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Plasma Physics Reports

, Volume 42, Issue 5, pp 495–501 | Cite as

Neoclassical offset toroidal velocity and auxiliary ion heating in tokamaks

  • E. LazzaroEmail author
Tokamaks
  • 45 Downloads

Abstract

In conditions of ideal axisymmetry, for a magnetized plasma in a generic bounded domain, necessarily toroidal, the uniform absorption of external energy (e.g., RF or any isotropic auxiliary heating) cannot give rise to net forces or torques. Experimental evidence on contemporary tokamaks shows that the near central absorption of RF heating power (ICH and ECH) and current drive in presence of MHD activity drives a bulk plasma rotation in the co-I p direction, opposite to the initial one. Also the appearance of classical or neoclassical tearing modes provides a nonlinear magnetic braking that tends to clamp the rotation profile at the q-rational surfaces. The physical origin of the torque associated with P RF absorption could be due the effects of asymmetry in the equilibrium configuration or in power deposition, but here we point out also an effect of the response of the so-called neoclassical offset velocity to the power dependent heat flow increment. The neoclassical toroidal viscosity due to internal magnetic kink or tearing modes tends to relax the plasma rotation to this asymptotic speed, which in absence of auxiliary heating is of the order of the ion diamagnetic velocity. It can be shown by kinetic and fluid calculations, that the absorption of auxiliary power by ions modifies this offset proportionally to the injected power thereby forcing the plasma rotation in a direction opposite to the initial, to large values. The problem is discussed in the frame of the theoretical models of neoclassical toroidal viscosity.

