Numerical Modelling of the Magnetohydrodynamic Reconnection Shock Structure at the Terrestrial Magnetopause

The magnetic reconnection process is known to govern the transfer of solar wind plasma into the terrestrial magnetosphere. Numerical simulations were employed to qualitatively analyse the plasma flow and magnetic field across an MHD shock structure separating magnetosheath plasma from plasma in the magnetosphere at the onset as well as for the duration of continuing magnetic reconnection. The one-dimensional time-dependent Riemann problem was re-visited in this numerical study in order to qualitatively analyse the development of the MHD discontinuities for non-viscous and non-resistive conditions and thereby provide further in-sight into the initial development of discontinuities at an arbitrary reconnection site along the terrestrial magnetopause where the resistivity could be considered very small or negligible in comparison to the diffusion region. The two-dimensional steady-state Riemann problem was also numerically solved to obtain the ideal MHD 2D shock structure that is independent of time. The goal of modelling the 2D MHD shock structure was to obtain a greater understanding into the behaviour of the plasma flow and the magnetic field across the MHD discontinuities for ongoing magnetic reconnection conditions that occur at an arbitrary point on the dayside terrestrial magnetopause transition layer in the direction of the sub-solar point towards the cusp. The 1D as well as 2D models were solved by employing a Galerkin method of weighted residuals and a streamline diffusion technique was also employed to linearize the nonlinear ideal MHD equations governing the model. For a symmetric case with uniform plasma parameter conditions and exactly anitparallel magnetic fields in the tangential direction (z) across two equally divided plasma regions in the defined domain, four discontinuities were obtained in the solution for the 1D model as well as the 2D which were a pair of symmetric slow shocks and a pair of symmetric fast shocks. These results are in agreement with solution obtained by Lin & Lee (1993) for a similar 1D Riemann problem with symmetric conditions. On the other hand for an asymmetric case, the same two plasma regions had non-uniform plasma conditions and anitparallel magnetic fields in the tangential direction (z) with different magnitude. Five discontinuities were found to exist in the solution of the 1D as well as the 2D models which were a pair of asymmetric slow shocks, a pair of asymmetric fast shocks and a contact discontinuity. When the results obtained in this study are applied to the Earth's magnetosphere, MHD shocks and the contact discontinuity may be present at the magnetopause-boundary layer region with magnetic reconnection and a non-zero normal (x- direction) component of the magnetic field (in this case Bx= 0.3). Therefore, magnetic reconnection can occur under ideal MHD conditions devoid of resistivity and viscosity at an arbitrary point along the dayside magnetopause transition layer with the formation of five discontinuities about this layer for asymmetric conditions similar to those that are present in the terrestrial magnetosphere.Validerat; 20130220 (ysko