Plasma equilibrium evolution at the resistive diffusion timescale

This paper reviews plasma equilibrium evolution codes at the resistive diffusion timescale. The two-dimensional axisymmetric equilibrium equations are given, both for air-transformer and iron-transformer tokamaks, for fixed plasma boundary and for free-boundary cases. A model is written which describes the poloidal field circuits, the penetration of the eddy currents in the vacuum vessel and the diffusion of the pressure and toroidal field profiles inside the plasma. The two-dimensional Grad-Shafranov equilibrium equation is coupled with the set of one-dimensional diffusion equations obtained by averaging the transport equations over the magnetic surfaces. Various numerical methods are presented both for the equilibrium equations (flux coordinates or Eulerian grids, finite differences or finite elements, methods of linearization) and for the diffusion system (finite differences in space, implicit scheme in time). The various methods used to couple these two systems are presented and a general algorithm for such an evolution code is given. Finally detailed formulae are written for a particular discretization of these equilibrium and diffusion equations. (orig.)