Skip to main content
SpringerLink
Log in

A Multi Water Bag model of drift kinetic electron plasma

  • Regular Article
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

A Multi Water Bag model is proposed for describing drift kinetic plasmas in a magnetized cylindrical geometry, relevant for various experimental devices, solar wind modeling... The Multi Water Bag (MWB) model is adapted to the description of a plasma with kinetic electrons as well as an arbitrary number of kinetic ions. This allows to describe the kinetic dynamics of the electrons, making possible the study of electron temperature gradient (ETG) modes, in addition to the effects of non adiabatic electrons on the ion temperature gradient (ITG) modes, that are of prime importance in the magnetized plasmas micro-turbulence [X. Garbet, Y. Idomura, L. Villard, T.H. Watanabe, Nucl. Fusion 50, 043002 (2010); J.A. Krommes, Ann. Rev. Fluid Mech. 44, 175 (2012)]. The MWB model is shown to link kinetic and fluid descriptions, depending on the number of bags considered. Linear stability of the ETG modes is presented and compared to the existing results regarding cylindrical ITG modes [P. Morel, E. Gravier, N. Besse, R. Klein, A. Ghizzo, P. Bertrand, W. Garbet, Ph. Ghendrih, V. Grandgirard, Y. Sarazin, Phys. Plasmas 14, 112109 (2007)].

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. X. Garbet, Y. Idomura, L. Villard, T.H. Watanabe, Nucl. Fusion 50, 043002 (2010)

    Article  ADS  Google Scholar 

  2. J.A. Krommes, Ann. Rev. Fluid Mech. 44, 175 (2012)

    Article  MathSciNet  ADS  Google Scholar 

  3. P. Morel, E. Gravier, N. Besse, R. Klein, A. Ghizzo, P. Bertrand, W. Garbet, Ph. Ghendrih, V. Grandgirard, Y. Sarazin, Phys. Plasmas 14, 112109 (2007)

    Article  ADS  Google Scholar 

  4. T. Görler, F. Jenko, Phys. Rev. Lett. 100, 185002 (2008)

    Article  ADS  Google Scholar 

  5. Z. Lin, T.S. Hahm, W.W. Lee, W.M. Tang, R.B. White, Science 281, 1835 (1998)

    Article  ADS  Google Scholar 

  6. P.H. Diamond, S.-I. Itoh, K. Itoh, T.S. Hahm, Plasma Phys. Control. Fusion 47, R35 (2005)

    Article  ADS  Google Scholar 

  7. T. Estrada, T. Happel, C. Hidalgo, E. Ascasíbar, E. Blanco, Europhys. Lett. 92, 35001 (2010)

    Article  ADS  Google Scholar 

  8. V. Berionni, Ö.D. Gürcan, Phys. Plasmas 18, 112301 (2011)

    Article  ADS  Google Scholar 

  9. P. Morel, V. Berionni, Ö.D. Gürcan, Plasma Phys. Control. Fusion 56, 015002 (2014)

    Article  ADS  Google Scholar 

  10. W. Horton, B.G. Hong, W.M. Tang, Phys. Fluids 31, 2971 (1988)

    Article  ADS  MATH  Google Scholar 

  11. B.W. Stallard et al., Phys. Plasmas 6, 1978 (1999)

    Article  ADS  Google Scholar 

  12. W. Horton, P. Zhu, G.T. Hoang, T. Aniel, M. Ottaviani, X. Garbet, Phys. Plasmas 7, 1494 (2000)

    Article  ADS  Google Scholar 

  13. F. Jenko, W. Dorland, M. Kotschenreuther, B.N. Rogers, Phys. Plasmas 7, 1904 (2000)

    Article  ADS  Google Scholar 

  14. F. Jenko, W. Dorland, G.W. Hammett, Phys. Plasmas 8, 4096 (2001)

    Article  ADS  Google Scholar 

  15. F. Jenko, W. Dorland, Phys. Rev. Lett. 89, 225001 (2002)

    Article  ADS  Google Scholar 

  16. Ö.D. Gürcan, P.H. Diamond, Phys. Plasmas 11, 572 (2004)

