Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Parallel Simulations of Hall-Mhd Plasmas


Plasma processes such as magnetic reconnection, turbulent regimes or dynamo-generated magnetic fields, are well studied within the framework of one-fluid magnetohydrodynamics (MHD). However, there are processes such as the Hall current, which are not covered by the MHD description. The Hall effect is known to be relevant for the dynamics of several astrophysical plasmas, such as the interstellar medium, the early universe, or the solar wind at 1 AU. While the relevance of Hall currents in magnetic reconnection is intensively being studied (specially in connection with reconnection events at the Earth’s magnetopause and magnetotail), their role on turbulent regimes or on dynamo mechanisms is mostly unknown. We report results from parallel simulations of the incompressible Hall-MHD equations in 21÷2 and three dimensions to quantitatively investigate the role of Hall currents in different problems, such as magnetic reconnection in 21÷2 dimensions, the dynamo generation of magnetic fields in three-dimensional simulations, or the relaxation to stationary turbulent regimes.

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


  1. Balbus, S. A., and Terquem, C.: 2001, Astrophys. J. 552, 235.

  2. Birn, J. et al.: 2001, J. Geophys. Res. 106, 3715.

  3. Birn, J., and Hesse, M.: 1996, J. Geophys. Res. 101, 15345.

  4. Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A.: 1988, Spectral Methods in Fluid Dynamics, Springer, New York.

  5. Craig, I. J. D., and Watson, P. G.: 2003, Solar Phys. 214, 130.

  6. Dorelli, J. C.: 2003, Phys. Plasmas 10, 3310.

  7. Dorelli, J. C., and Birn, J.: 2003, J. Geophys. Res. 108, 1133.

  8. Ma, Z., and Bhattacharjee, A.: 2001, J. Geophys. Res. 106, 3773.

  9. Mininni, P. D., Gómez, D. O., and Mahajan, S. M.: 2002, Astrophys. J. Lett. 81.

  10. Mininni, P. D., Gómez, D. O., and Mahajan, S. M.: 2003, Astrophys. J. 587, 472.

  11. Mozer, F., Bale, S., and Phan, T. D.: 2002, Phys. Rev. Lett. 89, 015002.

  12. Priest, E. R.: 1984, in: Hones, E. W. (ed.), Magnetic Reconnection in Space and Laboratory Plasmas, Geophys. Monogr. Ser. 30, 63.

  13. Sano, T., and Stone, J. M.: 2002, Astrophys. J. 570, 314.

  14. Smith, D., Ghosh, S., Dmitruk, P., and Matthaeus, W. H.: 2004, Geophys. Res. Lett. 31, L02805.

  15. Sonnerup, B. U. O., et al.: 1981, J. Geophys. Res. 86, 10049.

  16. Tajima, T., Cable, S., Shibata, K., and Kulsrud, R. M.: 1992, Astrophys. J. 390, 309.

  17. Wardle, M., and Ng, C.: 1999, Mon. Not. R.A.S. 303, 239.

  18. Yakovlev, D. G., and Urpin, V. A.: 1980, Astr. Zh. 57, 526.

Download references

Author information

Correspondence to Daniel Gómez.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Gómez, D. Parallel Simulations of Hall-Mhd Plasmas. Space Sci Rev 122, 231–238 (2006). https://doi.org/10.1007/s11214-006-7287-y

Download citation


  • MHD
  • turbulence
  • MHD dynamo
  • magnetic reconnection