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

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

Apr 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009mnras.394.1379s&link_type=abstract

Monthly Notices of the Royal Astronomical Society, Volume 394, Issue 3, pp. 1379-1392.

Astronomy and Astrophysics

Astronomy

7

Plasmas, Planetary Systems: Protoplanetary Discs

Scientific paper

Axisymmetric steady-state weakly ionized Hall-magnetohydrodynamic (MHD) Keplerian thin discs are investigated by using asymptotic expansions in the small disc aspect ratio ɛ. The model incorporates the azimuthal and poloidal components of the magnetic fields in the leading order in ɛ. 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 >~ δ-k, 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.

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