop on Stellarators, Kharkov, 1991, IAEA, Vienna (1991), pp. 99–102.

    Google Scholar 

  271. V.I. Perevozchikov, Fiz. Plazmy, 18, 946–950 (1992). English translation: Sov. J. Plasma Phys., 18, 492-494 (1992).

    Google Scholar 

  272. M.V. Malyshev and V.D. Pustovitov, in: Proc. 20th Europ. Conf. on Controlled Fusion and Plasma Physics, Vol. 17C, Part I, Lisboa (1993), pp. 429–432.

    Google Scholar 

  273. D.L. Grekov and A.V. Zolotukhin, in: Proc. IAEA Tech. Committee Meeting on Stellarators and Other Helical Confinement Systems, Garching (1993), pp. 158–163.

    Google Scholar 

  274. J.F. Lyon, G. Grieger, F. Rau, et al., Nucl. Fusion, 30, 1695–1715 (1990).

    Article  Google Scholar 

  275. N.N. Bogolyubov and Yu. A. Mitropolskii, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York (1961).

    Google Scholar 

  276. A.I. Morozov and L.S. Solov’ev, in: Reviews of Plasma Physics (edited by M.A. Leontovich), Vol. 2, Gosatomizdat, Moscow (1963), pp. 177–261. English translation: Consultants Bureau, New York (1966), pp. 201-297.

    Google Scholar 

  277. T.C. Hender and B.A. Carreras, Phys. Fluids, 27, 2101–2109 (1984).

    Article  ADS  MATH  Google Scholar 

  278. J. Todoroki, J. Phys. Soc. Jpn., 56, 128–138 (1987).

    Article  ADS  Google Scholar 

  279. J. Todoroki, J. Phys. Soc. Jpn., 58, 3979–3992 (1989).

    Article  ADS  Google Scholar 

  280. V.D. Pustovitov, in: Itogi Naukii Tekhniki: Fizika Plazmy (Advances in Science and Technology: Plasma Physics) [in Russian, edited by V.D. Shafranov], Vol. 13, VINITI, Moscow (1993), pp. 3–84; V.D. Pustovitov, J. Plasma Fusion Res., (formerly Kakuyugo Kenkyu), 70, 943-991 (1994).

    Google Scholar 

  281. A.B. Kuznetsov, Yu. K. Kuznetsov, D.Yu. Sychugov, and S.V. Shchepetov, in: Voprosy Atomnoi Nauki i Tekhniki: Termoyaderny Sintez (Atomic Science and Technology: Thermonuclear Fusion) [in Russian], No. 3, Kurchatov Institute, Moscow (1991), pp. 69–75.

    Google Scholar 

  282. E.D. Andryukhina and O.I. Fedyanin, Fiz. Plazmy, 3, 792–798 (1977). English translation: Sov. J. Plasma Phys., 3, 447-450 (1977).

    Google Scholar 

  283. F. Herrnegger, P. Merkel, and J.L. Johnson, J. Comput. Phys., 66, 445–457 (1986).

    Article  ADS  MATH  Google Scholar 

  284. A.A. Shishkin, in: Voprosy Atomnoi Nauki i Tekhniki: Termoyaderny Sintez (Atomic Science and Technology: Thermonuclear Fusion) [in Russian], No. 2, Kurchatov Institute, Moscow (1987), pp. 15–19.

    Google Scholar 

  285. V.D. Pustovitov, Fiz. Plazmy, 21, 1027–1038 (1995). English translation: Plasma Phys. Rep., 21, 969-980 (1995).

    Google Scholar 

  286. V.D. Pustovitov, Fiz. Plazmy, 16, 732–737 (1990). English translation: Sov. J. Plasma Phys., 16, 424-427 (1990).

    Google Scholar 

  287. F. Herrnegger and E.K. Maschke, Nucl. Fusion, 14, 119–121 (1974).

    Article  Google Scholar 

  288. D. Pfirsch and E. Rebhan, Nucl. Fusion, 14, 547–551 (1974).

    Article  Google Scholar 

  289. H. Oshiyama and Y. Fukutani, Nucl. Fusion, 14, 793–796 (1974).

    Article  Google Scholar 

  290. J.P. Christiansen and J.B. Taylor, Nucl. Fusion, 22, 111–115 (1982).

    Article  Google Scholar 

  291. M.S. Chu, Nucl. Fusion, 27, 611–615 (1987).

    Article  Google Scholar 

  292. N.A. Madden and R.J. Hastie, Nucl. Fusion, 34, 519–526 (1994).

    Article  ADS  Google Scholar 

  293. A.B. Mikhailovskii, Fiz. Plazmy, 22, 1111–1118 (1996). English translation: Plasma Phys. Rep., 22, 1009 (1996).

    Google Scholar 

  294. D.J. Braams, “The interpretation of tokamak magnetic diagnostics: status and prospects,” Preprint IPP 5/2, Garching (1985).

