Advertisement

Resistive Wall Mode (RWM)

  • Valentin Igochine
Chapter
Part of the Springer Series on Atomic, Optical, and Plasma Physics book series (SSAOPP, volume 83)

Abstract

The advanced tokamak regime is a promising candidate for steady state tokamak operation, desirable for a fusion reactor. This regime is characterized by a high bootstrap current fraction and a flat or reversed safety factor profile, which leads to operation close to the pressure limit (see Chap.  2). At this limit, an external ideal kink mode becomes unstable. This external kink is converted into the slowly growing Resistive Wall Mode (RWM) by the presence of a conducting wall. Reduction of the growth rate allows one to act on the mode and to stabilize it. There are two main factors which determine the stability of the RWM. The first factor comes from external magnetic perturbations (error fields, resistive wall, feedback coils, etc.). This part of RWM physics is the same for tokamaks and reversed field pinch (RFP) configurations. The physics of this interaction is relatively well understood, since it is based on classical electrodynamics, and is used for RWM control with external coils. The second ingredient of RWM physics is the interaction of the mode with plasma flow and fast particles. These interactions are particularly important for tokamaks, which have higher plasma flow and stronger trapped particle effects compared to the present day reversed field pinch device. The influence of the fast particles will also be increasingly more important in ITER and DEMO, which will have a large fraction of fusion born alpha particles. These interactions have kinetic origins that make the computations challenging. Correct prediction of the “plasma-RWM” interaction is an important ingredient which has to be combined with the influence of external fields (resistive wall, error fields and feedback) to make reliable predictions for RWM control in a future reactor.

Keywords

Unstable Mode Kinetic Effect Kink Mode Error Field Resistive Wall 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    N.J. Fisch, Rev. Mod. Phys. 59, 175 (1987)ADSCrossRefGoogle Scholar
  2. 2.
    A.G. Peeters, Plasma Phys. Control. Fusion 42, B231 (2000)ADSCrossRefGoogle Scholar
  3. 3.
    M.S. Chu, M. Okabayashi, Plasma Phys. Control. Fusion 52, 123001 (2010)ADSCrossRefGoogle Scholar
  4. 4.
    A. Bondeson, D.J. Ward, Phys. Rev. Let. 72, 2709 (1994)ADSCrossRefGoogle Scholar
  5. 5.
    H. Reimedes et al., Phys. Plasmas 13, 056107 (2006)ADSCrossRefGoogle Scholar
  6. 6.
    J. Manickam et al., Phys. Plasmas 1, 1601 (1994)ADSCrossRefGoogle Scholar
  7. 7.
    V. Igochine, Nucl. Fusion 52, 074010 (2012)ADSCrossRefGoogle Scholar
  8. 8.
    A.M. Garofalo, Nucl. Fusion 40, 1491 (2000)ADSCrossRefGoogle Scholar
  9. 9.
    E.J. Strait et al., in Fusion Energy 2002 (Proc. 19th Int. Conf. Lyon, 2002) (Vienna: IAEA) CD-ROM file EX/S2-1 and, http://www-pub.iaea.org/MTCD/publications/PDF/csp_019c/html/node137.htm
  10. 10.
    H. Reimerdes, Phys. Plasmas 13, 056107 (2006)ADSCrossRefGoogle Scholar
  11. 11.
    M.S. Chu et al., Phys. Plasmas 2, 2236 (1995)ADSCrossRefGoogle Scholar
  12. 12.
    R. Betti, J.P. Freidberg, Phys. Rev. Lett. 74, 2949 (1995)ADSCrossRefGoogle Scholar
  13. 13.
    A.M. Garofalo et al., Phys. Rev. Lett. 82, 3811 (1999)ADSCrossRefGoogle Scholar
  14. 14.
    A.M. Garofalo et al., Phys. Plasmas 10, 4776 (2003)ADSCrossRefGoogle Scholar
  15. 15.
    M. Okabayashi, Plasma Phys. Control. Fusion 44, B339 (2002)CrossRefGoogle Scholar
  16. 16.
