Numerical simulation of tokamak plasma equilibrium evolution

Abstract

This paper focuses on the numerical methods recently developed in order to simulate the time evolution of a tokamak plasma equilibrium at the resistive diffusion time scale. Starting from the method proposed by Heumann in 2021 for the coupling of magnetic equilibrium and current diffusion, we introduce a new space discretization for the poloidal flux using coupled $C^0$ and $C^1$ finite elements. This, together with the use of cubic spline functions to represent the poloidal current function in the resistive diffusion equation, enables to restrain numerical oscillations which can occur with the original method. In order to compute consistently the plasma resistivity and the non-inductive bootstrap current terms needed in the resistive diffusion equation we add to the model an evolution equation for electron temperature in the plasma. It is also used to evolve the pressure term in the simulation. These numerical methods are implemented in the plasma equilibrium code NICE. A free plasma displacement is simulated and comparison with experimental results from the WEST tokamak are used to validate the simulation. The code is also coupled to a magnetic feedback controller making it possible to simulate a prescribed plasma scenario. The results for an X-point formation scenario in the WEST tokamak are presented as an illustration of the efficiency of the developed numerical methods.