Litvinenko, 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: http://hdl.handle.net/10289/9385
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.
This is an author’s accepted version of an article published in the journal: Applied Mathematics Letters. ©2015 Elsevier Ltd.