    A.M. Garofalo et al., Nucl. Fusion 42, 1335 (2002)ADSCrossRefGoogle Scholar
  17. 17.
    S. Sabbagh et al., Nucl. Fusion 46, 635 (2006)ADSCrossRefGoogle Scholar
  18. 18.
    A.J. Webster, Phys. Plasmas 17, 110708 (2010)ADSCrossRefGoogle Scholar
  19. 19.
    L.E. Zakharov, Phys. Plasmas 15, 062507 (2008)ADSCrossRefGoogle Scholar
  20. 20.
    M. Okabayashi, Nucl. Fusion 49, 125003 (2009)ADSCrossRefGoogle Scholar
  21. 21.
    I.T. Chapman et al., Plasma Phys. Control. Fusion 51, 055015 (2009)ADSCrossRefGoogle Scholar
  22. 22.
    A. Bondeson et al., Plasma Phys. Control. Fusion 45, A253 (2003)ADSCrossRefGoogle Scholar
  23. 23.
    Y. Liu, Plasma Phys. Control. Fusion 51, 115006 (2009)ADSCrossRefGoogle Scholar
  24. 24.
    M. Takechi et al., 37th EPS Conference on Plasma Physics, Dublin, Ireland, P2.192, http://ocs.ciemat.es/EPS2010PAP/html/author.html. Accessed 21–25 June 2010
  25. 25.
    V.D. Pustovitov, M.S. Mayorova, Plasma Phys. Control. Fusion 48, 51 (2006)ADSCrossRefGoogle Scholar
  26. 26.
    V.D. Pustovitov, Plasma Phys. Rep. 30, 187 (2004)ADSCrossRefGoogle Scholar
  27. 27.
    A.H. Boozer, Phys. Rev. Let. 86, 5059 (2001)ADSCrossRefGoogle Scholar
  28. 28.
    M. Okabayshi, N. Pomphrey, R.E. Hatcher, Nucl. Fusion 38, 1607 (1998)ADSCrossRefGoogle Scholar
  29. 29.
    J.M. Finn, Phys. Plasmas 2, 198 (1995)MathSciNetADSCrossRefGoogle Scholar
  30. 30.
    R. Fitzpatrick, Phys. Plasmas 9, 3459 (2002)ADSCrossRefGoogle Scholar
  31. 31.
    S.C. Guo, Phys. Plasmas 6, 3868 (1999)ADSCrossRefGoogle Scholar
  32. 32.
    D. Yadykin et al., Plasma Phys. Control. Fusion 53, 085024 (2011)ADSCrossRefGoogle Scholar
  33. 33.
    M. Okabayashi et al., 36th EPS Conference on Plasma Physics, Sofia, Bulgaria, ECA Vol.33E, P-4.141 (2009) or CD-ROM file P4.141 http://epsppd.epfl.ch/Sofia/start.htm. Accessed 29 June–3 July 2009
  34. 34.
    Y. In et al., Plasma Phys. Control. Fusion 52, 104004 (2010)ADSCrossRefGoogle Scholar
  35. 35.
    Y. Liu et al., Phys. Plasmas 17, 072510 (2010)ADSCrossRefGoogle Scholar
  36. 36.
    E.J. Strait et al., Nucl. Fusion 43, 430 (2003)ADSCrossRefGoogle Scholar
  37. 37.
    Liu et al., Phys. Plasmas 7, 3681 (2000)ADSCrossRefGoogle Scholar
  38. 38.
    A. Bondeson et al., Nucl. Fusion 41, 455 (2001)ADSCrossRefGoogle Scholar
  39. 39.
    M. Okabayashi et al., Phys. Plasmas 8, 2071 (2001)ADSCrossRefGoogle Scholar
  40. 40.
    V.D. Pustovitov, Plasma Phys. Control. Fusion 44, 295 (2002)ADSCrossRefGoogle Scholar
  41. 41.
    C.M. Bishop, Plasma Phys. Control. Fusion 31, 1179 (1989)ADSCrossRefGoogle Scholar
  42. 42.
