Linear stability analysis of collisionless reconnection in the presence of an equilibrium flow aligned with the guide field

  • Emanuele TassiEmail author
  • Daniela Grasso
  • Luca Comisso
Regular Article


The influence of a velocity jet, directed along a magnetic guide field, on the linear evolution of collisionless reconnection is investigated both analytically and numerically. The analysis covers both the small and large Δ′ regimes, with Δ′ indicating the standard tearing stability parameter, and is carried out, in slab geometry, by means of a reduced four-field model for magnetic reconnection accounting for two-fluid effects. Analytical dispersion relations are derived in both regimes and their predictions on the growth rates are tested against numerical simulations. In both regimes the presence of the flow is shown to have a stabilizing effect, with growth rates decreasing when increasing the amplitude of the equilibrium flow. The analytical results predict that a decrease in the growth rate could be obtained also by reducing the characteristic width of the equilibrium flow profile. Such stabilizing effects appear to be stronger in the small Δ′ regime. A very good quantitative agreement is found between the analytical predictions and the numerical results. As a complement to the analysis, we also consider, in the small Δ′ regime, the dispersion relation in the absence of equilibrium flow, which extends a previously derived dispersion relation by including a corrective term due to plasma parallel compressibility. It is shown that such correction can have a stabilizing effect and yields a better agreement with the numerical results.


Plasma Physics 


  1. 1.
    A.Y. Aydemir, Phys. Rev. Lett. 98, 225002 (2007) ADSCrossRefGoogle Scholar
  2. 2.
    Y. Lin, J.E. Rice, S.J. Wukitch, M.J. Greenwald, A.E. Hubbard, A. Ince-Cushman, L. Lin, M. Porkolab, M.L. Reinke, N. Tsujii, Phys. Rev. Lett. 101, 235002 (2008) ADSCrossRefGoogle Scholar
  3. 3.
    J. Wang, M.W. Dunlop, Z.Y. Pu, X.Z. Zhou, X.G. Zhang, Y. Wei, S.Y. Fu, C.J. Xiao, A. Fazakerley, H. Laakso, M.G.G.T. Taylor, Y. Bogdanova, F. Pitout, J. Davies, Q.G. Zong, C. Shen, Z.X. Liu, C. Carr, C. Perry, H. Rème, I. Dandouras, P. Escoubet, C.J. Owen, Geophys. Res. Lett. 34, L03106 (2007) ADSGoogle Scholar
  4. 4.
    I. Hofmann, Plasma Phys. 17, 143 (1975) ADSCrossRefGoogle Scholar
  5. 5.
    G. Einaudi, F. Rubini, Phys. Fluids B 29, 2563 (1986) ADSCrossRefzbMATHGoogle Scholar
  6. 6.
    R.B. Paris, W.N.-C. Sy, Phys. Fluids 26, 2966 (1983) ADSCrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    X.L. Chen, P.J. Morrison, Phys. Fluids B 2, 495 (1990) ADSCrossRefMathSciNetGoogle Scholar
  8. 8.
    L. Ofman, X.L. Chen, P.J. Morrison, R.S. Steinolfson, Phys. Fluids B 3, 921 (1991) CrossRefGoogle Scholar
  9. 9.
    M. Faganello, F. Pegoraro, F. Califano, L. Marradi, Phys. Plasmas 17, 062102 (2010) ADSCrossRefGoogle Scholar
  10. 10.
    S.V. Bulanov, S.I. Syrovatskii, J. Sakai, J. Exp. Theor. Phys. Lett. 28, 177 (1979) Google Scholar
  11. 11.
    K.P. Wessen, M. Persson, J. Plasma Phys. 45, 267 (1991) ADSCrossRefGoogle Scholar
  12. 12.
    D. Chandra, A. Sen, P. Kaw, Nucl. Fusion 47, 1238 (2007) ADSCrossRefGoogle Scholar
  13. 13.
    J. Wang, X. Wang, C. Xiao, Phys. Lett. A 372, 4614 (2008) ADSCrossRefzbMATHGoogle Scholar
  14. 14.
    J. Wang, C. Xiao, X. Wang, Phys. Plasmas 19, 032905 (2012) ADSCrossRefGoogle Scholar
  15. 15.
    D. Chandra, A. Sen, P. Kaw, M.P. Bora, S. Kruger, Nucl. Fusion 45, 524 (2005) ADSCrossRefGoogle Scholar
  16. 16.
    A. Sen, D. Chandra, P. Kaw, Nucl. Fusion 53, 053006 (2013) ADSCrossRefGoogle Scholar
  17. 17.
    R. Fitzpatrick, F. Porcelli, Phys. Plasmas 11, 4713 (2004) ADSCrossRefGoogle Scholar
  18. 18.
    R. Fitzpatrick, F. Porcelli, Phys. Plasmas 14, 049902 (2007) ADSCrossRefGoogle Scholar
  19. 19.
    E. Tassi, P.J. Morrison, F.L. Waelbroeck, D. Grasso, Plasma Phys. Control. Fusion 50, 085014 (2008) ADSCrossRefGoogle Scholar
  20. 20.
    G. Ara, B. Basu, B. Coppi, G. Laval, M.N. Rosenbluth, B.V. Waddell, Ann. Phys. 112, 443 (1978) ADSCrossRefGoogle Scholar
  21. 21.
    D. Grasso, M. Ottaviani, F. Porcelli, Nucl. Fusion 42, 1067 (2002) ADSCrossRefGoogle Scholar
  22. 22.
    R. Fitzpatrick, Phys. Plasmas 17, 042101 (2010) ADSCrossRefGoogle Scholar
  23. 23.
    D. Biskamp, E. Schwarz, A. Zeiler, Phys. Plasmas 5, 2485 (1998) ADSCrossRefMathSciNetGoogle Scholar
  24. 24.
    D. Biskamp, Magnetic Reconnection in Plasmas (Cambridge University Press, Cambridge, 2000) Google Scholar
  25. 25.
    R.G. Kleva, P.N. Guzdar, Phys. Plasmas 9, 3013 (2002) ADSCrossRefGoogle Scholar
  26. 26.
    R.G. Kleva, P.N. Guzdar, Phys. Plasmas 9, 2655 (2002) ADSCrossRefGoogle Scholar
  27. 27.
    R.B. White, Rev. Mod. Phys. 58, 183 (1986) ADSCrossRefGoogle Scholar
  28. 28.
    H.P. Furth, J. Killeen, M.N. Rosenbluth, Phys. Fluids 6, 459 (1963) ADSCrossRefGoogle Scholar
  29. 29.
    M.N. Bussac, D. Edery, R. Pellat, J.L. Soule, Phys. Rev. Lett. 40, 1500 (1978) ADSCrossRefGoogle Scholar
  30. 30.
    F. Porcelli, Phys. Rev. Lett. 66, 425 (1991) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Aix-Marseille Université, CNRS, CPT, UMR 7332MarseilleFrance
  2. 2.Université de Toulon, CNRS, CPT, UMR 7332La GardeFrance
  3. 3.Istituto dei Sistemi Complessi-CNR and Politecnico di Torino, Dipartimento EnergiaTorinoItaly

Personalised recommendations