Application of extended magnetohydrodynamic model to plasma-vacuum systems

It is well-known that the magnetohydrodynamic (MHD) equations are derived from the two-fluid equations by assuming quasi-neutrality and neglecting the Hall and electron-inertia effects. This MHD approximation is invalid, for instance, when plasma density becomes extremely low and Alfven velocity approaches infinity. The plasma-vacuum boundary is therefore difficult to treat within the framework of standard MHD. This problem is attempted to be resolved by using extended MHD (XMHD) model that include Hall terms and electron inertia. Although the electron inertial length is often negligible in plasma region, it is inversely proportional to the square root of density and, hence, electron inertia becomes the most dominant in vacuum region. By introducing electron viscosity as well and imposing physically appropriate boundary conditions, the whole plasma-vacuum system can be governed by the XMHD equations. Existence of cylindrical plasma equilibria surrounded by vacuum magnetic field and a conducting wall are investigated by solving the XMHD equations. Numerical schemes needed for XMHD simulation are also presented and demonstrated.