    L. Piron et al., Plasma Phys. Control. Fusion 53, 084004 (2011)ADSCrossRefGoogle Scholar
  43. 43.
    P.R. Brunsell et al., Phys. Rev. Lett. 93, 225001 (2004)ADSCrossRefGoogle Scholar
  44. 44.
    P.R. Brunsell et al., Plasma Phys. Control. Fusion 47, B25 (2005)CrossRefGoogle Scholar
  45. 45.
    M. Cavinato et al., IEEE Transaction of nuclear science 53, 1015 (2006)ADSCrossRefGoogle Scholar
  46. 46.
    P. Zanca et al., Nucl. Fusion 47, 1425 (2007)ADSCrossRefGoogle Scholar
  47. 47.
    K.E.J. Olofsson et al., Plasma Phys. Control. Fusion 53, 084003 (2011)ADSCrossRefGoogle Scholar
  48. 48.
    J.R. Drake, Nucl. Fusion 45, 557 (2005)ADSCrossRefGoogle Scholar
  49. 49.
    K.E.J. Olofsson et al., Plasma Phys. Control. Fusion 52, 104005 (2010)ADSCrossRefGoogle Scholar
  50. 50.
    V. Igochine, Plasma Phys. Control. Fusion 51, 055008 (2009)ADSCrossRefGoogle Scholar
  51. 51.
    T. Bolzonella, Phys. Rev. Lett. 101, 165003 (2008)ADSCrossRefGoogle Scholar
  52. 52.
    Y.Q. Liu, A. Bondeson, Phys. Rev. Lett. 84, 907 (2000)ADSCrossRefGoogle Scholar
  53. 53.
    T.E. Evans et al., Phys. Rev. Lett. 92, 235003 (2004)ADSCrossRefGoogle Scholar
  54. 54.
    W. Suttrop et al., Phys. Rev. Lett. 106, 225004 (2011)ADSCrossRefGoogle Scholar
  55. 55.
    M. Okabayshi, et al., Nucl. Fusion 38, 1607 (1998)Google Scholar
  56. 56.
    V.D. Pustovitov, Plasma Phys. Rep. 27, 195 (2001)Google Scholar
  57. 57.
    V.D. Pustovitov, Phys. Plasmas. 15, 072501 (2008)Google Scholar
  58. 58.
    V.D. Pustovitov, Plasma Phys. Rep. 37, 35 (2011)Google Scholar
  59. 59.
    J. Bialek et al., Phys. Plasmas 8, 2170 (2001)ADSCrossRefGoogle Scholar
  60. 60.
    P.Merkel et al., 2006 21st IAEA Fusion Energy Conf. 2006 (Chengdu, China)(Vienna: IAEA) TH/P3-8Google Scholar
  61. 61.
    E. Strumberger et al., Phys. Plasmas 15, 056110 (2008)Google Scholar
  62. 62.
    R. Albanese et al., IEEE Trans. Magn. 44, 1654 (2008)ADSCrossRefGoogle Scholar
  63. 63.
    A. Portone et al., Plasma Phys. Control. Fusion 50, 085004 (2008)ADSCrossRefGoogle Scholar
  64. 64.
    F. Villone et al., Phys. Rev. Lett. 100, 255005 (2008)ADSCrossRefGoogle Scholar
  65. 65.
    F. Villone et al., Nucl. Fusion 50, 125011 (2010)ADSCrossRefGoogle Scholar
  66. 66.
    V.D. Pustovitov, Pl. Phys. Rep. 38, 697 (2012)CrossRefGoogle Scholar
  67. 67.
    F. Villone, V.D. Pustovitov, Phys. Lett. A 377, 2780 (2013)ADSCrossRefGoogle Scholar
  68. 68.
    V.D. Pustovitov, Nucl. Fusion 53, 033001 (2013)ADSCrossRefGoogle Scholar
  69. 69.
    V.D. Pustovitov, Phys. Plasmas 19, 062503 (2012)ADSCrossRefGoogle Scholar
  70. 70.
