Finite-time singularity formation at a magnetic neutral line in Hall magnetohydrodynamics
Citation
Export citationLitvinenko, Y. E., & McMahon, L. C. (2015). Finite-time singularity formation at a magnetic neutral line in Hall magnetohydrodynamics. Applied Mathematics Letters, 45, 76–80. http://doi.org/10.1016/j.aml.2015.01.012
Permanent Research Commons link: https://hdl.handle.net/10289/9385
Abstract
The formation of a current sheet in a weakly collisional plasma can be modelled as a finite-time singularity solution of magnetohydrodynamic equations. We use an exact self-similar solution to confirm and generalise a previous finding that, in sharp contrast to two-dimensional solutions in standard MHD, a finite-time collapse to a current sheet can occur in Hall MHD. We derive a criterion for the finite-time singularity in terms of initial conditions, and we use an intermediate asymptotic solution for the evolution of an axial magnetic field to obtain a general expression for the singularity formation time. We illustrate the analytical results by numerical solutions.
Date
2015Type
Publisher
Elsevier Ltd
Rights
This is an author’s accepted version of an article published in the journal: Applied Mathematics Letters. ©2015 Elsevier Ltd.