Journal Article

Hall equilibrium of thin Keplerian discs embedded in mixed poloidal and toroidal magnetic fields

Yuri M. Shtemler, Michael Mond and Günther Rüdiger

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 394, issue 3, pages 1379-1392
Published in print April 2009 | ISSN: 0035-8711
Published online April 2009 | e-ISSN: 1365-2966 | DOI:
Hall equilibrium of thin Keplerian discs embedded in mixed poloidal and toroidal magnetic fields

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Axisymmetric steady-state weakly ionized Hall–magnetohydrodynamic (MHD) Keplerian thin discs are investigated by using asymptotic expansions in the small disc aspect ratio ε. The model incorporates the azimuthal and poloidal components of the magnetic fields in the leading order in ε. The disc structure is described by an appropriate Grad–Shafranov equation for the poloidal flux function ψ that involves two arbitrary functions of ψ for the toroidal and poloidal currents. The flux function is symmetric about the mid-plane and satisfies certain boundary conditions at the near-horizontal disc edges. The boundary conditions model the combined effect of the primordial as well as the dipole-like magnetic fields. An analytical solution for the Hall equilibrium is achieved by further expanding the relevant equations in an additional small parameter δ that is inversely proportional to the Hall parameter. It is thus found that the Hall equilibrium discs fall into two types: Keplerian discs with (i) small (Rd∼δ0) and (ii) large (Rd≳δk, k > 0) radius of the disc. The numerical examples that are presented demonstrate the richness and great variety of magnetic and density configurations that may be achieved under the Hall–MHD equilibrium.

Keywords: plasmas; planetary systems: protoplanetary discs

Journal Article.  7995 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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