An electromagnetic model in SOLEDGE3X for edge plasma turbulence simulations in tokamaks

Even small fluctuations in the magnetic field are known to impact edge plasma turbulence and transport properties in magnetic confinement fusion devices. Magnetic induction modifies the parallel electric field, and as such, it impacts the parallel current in Ohm’s law. In addition, magnetic fluctuations can induce geometrical and topological changes in the magnetic field structure, leading to parallel transport across the equilibrium magnetic surfaces. This paper presents the new drift-reduced fluid electromagnetic model implemented in SOLEDGE3X [Bufferand et al., Nuc. Fus. 2021]. Based on a domain decomposition, a specific numerical scheme is proposed using conservative second-order finite volumes associated with a semi-implicit time advancement. The coupling between the parallel current $j_{\parallel }$ and the parallel electromagnetic potential $A_{\parallel }$ in Ohm’s and Ampere’s laws is treated using a new toroidally and poloidally staggered grid. While adding $A_{\parallel }$ doubles the size of the vorticity operator to be inverted, numerical tests show that the inclusion of the finite mass of the electrons in the new model acts as an upper limit on the parallel diffusion coefficient, thus improving the conditioning of the matrix at high plasma temperatures when the parallel resistivity ${\eta }_{\parallel }$ approaches zero. The changes in the algorithm are verified using the method of manufactured solutions. The implementation is first validated with respect to theoretical linear stability results, recovering the transition from Alfvén to thermal electron waves as the perpendicular wavenumber increased. Comparisons with available results in the literature show a qualitative agreement on a single blob propagation in a limited slab geometry. The first 3D simulations of plasma edge turbulence in TCV demonstrate the capability of the new solver to handle realistic tokamak configurations. The explicit-implicit time integration scheme enables one to compare electrostatic and electromagnetic effects using the same solver, with or without electron inertia and magnetic flutter. This ability opens the way to a better understanding of the impact of the electrostatic and electromagnetic mechanisms on the transport and turbulence properties in realistic tokamak configurations.