    Article  ADS  Google Scholar 

  17. Ö.D. Gürcan, P.H. Diamond, Phys. Plasmas 11, 4973 (2004)

    Article  ADS  Google Scholar 

  18. Z. Lin, L. Chen, F. Zonca, Phys. Plasmas 12, 056125 (2005)

    Article  ADS  Google Scholar 

  19. W.M. Nevins, J. Candy, S. Cowley, T. Dannert, A. Dimits, W. Dorland, C. Estrada-Mila, G.W. Hammett, F. Jenko, M.J. Pueschel, D.E. Shumaker, Phys. Plasmas 13, 122306 (2006)

    Article  ADS  Google Scholar 

  20. A. Brizard, T.S. Hahm, Rev. Mod. Phys. 79, 421 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. D.C. DePackh, J. Electron. Control 13, 417 (1962)

    Article  Google Scholar 

  22. M.R. Feix, F. Hohl, L.D. Staton, in Nonlinear Effects in Plasmas, edited by G. Kalmann, M.R. Feix (Gordon and Breach, New York, 1969), pp. 3–21

  23. P. Bertrand, M.R. Feix, Phys. Lett. A 28, 68 (1968)

    Article  ADS  Google Scholar 

  24. P. Bertrand, M.R. Feix, Phys. Lett. A 29, 489 (1969)

    Article  ADS  Google Scholar 

  25. H.L. Berk, K.V. Roberts, in Methods in Computational Physics, edited by B. Alder, S. Fernbach, M. Rotenberg (Academic Press, New York, 1970), Vol. 9, p. 29

  26. N. Besse, P. Bertrand, P. Morel, E. Gravier, Phys. Rev. E 77, 056410 (2008)

    Article  ADS  Google Scholar 

  27. R. Klein, E. Gravier, J.H. Chatenet, N. Besse, P. Bertrand, X. Garbet, Eur. Phys. J. D 62, 413 (2011)

    Article  ADS  Google Scholar 

  28. E. Gravier, R. Klein, P. Morel, N. Besse, P. Bertrand, Phys. Plasmas 15, 122103 (2008)

    Article  ADS  Google Scholar 

  29. E. Gravier, E. Plaut, Phys. Plasmas 20, 042105 (2013)

    Article  ADS  Google Scholar 

  30. G.G. Howes, S.C. Cowley, W. Dorland, G.W. Hammett, E. Quataert, A.A. Schekochihin, Astrophys. J. 651, 590 (2006)

    Article  ADS  Google Scholar 

  31. U. Finzi, Plasma Phys. 14, 327 (1972)

    Article  ADS  Google Scholar 

  32. M.R. Feix, P. Bertrand, A. Ghizzo, in Advances in Kinetic Theory and Computing, Series on Advances in Mathematics and Applied Science, edited by B. Perthame (World Scientific, Singapore, 1994), Vol. 22, pp. 42–82

  33. M. Navet, P. Bertrand, Phys. Lett. A 34, 117 (1971)

    Article  ADS  Google Scholar 

  34. P. Bertrand, Ph.D. thesis, Université de Nancy, France, 1972

  35. P. Bertrand, J.P. Doremus, G. Baumann, M.R. Feix, Phys. Fluids 15, 1275 (1972)

    Article  ADS  Google Scholar 

  36. P. Bertrand, M. Gros, G. Baumann, Phys. Fluids 19, 1183 (1976)

    Article  ADS  Google Scholar 

  37. P.J. Catto, Plasma Phys. 20, 719 (1978)

    Article  ADS  Google Scholar 

  38. R.G. Littlejohn, J. Math. Phys. 23, 742 (1982)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  39. E.A. Frieman, L. Chen, Phys. Fluids 25, 502 (1982)

