Skip to main content
Log in

Kinetic effects on the currents determining the stability of a magnetic island in tokamaks

  • Tokamaks
  • Published:
Plasma Physics Reports Aims and scope Submit manuscript

Abstract

The role of the bootstrap and polarization currents for the stability of neoclassical tearing modes is investigated employing both a drift kinetic and a gyrokinetic approach. The adiabatic response of the ions around the island separatrix implies, for island widths below or around the ion thermal banana width, density flattening for islands rotating at the ion diamagnetic frequency, while for islands rotating at the electron diamagnetic frequency the density is unperturbed and the only contribution to the neoclassical drive arises from electron temperature flattening. As for the polarization current, the full inclusion of finite orbit width effects in the calculation of the potential developing in a rotating island leads to a smoothing of the discontinuous derivatives exhibited by the analytic potential on which the polarization term used in the modeling is based. This leads to a reduction of the polarization-current contribution with respect to the analytic estimate, in line with other studies. Other contributions to the perpendicular ion current, related to the response of the particles around the island separatrix, are found to compete or even dominate the polarization-current term for realistic island rotation frequencies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. H. P. Furth, J. Killeen, and M. N. Rosenbluth, Phys. Fluids 6, 459 (1963).

    Article  ADS  Google Scholar 

  2. P. H. Rutherford, Phys. Fluids 16, 1903 (1973).

    Article  ADS  Google Scholar 

  3. F. L. Waelbroeck, Nucl. Fusion 49, 104025 (2009).

    Article  ADS  Google Scholar 

  4. B. Coppi, Phys. Fluids 8, 2273 (1965).

    Article  ADS  Google Scholar 

  5. J. F. Drake, T. M. J. Antonsen, A. B. Hassam, and N. T. Gladd, Phys. Fluids 26, 2509 (1983).

    Article  ADS  Google Scholar 

  6. B. D. Scott, A. B. Hassam, and J. F. Drake, Phys. Fluids 28, 275 (1985).

    Article  ADS  Google Scholar 

  7. R. D. Hazeltine, D. Dobrott, and T. S. Wang, Phys. Fluids 18, 1778 (1975).

    Article  ADS  Google Scholar 

  8. J. F. Drake and Y. C. Lee, Phys. Fluids 20, 1341 (1977).

    Article  ADS  Google Scholar 

  9. P. H. Rebut and M. Hugon, Plasma Phys. Controlled Fusion 33, 1085 (1991).

    Article  ADS  Google Scholar 

  10. J. W. Connor and H. R. Wilson, Phys. Plasmas 2, 4575 (1995).

    Article  ADS  Google Scholar 

  11. F. L. Waelbroeck, J. W. Connor, and H. R. Wilson, Phys. Rev. Lett. 87, 215003 (2001).

    Article  ADS  Google Scholar 

  12. A. H. Glasser, J. M. Greene, and J. L. Johnson, Phys. Fluids 18, 875 (1975).

    Article  ADS  Google Scholar 

  13. M. Kotschenreuther, R. D. Hazeltine, and P. J. Morrison, Phys. Fluids 28, 294 (1985).

    Article  ADS  Google Scholar 

  14. A. I. Smolyakov, A. Hirose, E. Lazzaro, G. B. Re, and J. D. Callen, Phys. Plasmas 2, 1581 (1995).

    Article  ADS  Google Scholar 

  15. H. R. Wilson, J. W. Connor, R. J. Hastie, and C. C. Hegna, Phys. Plasmas 3, 248 (1996).

    Article  ADS  Google Scholar 

  16. W. X. Qu and J. D. Callen, Plasma Report No. UWPR 85-5 (University of Wisconsin, Madison, WI, 1985).

    Google Scholar 

  17. R. Carrera, R. D. Hazeltine, and M. Kotschenreuther, Phys. Fluids 29, 899 (1986).

    Article  ADS  Google Scholar 

  18. O. Sauter, R. J. La Haye, Z. Chang, D. A. Gates, Y. Kamada, H. Zohm, A. Bondeson, D. Boucher, J. D. Callen, M. S. Chu, T. A. Gianakon, O. Gruber, R. W. Harvey, C. C. Hegna, L. L. Lao, et al., Phys. Plasmas 9, 2051 (2002).

    Article  Google Scholar 

  19. R. J. LaHaye, S. Günter, D. A. Humphreys, J. Lohr, T. C. Luce, M. E. Maraschek, C. C. Petty, R. Prater, J. T. Scoville, and E. J. Strait, Phys. Plasmas 9, 2051 (2002).

    Article  ADS  Google Scholar 

  20. A. Isayama, Y. Kamada, N. Hayashi, T. Suzuki, T. Oikawa, T. Fujita, T. Fukuda, S. Ide, H. Takenaga, and K. Ushigusa, Nucl. Fusion 43, 1272 (2003).

