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Hall MHD and Electron Inertia Effects in Current Sheet Formation at a Magnetic Neutral Line

Published online by Cambridge University Press:  28 May 2015

Yuri E. Litvinenko  and
Liam C. McMahon
Yuri E. Litvinenko
Affiliation:
Department of Mathematics, University of Waikato, Private Bag 3105, Hamilton, New Zealand
Liam C. McMahon*
Affiliation:
Department of Mathematics, University of Waikato, Private Bag 3105, Hamilton, New Zealand
*
*Corresponding author. Email address: lcm21@students.waikato.ac.nz (L. C. McMahon)
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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.

Keywords

76W0585A30Finite-time singularitiesHall MHDmagnetic reconnectioncurrent sheet formation
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 5 , Issue 2 , May 2015 , pp. 109 - 125
Copyright
Copyright © Global-Science Press 2015 

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