arrow
Volume 5, Issue 2
Hall MHD and Electron Inertia Effects in Current Sheet Formation at a Magnetic Neutral Line

Yuri E. Litvinenko & Liam C. McMahon

East Asian J. Appl. Math., 5 (2015), pp. 109-125.

Published online: 2018-02

Export citation
  • 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.

  • AMS Subject Headings

76W05, 85A30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{EAJAM-5-109, author = {}, 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 = {

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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.160914.060315a}, url = {http://global-sci.org/intro/article_detail/eajam/10782.html} }
TY - JOUR T1 - Hall MHD and Electron Inertia Effects in Current Sheet Formation at a Magnetic Neutral Line JO - East Asian Journal on Applied Mathematics VL - 2 SP - 109 EP - 125 PY - 2018 DA - 2018/02 SN - 5 DO - http://doi.org/10.4208/eajam.160914.060315a UR - https://global-sci.org/intro/article_detail/eajam/10782.html KW - Finite-time singularities, Hall MHD, magnetic reconnection, current sheet formation. AB -

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.

Yuri E. Litvinenko & Liam C. McMahon. (1970). Hall MHD and Electron Inertia Effects in Current Sheet Formation at a Magnetic Neutral Line. East Asian Journal on Applied Mathematics. 5 (2). 109-125. doi:10.4208/eajam.160914.060315a
Copy to clipboard
The citation has been copied to your clipboard