    Google Scholar 

  295. I.S. Danilkin, in: Stellarators, Trudy Fiz. Inst. Akad. Nauk SSSR [in Russian], Vol. 65, Moscow (1973), pp. 26–49. English translation: Proc. Lebedev Phys. Inst. Acad. Sci. USSR, Vol. 65 (1973).

    Google Scholar 

  296. D.K. Lee, J.H. Harris, S.P. Hirshman, and G.H. Neilson, Nucl. Fusion, 28, 1351–1364 (1988).

    Article  Google Scholar 

  297. W.A. Cooper, S.P. Hirshman, and D.K. Lee, Nucl Fusion, 29, 617–627 (1989).

    Article  Google Scholar 

  298. Y. Nakamura, M. Wakatani, and J.L. Johnson, “Choice of LHD stellarator equilibrium for the comparison of stability property calculations with KSTEP and other MHD stability codes,” Preprint PPLK-R-58, PPL Kyoto University, Kyoto (1992).

    Google Scholar 

  299. Y. Nakamura, T. Matsumoto, M. Wakatani, et al., J. Comput. Phys., 128, 43–57 (1996).

    Article  ADS  MATH  Google Scholar 

  300. N. Nakajima, J. Todoroki, and M. Okamoto, Kakuyugo Kenkyu, 68, 395–403 (1992).

    Article  Google Scholar 

  301. R.B. White, A.H. Boozer, and R. Hay, Phys. Fluids, 25, 575–576 (1982).

    Article  ADS  MATH  Google Scholar 

  302. A.H. Boozer, Phys. Fluids, 27, 2441–2445 (1984).

    Article  ADS  MATH  Google Scholar 

  303. J.R. Cary, C.L. Hedrick, and J.S. Tolliver, Phys. Fluids, 31, 1586–1600 (1988).

    Article  ADS  Google Scholar 

  304. J. Todoroki, J. Phys. Soc. Jpn., 62, 1562–1582 (1993).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  305. K.C. Shaing and J.D. Callen, Phys. Fluids, 26, 3315–3326 (1983).

    Article  ADS  MATH  Google Scholar 

  306. N. Nakajima, M. Okamoto, J. Todoroki, Y. Nakamura, and M. Wakatani, Nucl. Fusion, 29, 605–616 (1989).

    Article  Google Scholar 

  307. K.Y. Watanabe, N. Nakajima, M. Okamoto, K. Yamazaki, Y. Nakamura, and M. Wakatani, Nucl Fusion, 35, 335–345 (1995).

    Article  ADS  Google Scholar 

  308. H.E. Mynick, T.K. Chu, and A.H. Boozer, Phys. Rev. Lett., 48, 322–326 (1982).

    Article  ADS  Google Scholar 

  309. K.C. Shaing and S.A. Hokin, Phys. Fluids, 26, 2136–2139 (1983).

    Article  ADS  MATH  Google Scholar 

  310. L.M. Kovrizhnykh, Nucl. Fusion, 24, 851–936 (1984).

    Article  Google Scholar 

  311. V.E. Bykov, A.V. Georgievskii, V.G. Peletminskaya, Yu. F. Sergeev, A.V. Khodyachikh, and A.A. Shishkin, in: Voprosy Atomnoi Nauki i Tekhniki: Termoyaderny Sintez (Atomic Science and Technology: Thermonuclear Fusion) [in Russian], No. 4, Kurchatov Institute, Moscow (1984), pp. 19–29.

    Google Scholar 

  312. V.E. Bykov, A.V. Georgievskij, V.G. Peletminskaya, A.V. Khodyachikh, and A.A. Shishkin, Nucl. Fusion, 24, 1195–1203 (1984).

