The self-consistent equilibrium and diffusion code sced

Abstract

The SCED code solves the equilibrium equations for a Tokamak axisymmetric configuration and the plasma diffusion equations. The equilibrium system takes into account the presence of a magnetic circuit made of iron, the currents in the poloidal coils and the plasma pressure and toroidal field profiles. The plasma boundary is a free boundary defined by its contact with a limiter. A variational formulation of the problem is written and the equations of the poloidal flux ψ are solved by a finite element method; the Picard and the Newton algorithms are tested for the treatment of the non-linearities and compared on TFR and JET equilibrium configurations. The variation of the plasma position with respect to the currents in the coils is then studied by a continuation method and the link between the convergence of the Picard method and the stability of the plasma motions is proved. The evolution problem takes into account the induction of the primary coils and the penetration of the eddy currents in the vacuum vessel. The 2D diffusion equations for the electronic and ionic densities and temperatures and for the poloidal flux are written in terms of the toroidal flux by averaging over the magnetic surfaces. These equations are solved by an implicit scheme in time and by a finite difference scheme in space; the non-linearities are treated by the Newton method. The coupling between the equilibrium system and the diffusion equations enables one to follow the evolution of the plasma boundary. The study of the plasma motions in TFR, in the presence or absence of a feedback system, has been performed with this code and compared with the experimental observations.