    Article  ADS  Google Scholar 

  21. L. Urso, H. Zohm, A. Isayama, M. Maraschek, and E. Poli, Nucl. Fusion 50, 025010 (2010).

    Article  ADS  Google Scholar 

  22. N. Hayashi, T. Ozeki, K. Hamamatsu, and T. Takizuka, Nucl. Fusion 44, 477 (2004).

    Article  ADS  Google Scholar 

  23. R. J. LaHaye, A. Isayama, and M. Maraschek, Nucl. Fusion 49, 045005 (2009).

    Article  ADS  Google Scholar 

  24. E. Poli, C. Angioni, F. J. Casson, D. Farina, L. Figini, T. P. Goodman, O. Maj, O. Sauter, H. Weber, H. Zohm, G. Saibene, and M. A. Henderson, Nucl. Fusion 55, 013023 (2015).

    Article  ADS  Google Scholar 

  25. V. S. Marchenko, Nucl. Fusion 39, 1541 (1999).

    Article  ADS  Google Scholar 

  26. B. D. Scott and A. B. Hassam, Phys. Fluids 30, 90 (1987).

    Article  ADS  Google Scholar 

  27. A. I. Smolyakov, Plasma Phys. Controlled Fusion 35, 657 (1993).

    Article  ADS  Google Scholar 

  28. R. Fitzpatrick, Phys. Plasmas 2, 825 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  29. E. Poli, A. G. Peeters, A. Bergmann, S. Günter, and S. D. Pinches, Phys. Rev. Lett. 88, 075001 (2002).

    Article  ADS  Google Scholar 

  30. E. Poli, A. G. Peeters, A. Bergmann, S. Günter, and S. D. Pinches, Plasma Phys. Controlled Fusion 45, 71 (2003).

    Article  ADS  Google Scholar 

  31. O. Sauter, R. J. Buttery, R. Felton, T. C. Hender, and F. Howell, Plasma Phys. Controlled Fusion 44, 1999 (2002).

    Article  ADS  Google Scholar 

  32. A. Gude, S. Günter, and S. Sesnic, Nucl. Fusion 39, 127 (1999).

    Article  ADS  Google Scholar 

  33. A. Bergmann, E. Poli, and A. G. Peeters, Phys. Plasmas 16, 092507 (2009).

    Article  ADS  Google Scholar 

  34. M. Siccinio, E. Poli, F. J. Casson, W. A. Hornsby, and A. G. Peeters, Phys. Plasmas 18, 122506 (2011).

    Article  ADS  Google Scholar 

  35. D. Zarzoso, F. J. Casson, W. A. Hornsby, E. Poli, and A. G. Peeters, Phys. Plasmas 22, 022127 (2015).

    Article  ADS  Google Scholar 

  36. D. Zarzoso, W. A. Hornsby, E. Poli, F. J. Casson, A. G. Peeters, and S. Nasr, Nucl. Fusion 55, 113018 (2015).

    Article  ADS  Google Scholar 

  37. W. A. Hornsby, M. Siccinio, A. G. Peeters, E. Poli, A. P. Snodin, F. J. Casson, Y. Camenen, and G. Szepesi, Plasma Phys. Controlled Fusion 53, 054008 (2011).

    Article  ADS  Google Scholar 

  38. A. I. Smolyakov, Sov. J. Plasma Phys. 15, 667 (1989).

    Google Scholar 

  39. H. R. Wilson, M. M Alexander, J. W. Connor, A. M. Edwards, D. Gates, O. Gruber, R. J. Hastie, C. C. Hegna, T. C. Hender, R. J. La Haye, L. L. Lao, A. W. Morris, C. M. Roach, E. J. Strait, T. S. Taylor, et al., Plasma Phys. Controlled Fusion 38, A149 (1996).