    V.D. Pustovitov, Plasma Phys. Control. Fusion 50, 105001 (2008)ADSCrossRefGoogle Scholar
  71. 71.
    Y. Liu, F. Villone, Plasma Phys. Control. Fusion 51, 115008 (2009)ADSCrossRefGoogle Scholar
  72. 72.
    G.W. Hammet, F.W. Perkins, Phys. Rev. Lett. 64, 3019 (1990)ADSCrossRefGoogle Scholar
  73. 73.
    A. Bondeson, M.S. Chu, Phys. Plasmas 3, 3013 (1996)ADSCrossRefGoogle Scholar
  74. 74.
    E.J. Strait et al., Phys. Plasmas 14, 056101 (2007)ADSCrossRefGoogle Scholar
  75. 75.
    H. Reimerders et. al., Phys. Rev. Lett. 98, 055001 (2007)Google Scholar
  76. 76.
    M. Takechi et al., Phys. Rev. Lett. 98, 055002 (2007)ADSCrossRefGoogle Scholar
  77. 77.
    S.A. Sabbagh et al., Phys. Rev. Lett. 97, 045004 (2006)ADSCrossRefGoogle Scholar
  78. 78.
    S.W. Haney, J.P. Friedberg, Phys. Fluids B 1, 1637 (1989)ADSCrossRefGoogle Scholar
  79. 79.
    B. Hu, R. Betti, Phys. Rev. Lett. 93, 105002 (2004)ADSCrossRefGoogle Scholar
  80. 80.
    B. Hu et al., Phys. Plasmas 12, 057301 (2005)ADSCrossRefGoogle Scholar
  81. 81.
    Y. Liu et al., Phys. Plasmas 15, 112503 (2008)ADSCrossRefGoogle Scholar
  82. 82.
    B.N. Breizman et al., Phys. Plasmas 5, 2326 (1998)MathSciNetADSCrossRefGoogle Scholar
  83. 83.
    Y. Liu et al., Phys. Plasmas 15, 092505 (2008)ADSCrossRefGoogle Scholar
  84. 84.
    H. Reimerdes et al., Phys. Rev. Lett. 106, 215002 (2011)ADSCrossRefGoogle Scholar
  85. 85.
    S.A. Sabbagh et al., Nucl. Fusion 50, 025020 (2010)ADSCrossRefGoogle Scholar
  86. 86.
    M. Shimada et al., Nucl. Fusion 47, S1 (2007)MathSciNetADSCrossRefGoogle Scholar
  87. 87.
    T.C. Hender et al., Nucl. Fusion 47, S128 (2007)ADSCrossRefGoogle Scholar
  88. 88.
    C. Gormezano et al., Nucl. Fusion 47, S285 (2007)ADSCrossRefGoogle Scholar
  89. 89.
    V. Mukhovatov et al., Nucl. Fusion 47, S404–S413 (2007)ADSCrossRefGoogle Scholar
  90. 90.
    J. Garcia et al., Nucl. Fusion 48, 075007 (2008)ADSCrossRefGoogle Scholar
  91. 91.
    W.M Stacey. in Front Matter, in Fusion: An Introduction to the Physics and Technology of Magnetic Confinement Fusion, 2nd edn. (Wiley, New York, 2010)Google Scholar
  92. 92.
    I.T. Chapman et al., Fusion Engin. and Design 86, 141 (2011)CrossRefGoogle Scholar
  93. 93.
    H. Zohm, Fusion Sci. Technol. 58, 613 (2010)Google Scholar
  94. 94.
    Y. Liu, Nucl. Fusion 49, 035004 (2009)ADSCrossRefGoogle Scholar
  95. 95.
    A. Polevoi et all, in Fusion Energy 2002 (Proc. 19th Int. Conf. Lyon, 2002) (Vienna: IAEA) CD-ROM file and http://www.iaea.org/programmes/ripc/physics/fec2002/html/fec2002.htm
  96. 96.
