Current Sheet Formation Near a Hyperbolic Magnetic Neutral Line in a Variable Density Plasma

\textit{Current-sheet formation} near a \textit{hyperbolic} magnetic neutral line has been investigated by including the effects of sweeping and shearing of the magnetic field lines by the plasma flow and \textit{exact} solutions of the MHD equations appropriate for these situations were given by Shivamoggi [1], [2]. The \textit{current-sheet} evolution described by this solution is in agreement with laboratory experiments (Kirii et al [3]). For the case with no \textit{shearing} of the field lines, this solution exhibits a \textit{finite-time} singularity. The \textit{shearing} of the magnetic field lines tends to \textit{impede} the \textit{current-sheet} formation. Investigation of the \textit{integrability} aspects of the system of nonlinearly-coupled differential equations governing these dynamics has been made (Rollins and Shivamoggi [4]) which indicated the possibility of shear-induced chaotic evolution in the dynamical system in question. The investigation is extended to include the effects of density variation of the plasma (Shivamoggi and Rollins [5]). The \textit{current-sheet formation }process is found to \textit{speed up} in the presence of a plasma density \textit{build-up} near the current sheet in agreement with the numerical simulation of Brunnel et al. [6] which described an enhanced reconnected magnetic flux when there is plasma density build up near the magnetic neutral point. This plasma density \textit{build-up} produces a new \textit{finite-time} singularity in the \textit{variable-density} MHD solution.