MHD Equilibrium with Reversed Current Density and Magnetic Islands Revisited: the Vacuum Vector Potential Calculus

The solution of Grad-Shafranov equation determines the stationary behavior of fu- sion plasma inside a tokamak. To solve the equation it is necessary to know the toroidal current density profile. Recent works show that it is possible to determine a magnetohydrodynamic (MHD) equilibrium with reversed current density (RCD) profiles that presents magnetic islands. In this work we show analytical MHD equilibrium with a RCD profile and analyze the structure of the vacuum vector potential associated with these equilibria using the virtual casing principle.