    Y. Liu et all, in Fusion Energy 2010 (Proc. 23rd Int. Conf. Daejeon, 2010) (Vienna: IAEA) CD-ROM file [TH/P9-26] and, http://www-naweb.iaea.org/napc/physics/FEC/FEC2010/html/index.htm
  97. 97.
    Y. Liu, Nucl. Fusion 50, 095008 (2010)ADSCrossRefGoogle Scholar
  98. 98.
    I.T. Chapman et al., Phys. Plasmas 19, 052502 (2012)ADSCrossRefGoogle Scholar
  99. 99.
    A.H. Reiman, D. Monticello, Phys. Fluids B 3, 2230 (1991)ADSCrossRefGoogle Scholar
  100. 100.
    M.P. Gryaznevich et al., Plasma Phys. Control. Fusion 50, 124030 (2008)ADSCrossRefGoogle Scholar
  101. 101.
    A.M. Garofalo, R.J. La Haye, J.T. Scoville, Nucl. Fusion 42, 1335 (2002)ADSCrossRefGoogle Scholar
  102. 102.
    M.P. Gryaznevich et al., Nucl. Fusion 52, 083018 (2012)ADSCrossRefGoogle Scholar
  103. 103.
    V. Igochine et al., 40th EPS Conference on Plasma Physics, 2013, P5.147Google Scholar
  104. 104.
    Y. Liu et al., Plasma Phys. Control. Fusion 51, 115005 (2009)ADSCrossRefGoogle Scholar
  105. 105.
    Y. Liu, Phys. Plasmas 17, 072510 (2010)ADSCrossRefGoogle Scholar
  106. 106.
    H. Reimerdes, Nucl. Fusion 45, 368 (2005)ADSCrossRefGoogle Scholar
  107. 107.
    H. Reimerdes et al., Phys. Rev. Lett. 93, 135002 (2004)ADSCrossRefGoogle Scholar
  108. 108.
    G. Matsunaga et al., Phys. Rev. Lett. 103, 045001 (2009)ADSCrossRefGoogle Scholar
  109. 109.
    M. Okabayashi et al., Phys. Plasmas 18, 056112 (2011)ADSCrossRefGoogle Scholar
  110. 110.
    T.C. Luce, Phys. Plasmas 18, 030501 (2011)ADSCrossRefGoogle Scholar
  111. 111.
    D.P. Brennan et al., Phys. Plasmas 10, 1643 (2003)ADSCrossRefGoogle Scholar
  112. 112.
    S.A. Sabbagh et al., Nucl. Fusion 50, 025020 (2010)ADSCrossRefGoogle Scholar
  113. 113.
    M. Holzl et al., Journal of physics. Conference Series 401, 012010 (2012)CrossRefGoogle Scholar
  114. 114.
    V. Igochine et al., in Proceedings of the 35th EPS Conference on Plasma Physics, Hersonissos, 2008, ECA 32D, P2.066 and, http://epsppd.epfl.ch/Hersonissos/html/i_index.htm
  115. 115.
    T. Boltzonella et al., in Fusion Energy 2010 (Proc. 23rd Int. Conf. Daejeon, 2010) (Vienna: IAEA) CD-ROM file [EXS/P5-01] and, http://www-pub.iaea.org/mtcd/meetings/cn180_papers.asp
  116. 116.
    T. Boltzonella et al., 37th EPS Conference on Plasma Physics, Dublin, Ireland, 21 - 25 June, 2010, P2.176, http://ocs.ciemat.es/EPS2010PAP/html/author.html
  117. 117.
    D. Yadikin, P.R. Brunsell, J.R. Drake, Plasma Phys. Control. Fusion 48, 1 (2006)ADSCrossRefGoogle Scholar
  118. 118.
    D.J. Ward et al., in Fusion Energy 2000 (Proc. 18th Int. Conf. Sorrento, 2000) (Vienna: IAEA) CD-ROM file FT/P2-20 and, http://www.iaea.org/programmes/ripc/physics/fec2000/html/node1.htm

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Max Planck Institute for Plasma PhysicsGarchingGermany

Personalised recommendations