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Plasma Relaxation in Hall Magnetohydrodynamics

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Multi-scale Dynamical Processes in Space and Astrophysical Plasmas

Part of the book series: Astrophysics and Space Science Proceedings ((ASSSP,volume 33))

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Abstract

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.

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Notes

  1. 1.

    In this process, the magnetic field lines extending between the planes z = 0 and L are wrapped around and intermixed by the motion of their foot points on these planes (Parker [5–7]).

  2. 2.

    Equation 24 is sufficient but not necessary to obtain Eq. (25).

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Acknowledgements

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.

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Authors and Affiliations

  1. University of Central Florida, Orlando, FL, 32816-1364, USA

    Bhimsen K. Shivamoggi

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  1. Bhimsen K. Shivamoggi
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Correspondence to Bhimsen K. Shivamoggi .

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Editors and Affiliations

  1. , Inst. of Astro- and Particle Physics, University of Innsbruck, Technikerstr. 25, Innsbruck, 6020, Austria

    Manfred P. Leubner

  2. , Inst. of Astro- and Particle Physics, University of Innsbruck, Technikerstr. 25, Innsbruck, 6020, Austria

    Zoltán Vörös

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Shivamoggi, B.K. (2012). Plasma Relaxation in Hall Magnetohydrodynamics. In: Leubner, M., Vörös, Z. (eds) Multi-scale Dynamical Processes in Space and Astrophysical Plasmas. Astrophysics and Space Science Proceedings, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30442-2_9

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  • DOI: https://doi.org/10.1007/978-3-642-30442-2_9

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  • Online ISBN: 978-3-642-30442-2

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