Equilibrium topology for plasmas with reversed current density.

Actually, transition from positive to negative plasma current and quasi-steady-state alternated current (AC) operation have been achieved experimentally without loss of ionization. The large transition times suggest the use of MHD equilibrium to model the intermediate magnetic field configurations for corresponding current density reversals. In the present work we show, by means of Maxwell equations, that the most robust equilibrium for any axisymmetric configuration with reversed current density requires the existence of several nonested families of magnetic surfaces inside the plasma. We also show that the currents inside the nonested families satisfy additive rules restricting the geometry and sizes of the axisymmetric magnetic islands; this is done without restricting the equilibrium through arbitrary functions. Finally, we introduce a local successive approximations method to describe the equilibrium about an arbitrary reversed current density minimum and, consequently, the transition between different nonested topologies is understood in terms of the eccentricity of the toroidal current density level sets.