@Article{EAJAM-5-109,
author = {Yuri E. Litvinenko and Liam C. McMahon},
title = {Hall MHD and Electron Inertia Effects in Current Sheet Formation at a Magnetic Neutral Line},
journal = {East Asian Journal on Applied Mathematics},
year = {2018},
volume = {5},
number = {2},
pages = {109--125},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.160914.060315a},
url = {http://global-sci.org/intro/article_detail/eajam/10782.html}
}