Upgrade of the APEC code: Implementation of halo currents and multi-turn coils analyses

The APEC code, implemented for the simulation of the plasma equilibrium and its evolution in presence of 3D passive structures [1] [2], has been upgraded to simulate the effect of the eddy currents in the coils and the halo current in the plasma. The effect of the eddy currents in the coils is implemented considering each coil voltage driven and characterized by its number of turns with its corresponding resistivity. An additional degree of freedom in the finite element regions of the coils is in this case needed corresponding to the electrical current in each turn. The effect of the halo current is instead taken into account by applying both toroidal and poloidal plasma current also outside the last closed surface. The halo width is proportional to a fraction of the plasma core flux. The part of the plasma poloidal halo current intersecting the first wall is injected to the passive structures. Simulation with the upgraded version of APEC have been run for the ITER machine to show the soundness of the new APEC features.