Extended MHD equilibrium having boundary layer at plasma-vacuum interface

The conventional MHD equations are known to be invalid when plasma density decreases to a certain level. Since the ion's and electron's inertial lengths are inversely proportional to the square root of density, the Hall and electron-inertia effects should be no longer negligible especially around plasma-vacuum interface. In this study, the cylindrical Z pinch equilibrium is considered as a simplest solution with plasma-vacuum interface and the extended MHD (XMHD) equations, which legitimately include the Hall and electron-inertia terms, are solved. If the collisional effects (resistivity, viscosity and collision with neutrals) are dominant, the solution can be close to the MHD equilibrium. However, at low collisionality, the electron-inertia effect becomes dominant and plays the role of singular perturbation. Namely, the solution of XMHD has a boundary layer that connects the inner MHD solution and the outer vacuum solution, inside of which surface current is generated. The solution is, therefore, different from that of MHD even in the limit of small electron inertia. By considering matching conditions, the equilibrium position of the plasma-vacuum interface can be predicted theoretically.