Plasma Relaxation in Hall Magnetohydrodynamics

  • Bhimsen K. Shivamoggi
Conference paper
Part of the Astrophysics and Space Science Proceedings book series (ASSSP, volume 33)


Parker’s formulation of isotopological plasma relaxation process in magnetohydrodynamics (MHD) is extended to Hall MHD. The torsion coefficient α in the Hall MHD Beltrami condition turns out now to be proportional to the potential vorticity. The Hall MHD Beltrami condition becomes equivalent to the potential vorticity conservation equation in two-dimensional (2D) hydrodynamics if the Hall MHD Lagrange multiplier β is taken to be proportional to the potential vorticity as well. The winding pattern of the magnetic field lines in Hall MHD then appears to evolve in the same way as potential vorticity lines in 2D hydrodynamics.


Potential Vorticity Magnetic Field Line Whistler Wave Magnetic Reconnection Process Fast Magnetic Reconnection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was a result of my participation at the International Astrophysics Forum, Alpbach, 2011. I am thankful to Professor Eugene Parker for helpful suggestions and giving me access to Ref. [7] prior to publication and Professors Manfred Leubner and Zoltán Vörös for their hospitality.


  1. 1.
    S. Lundquist: Arkiv. Fysik 2, 361, (1950).Google Scholar
  2. 2.
    R. Lust and A. Schluter: Z. Astrophys. 34, 263, (1954).Google Scholar
  3. 3.
    E. R. Priest and T. Forbes: Magnetic Reconnection, Cambridge Univ. Press, (2000).Google Scholar
  4. 4.
    K. Schindler: Physics of Space Plasma Activity, Cambridge Univ. Press, (2007).Google Scholar
  5. 5.
    E. N. Parker: Geophys. Astrophys. Fluid Dyn. 34, 243, (1986).Google Scholar
  6. 6.
    E. N. Parker: Conversations on Electric and Magnetic Fields in the Cosmos, Princeton Univ. Press, Ch. 10, (2007).Google Scholar
  7. 7.
    E. N. Parker: Field line topology and rapid reconnection, in International Astrophysics Forum, Alpbach, (2011).Google Scholar
  8. 8.
    B. U. O. Sonnerup: in Solar System Plasma Physics, Ed. L. J. Lanzerotti, C. F. Kennel and E. N. Parker, North Holland, p. 45, (1979).Google Scholar
  9. 9.
    M. E. Mandt, R. E. Denton and J. F. Drake: Geophys. Res. Lett. 21, 73, (1994).Google Scholar
  10. 10.
    M. J. Lighthill: Phil. Trans. Roy. Soc. (London) A 252, 397, (1960).Google Scholar
  11. 11.
    L. Turner: IEEE Trans. Plasma Sci. PS-14, B49, (1986).Google Scholar
  12. 12.
    B. K. Shivamoggi: Euro. Phys. J. D 64, 404, (2011).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.University of Central FloridaOrlandoUSA

Personalised recommendations