    Article  Google Scholar 

  313. L.M. Kovrizhnykh, Nucl Fusion, 25, 1391–1397 (1985).

    Article  Google Scholar 

  314. C.D. Beidler, W.N.S. Hitchon, W.I. van Rij, S.P. Hirshman, and J.L. Shohet, Phys. Rev. Lett., 58, 1745–1747 (1987).

    Article  ADS  Google Scholar 

  315. C.D. Beidler, W.N.S. Hitchon, D.L. Grekov, and A.A. Shishkin, Nucl. Fusion, 30, 405–411 (1990).

    Article  Google Scholar 

  316. A. Kato, Y. Nakamura, and M. Wakatani, J. Phys. Soc. Jpn., 60, 494–511 (1991).

    Article  ADS  Google Scholar 

  317. I.S. Danilkin and O.E. Khadin, in: Voprosy Atomnoi Nauki i Tekhniki: Termoyaderny Sintez (Atomic Science and Technology: Thermonuclear Fusion) [in Russian], No. 3, Kurchatov Institute, Moscow (1992), pp. 39–44.

    Google Scholar 

  318. M.S. Smirnova and A.A. Shishkin, Nucl. Fusion, 32, 1147–1160 (1992).

    Article  ADS  Google Scholar 

  319. G.H. Neilson and J.H. Harris, Nucl Fusion, 27, 711–724 (1987).

    Article  Google Scholar 

  320. L.D. Landau and E.M. Lifshitz, Electrodynamics of Continuous Media, Pergamon, New York (1960).

    MATH  Google Scholar 

  321. V.D. Shafranov, At. Energ., 19, 175 (1965).

    ADS  Google Scholar 

  322. V.D. Pustovitov, J. Plasma Fusion Res. (formerly Kakuyugo Kenkyu), 69, 34–40 (1993).

    Google Scholar 

  323. I.S. Gradshtein and I.M. Ryzhik, Tables of Series, Products and Integrals, Plenum Press, New York (1963).

    Google Scholar 

  324. R.D. Woolley, M. Bell, J. Coonrod, et al., Fusion Technol, 8, 1807–1812 (1985).

    Google Scholar 

  325. W. Woyke, J. Gernhardt, O. Gruber, et al., in: Proc. 19th Europ. Conf. on Controlled Fusion and Plasma Physics, Vol. 16C, Part I, Innsbruck (1992), pp. 455–458.

    Google Scholar 

  326. K. Kurihara, Nucl. Fusion, 33, 399–412 (1993).

    Article  Google Scholar 

  327. J.B. Lister, F. Hofmann, J.-M. Moret, et al., Fusion Technol., 32, 321–373 (1997).

    Google Scholar 

  328. A. Portone, R. Albanese, Yu. V. Gribov, et al., Fusion Technol, 32, 374–389 (1997).

    Google Scholar 

  329. V.D. Pustovitov, Nucl. Fusion, 36, 583–591 (1996).

    Article  ADS  Google Scholar 

  330. V.D. Pustovitov, Nucl. Fusion, 36, 1281–1290 (1996).

    Article  ADS  Google Scholar 

  331. A.I. Morozov, Pis’ma Zh. Tekh. Fiz., 16, No. 15, 86–89 (1990). English translation: Sov. Tech. Phys. Lett., 16, (1990).

    Google Scholar 

  332. A.I. Morozov, Fiz. Plazmy, 18, 305–316 (1992). English translation: Plasma Phis. Rep., 18, (1992).

    Google Scholar 

  333. S. Besshou, V.D. Pustovitov, N. Fujita, et al., Phys. Plasmas, 5, 481–485 (1998).

    Article  ADS  Google Scholar 

  334. K. Tomabechi, J.R. Gilleland, Yu. A. Sokolov, R., Toschi, and the ITER Team, Nucl. Fusion, 31, 1135–1224 (1991).

    Article  Google Scholar 

  335. O. Motojima, K.Y. Watanabe, A. Sagara, et al., Trans. Fusion Technol., 27, 264–269 (1995).

    Google Scholar 

  336. N.A. Manzyuk, V.N. Pyatov, A.M. Rozhkov, and V.P. Sebko, Fiz. Plazmy, 3, 14–17 (1977). English translation: Sov. J. Plasma Phys., 3, 7-9 (1977).

    Google Scholar 

  337. D. Dorst, A. Eisner, G. Grieger, et al., Plasma Phys. Contr. Fusion, 26, 183–194 (1984).

    Article  Google Scholar 

  338. G. Cattanei, D. Dorst, A. Eisner, et al., in: Proc. 12th Europ. Conf. on Controlled Fusion and Plasma Physics, Vol. 9F, Part I, Budapest (1985), pp. 393–396.

    Google Scholar 

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B. B. Kadomtsev V. D. Shafranov

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Pustovitov, V.D. (2000). Theoretical Principles of the Plasma-Equilibrium Control in Stellarators. In: Kadomtsev, B.B., Shafranov, V.D. (eds) Reviews of Plasma Physics. Reviews of Plasma Physics, vol 21. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4309-1_1

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