Current sheet formation near a hyperbolic magnetic neutral line in a variable-density plasma: An exact solution

Current-sheet formation near a hyperbolic magnetic neutral line in the MHD model is investigated. In this model, the magnetic field lines are swept by the plasma flow toward the X-point. Effects of density-variation of the plasma are included. An exact analytic solution is given. This solution exhibits a finite-time singularity that is peculiar to the variable-density plasma case and this finite-time singularity occurs when there is a plasma density build-up near the magnetic neutral line.