Year: 2015
East Asian Journal on Applied Mathematics, Vol. 5 (2015), Iss. 2 : pp. 109–125
Abstract
An exact self-similar solution is used to investigate current sheet formation at a magnetic neutral line in incompressible Hall magnetohydrodynamics. The collapse to a current sheet is modelled as a finite-time singularity in the solution for electric current density at the neutral line. We establish that a finite-time collapse to the current sheet can occur in Hall magnetohydrodynamics, and we find a criterion for the finite-time singularity in terms of the initial conditions. We derive an asymptotic solution for the singularity formation and a formula for the singularity formation time. The analytical results are illustrated by numerical solutions, and we also investigate an alternative similarity reduction. Finally, we generalise our solution to incorporate resistive, viscous and electron inertia terms.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.160914.060315a
East Asian Journal on Applied Mathematics, Vol. 5 (2015), Iss. 2 : pp. 109–125
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Finite-time singularities Hall MHD magnetic reconnection current sheet formation.