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References

  1. 1.
    Y. Lin, J. E. Rice, S. J. Wukitch, M. J. Greenwald, A. E. Hubbard, A. Ince-Cushman, L. Lin, E. S. Marmar, M. Porkolab, M. L. Reinke, N. Tsujii, J. C. Wright, Phys. Plasmas 16, 05610 (2009).Google Scholar
  2. 2.
    C. L. Fiore, D. R. Ernst, Y. A. Podpaly, D. Mikkelsen, N. T. Howard, J. Lee, M. L. Reinke, J. E. Rice, J. W. Hughes, Y. Ma, W. L. Rowan, and I. Bespamyatno, Phys. Plasmas 19, 056113 (2012).ADSCrossRefGoogle Scholar
  3. 3.
    R. M. McDermott, C. Angioni, R. Dux, A. Gude, T. Puetterich, F. Ryter, G. Tardini, Plasma Phys. Controlled Fusion 53, 035007 (2011).ADSCrossRefGoogle Scholar
  4. 4.
    B. P. Duval, A. Bortolon, A. Karpushov, R. A. Pitts, A. Pochelon, A. Scarabosio, Plasma Phys. Controlled Fusion 49, B195 (2007).ADSCrossRefGoogle Scholar
  5. 5.
    B.P. Duval, A. Bortolon, A. Karpushov, R. A. Pitts, A. Pochelon, O. Sauter, A. Scarabosio, and G. Turri, Phys. Plasmas 15,056113 (2008).ADSCrossRefGoogle Scholar
  6. 6.
    O. Sauter F. Felici, B. P. Duval, L. Federspiel, T. P. Goodman, A. Karpushov, B. Labit, and J. Rossel, in Proceedings of the 23rd IAEA Fusion Energy Conference, Daejeon, 2010, CD-ROM file EXS/P2-17.Google Scholar
  7. 7.
    J. Seol, S. G. Lee, B. H. Park, H. H. Lee, L. Terzolo, K. C. Shaing, K. I. You, G. S. Yun, C. C. Kim, K. D. Lee, W. H. Ko, J. G. Kwak, W. C. Kim, Y. K. Oh, J. Y. Kim, et al., Phys. Rev. Lett. 109, 195003 (2012).ADSCrossRefGoogle Scholar
  8. 8.
    R. M. McDermott, C. Angioni, R. Dux, E. Fable, T. Puetterich, F. Ryter, A. Salmi, T. Tala, G. Tardini, E. Viezzer, Plasma Phys. Controlled Fusion 53, 124013 (2011).ADSCrossRefGoogle Scholar
  9. 9.
    E. Lazzaro, S. Nowak, O. Sauter, G. Canal, B. Duval, L. Federspiel, A. N. Karpushov, D. Kim, H. Reimerdes, J. Rossel, D. Testa, and D. Wagner, Nucl. Fusion 55, 093031 (2015).CrossRefGoogle Scholar
  10. 10.
    H. Reimerdes, O. Sauter, T. Goodman, and A. Pochelon, Phys. Rev. Lett. 88, 105005 (2002).ADSCrossRefGoogle Scholar
  11. 11.
    Y. Camenen, A. G. Peeters, C. Angioni, F. J. Casson, W. A. Hornsby, A. P. Snodin, and D. Strintzi, Phys. Plasmas 16, 062501 (2009).ADSCrossRefGoogle Scholar
  12. 12.
    J. J. Martinell, and C. Gutierrez-Tapia, Phys. Plasmas 8, 2808 (2001).ADSCrossRefGoogle Scholar
  13. 13.
    De Bock, PhD Thesis (Eindhoven, Technische Universiteit Eindhoven, 2007).Google Scholar
  14. 14.
    J. D. Callen, W. X. Qu, K. D. Siebert, B. A. Carreras, K. C. Shaing, and D. A. Spong, in Proceedings of the 11th IAEA International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Kyoto, 1986 (IAEA, Vienna, 1987), Vol. 2, p. 157.Google Scholar
  15. 15.
    A. B. Mikhailovskii, Contrib. Plasma Phys. 43, 125 (2003).ADSCrossRefGoogle Scholar
  16. 16.
    A. B. Mikhailovskii, S. V. Konovalov, D. Pustovitov, and V. S. Tsypin, Phys. Plasmas 7, 2530 (2000).ADSCrossRefGoogle Scholar
  17. 17.
    A. B. Mikhailovskii, Phys. Lett. A 198, 131 (1995).ADSCrossRefGoogle Scholar
  18. 18.
    I. T. Chapman, S. E. Sharapov, G. T. A. Huysmans, and A. B. Mikhailovskii, Phys. Plasmas 13, 062511 (2006).ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    F. L. Hinton and R. D. Hazeltine, Rev. Mod. Phys. 48, 239 (1976).ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    S. P. Hirschman and D. Sigmar, Nucl. Fusion 18, 917 (1978).ADSCrossRefGoogle Scholar
  21. 21.
    Y. B. Kim, P. H. Diamond, and F. L. J. Groebner, Phys. Fluids B 3, 2050 (1991).ADSCrossRefGoogle Scholar
  22. 22.
    H. Sugama and W. Horton, Phys. Plasmas 4, 2215 (1997).ADSCrossRefGoogle Scholar
  23. 23.
    J. D. Callen, A. J. Cole, and C. C. Hegna, Nucl. Fusion 49, 085021 (2009).ADSCrossRefGoogle Scholar
  24. 24.
    J. D. Callen, C. C. Hegna, and A. J. Cole, Phys. Plasmas 17, 056113 (2010).ADSCrossRefGoogle Scholar
  25. 25.
    K. C. Shaing and S. A. Hokin, Phys. Fluids 26, 2136 (1983).ADSCrossRefGoogle Scholar
  26. 26.
    K. C. Shaing, Phys. Plasmas 10, 1443 (2003).ADSCrossRefGoogle Scholar
  27. 27.
    K. C. Shaing, M. S. Chu, C. T. Hsu, S. A. Sabbagh, J. Ch. Seol, and Y. Sun, Plasma Phys. Controlled Fusion 54, 124033 (2012).ADSCrossRefGoogle Scholar
  28. 28.
    A. I. Smolyakov, A. Hirose, E. Lazzaro, G. Re, and J. D. Callen, Phys. Plasmas 2, 1581 (1995).ADSCrossRefGoogle Scholar
  29. 29.
    E. Lazzaro and P. Zanca, Phys. Plasmas 6, 092504 (2003).Google Scholar
  30. 30.
    W. Zhu, S. A. Sabbagh, R. E. Bell, J. M. Bialek, M. G. Bell, B. P. LeBlanc, S. M. Kaye, F. M. Levinton, J. E. Menard, K. C. Shaing, A. C. Sontag, and H. Yuh, Phys. Rev. Lett. 96, 225002 (2006).ADSCrossRefGoogle Scholar
  31. 31.
    K. C. Shaing, S. Sabbagh, and M. S. Chu, Plasma Phys. Controlled Fusion 51, 035009, (2009).ADSCrossRefGoogle Scholar
  32. 32.
    A. M. Garofalo, K. H. Burrell, J. C. De Boo, J. S. de Grassie, G. L. Jackson, M. Lanctot, H. Reimerdes, M. J. Schaffer, W. M. Solomon, and E. J. Strait, Phys. Rev. Lett. 101, 195005 (2008).ADSCrossRefGoogle Scholar
  33. 33.
    M. Brambilla, Nucl. Fusion 47,175 (2007).ADSCrossRefGoogle Scholar
  34. 34.
    C. C. Hegna and J. D. Callen, Phys. Plasmas 16,112501 (2009).ADSCrossRefGoogle Scholar
  35. 35.
    J. Cole, C. C. Hegna, and J. D. Callen, Phys. Plasmas 15, 056102 (2008).ADSCrossRefGoogle Scholar
  36. 36.
    D. R. Hatch, M. J. Pueschel, F. Jenko, W. M. Nevins, P. W. Terry, and H. Doerk, Phys. Plasmas 20, 012307 (2013).ADSCrossRefGoogle Scholar
  37. 37.
    K. Ida, M. Yoshinuma, H. Tsuchiya, T. Kobayashi, C. Suzuki, M. Yokoyama, A. Shimizu, K. Nagaoka, S. Inagaki, K. Itoh, Nature Comm. 6, 5816 (2015).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Istituto di Fisica del Plasma CNRMilanoItaly

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