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 fusion 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.