    Article  ADS  Google Scholar 

  40. M. Maraschek, S. Günter, and H. Zohm, Plasma Phys. Controlled Fusion 41, L1 (1999).

    Article  ADS  Google Scholar 

  41. A. B. Mikhailovskii, Contrib. Plasma Phys. 43, 125 (2003).

    Article  ADS  Google Scholar 

  42. E. Poli, A. Bergmann, A. G. Peeters, L. Appel, and S. D. Pinches, Nucl. Fusion 45, 384 (2005).

    Article  ADS  Google Scholar 

  43. E. Poli, A. Bergmann, and A. G. Peeters, Phys. Rev. Lett. 94, 205001 (2005).

    Article  ADS  Google Scholar 

  44. M. Siccinio and E. Poli, Plasma Phys. Controlled Fusion 51, 075005 (2009).

    Article  ADS  Google Scholar 

  45. K. Imada and H. R. Wilson, Plasma Phys. Controlled Fusion 51, 105010 (2009).

    Article  ADS  Google Scholar 

  46. A. Bergmann, E. Poli, and A. G. Peeters, Phys. Plasmas 12, 072501 (2005).

    Article  ADS  Google Scholar 

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

    Google Scholar 

  48. S. V. Konovalov, A. B. Mikhailovskii, V. S. Tsypin, and S. E. Sharapov, Doklady Phys. 47, 488 (2002).

    Article  ADS  Google Scholar 

  49. J. W. Connor, F. L. Waelbroeck, and H. R. Wilson, Phys. Plasmas 8, 2835 (2001).

    Article  ADS  Google Scholar 

  50. M. James and H. R. Wilson, Plasma Phys. Controlled Fusion 48, 1647 (2006).

    Article  ADS  Google Scholar 

  51. M. James, H. R. Wilson, and J. W. Connor, Plasma Phys. Controlled Fusion 52, 075008 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  53. C. J. McDevitt and P. H. Diamond, Phys. Plasmas 13, 032302 (2006).

    Article  ADS  Google Scholar 

  54. A. Sen, R. Singh, D. Chandra, P. Kaw, and D. Raju, Nucl. Fusion 49, 115012 (2009).

    Article  ADS  Google Scholar 

  55. M. Yagi, S.-I. Itoh, K. Itoh, M. Azumi, P. H. Diamond, A. Fukuyama, and T. Hayashi, Plasma Fusion Res. 2, 025 (2007).

    Article  ADS  Google Scholar 

  56. F. Militello, F. L. Waelbroeck, R. Fitzpatrick, and W. Horton, Phys. Plasmas 15, 050701 (2008).

    Article  ADS  Google Scholar 

  57. M. Muraglia, O. Agullo, S. Benkadda, X. Garbet, P. Beyer, and A. Sen, Phys. Rev. Lett. 103, 145001 (2009).

    Article  ADS  Google Scholar 

  58. A. Ishizawa and F. L. Waelbroeck, Phys. Plasmas 20, 122301 (2013).

    Article  ADS  Google Scholar 

  59. O. Agullo, M. Muraglia, A. Poyé, S. Benkadda, M. Yagi, X. Garbet, and A. Sen, Phys. Plasmas 21, 092303 (2014).

    Article  ADS  Google Scholar 

  60. E. Poli, A. Bottino, and A. G. Peeters, Nucl. Fusion 49, 075010 (2009).

    Article  ADS  Google Scholar 

  61. E. Poli, A. Bottino, W. A. Hornsby, A. G. Peeters, T. Ribeiro, B. D. Scott, and M. Siccinio, Plasma Phys. Controlled Fusion 52, 124021 (2010).

    Article  ADS  Google Scholar 

  62. W. A. Hornsby, A. G. Peeters, F. J. Casson, Y. Camenen, G. Szepesi, M. Siccinio, and E. Poli, Phys. Plasmas 17, 092301 (2010).

    Article  ADS  Google Scholar 

  63. W. A. Hornsby, P. Migliano, R. Buchholz, L. Kroenert, A. Weikl, A. G. Peeters, D. Zarzoso, E. Poli, and F. J. Casson, Phys. Plasmas 22, 022118 (2015).

    Article  ADS  Google Scholar 

  64. W. A. Hornsby, P. Migliano, R. Buchholz, D. Zarzoso, F. J. Casson, E. Poli, and A. G. Peeters, Plasma Phys. Controlled Fusion 57, 054018 (2015).

    Article  ADS  Google Scholar 

  65. S. D. Pinches, L. C. Appel, J. Candy, S. E. Sharapov, H. L. Berk, D. Borba, B. N. Breizman, T. C. Hender, K. I. Hopcraft, G. T. A. Huysmans, and W. Kerner, Comp. Phys. Commun. 111, 133 (1998).

    Article  ADS  Google Scholar 

  66. A. Bergmann, A. G. Peeters, and S. D. Pinches, Phys. Plasmas 8, 5192 (2001).

    Article  ADS  Google Scholar 

  67. A. G. Peeters, Y. Camenen, F. J. Casson, W. A. Hornsby, A. P. Snodin, D. Strintzi, and G. Szepesi, Comp. Phys. Commun. 180, 2650 (2009).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. Poli.

Additional information

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Poli, E., Bergmann, A., Casson, F.J. et al. Kinetic effects on the currents determining the stability of a magnetic island in tokamaks. Plasma Phys. Rep. 42, 450–464 (2016). https://doi.org/10.1134/S1063780X16050135

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063780X16050135

Navigation