    Article  ADS  MATH  Google Scholar 

  40. D.H.E. Dubin, J.A. Krommes, C. Oberman, W.W. Lee, Phys. Fluids 26, 3524 (1983)

    Article  ADS  MATH  Google Scholar 

  41. W.W. Lee, Phys. Fluids 26, 556 (1983)

    Article  ADS  MATH  Google Scholar 

  42. T.S. Hahm, Phys. Fluids 31, 2670 (1988)

    Article  ADS  MATH  Google Scholar 

  43. T.S. Hahm, Phys. Plasmas 3, 4658 (1996)

    Article  ADS  Google Scholar 

  44. H. Sugama, Phys. Plasmas 7, 466 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  45. A.J. Brizard, Phys. Plasmas 7, 4816 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  46. A.A. Schekochihin, S.C. Cowley, W. Dorland, G.W. Hammett, G.G. Howes, G.G. Plunk, E. Quataert, T. Tatsuno, Plasma Phys. Control. Fusion 50, 124024 (2008)

    Article  ADS  Google Scholar 

  47. B. Scott, J. Smirnov, Phys. Plasmas 17, 112302 (2010)

    Article  ADS  Google Scholar 

  48. F.I. Parra, P.J. Catto, Phys. Plasmas 17, 056106 (2010)

    Article  ADS  Google Scholar 

  49. M. Gros, P. Bertrand, M.R. Feix, Plasma Phys. 20, 1075 (1978)

    Article  ADS  Google Scholar 

  50. P. Morel, E. Gravier, N. Besse, A. Ghizzo, P. Bertrand, Commun. Nonlinear Sci. Numer. Simul. 13, 11 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  51. Y. Sarazin, V. Grandgirard, G. Dif-Pradalier, X. Garbet, Ph. Ghendrih, Phys. Plasmas 13, 092307 (2006)

    Article  ADS  Google Scholar 

  52. J.L. Peterson, R. Bell, J. Candy, W. Guttenfelder, G.W. Hammett, S.M. Kaye, B. LeBlanc, D.R. Mikkelsen, D.R. Smith, H.Y. Yuh, Phys. Plasmas 19, 056120 (2012)

    Article  ADS  Google Scholar 

  53. D. Coulette, N. Besse, J. Comput. Phys. 248, 1 (2013)

    Article  ADS  Google Scholar 

  54. D. Coulette, N. Besse, Phys. Plasmas 20, 052107 (2013)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. UMR 7648, Laboratoire de Physique des Plasmas, Université Paris-Sud, 91128, Palaiseau, France

    Pierre Morel, Florent Dreydemy Ghiro, Vincent Berionni & Özgür D. Gürcan

  2. UMR 7648, Laboratoire de Physique des Plasmas, CNRS, 91128, Palaiseau, France

    Pierre Morel, Florent Dreydemy Ghiro, Vincent Berionni & Özgür D. Gürcan

  3. UMR 7648, Laboratoire de Physique des Plasmas, École Polytechnique, 91128, Palaiseau, France

    Pierre Morel, Florent Dreydemy Ghiro, Vincent Berionni & Özgür D. Gürcan

  4. UMR 7648, Laboratoire de Physique des Plasmas, Sorbonne Universités, UPMC Université Paris 06, 91128, Palaiseau, France

    Pierre Morel, Florent Dreydemy Ghiro, Vincent Berionni & Özgür D. Gürcan

  5. Inst Jean Lamour, UMR 7198, Université Lorraine, CNRS, 54506, Vandœuvre Les Nancy, France

    David Coulette & Nicolas Besse

Authors
  1. Pierre Morel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Florent Dreydemy Ghiro
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vincent Berionni
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. David Coulette
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Nicolas Besse
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Özgür D. Gürcan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pierre Morel.

Additional information

Contribution to the Topical Issue “Theory and Applications of the Vlasov Equation”, edited by Francesco Pegoraro, Francesco Califano, Giovanni Manfredi and Philip J. Morrison.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Morel, P., Ghiro, F.D., Berionni, V. et al. A Multi Water Bag model of drift kinetic electron plasma. Eur. Phys. J. D 68, 220 (2014). https://doi.org/10.1140/epjd/e2014-50165-8

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/e2014-50165-8

Keywords

Search

Navigation