Introducing electromagnetic effects in Soledge3X

In the pedestal region, electromagnetic effects affect the evolution of micro-instabilities and plasma turbulence. The transport code Soledge3X developed by the CEA offers an efficient framework for turbulent 3D simulation on an electrostatic model with a fixed magnetic field. The physical accuracy of the model is improved with electromagnetic induction, driven by the local value of the parallel component of the electromagnetic vector potential $A_{\parallel }$, known from Ampère's law. It is solved implicitly in a coupled system with the vorticity equation on the electric potential $\Phi$. The consequence is a basic electromagnetic behavior in the form of shear Alfvén waves. A finite electron mass prevents unphysical speeds but requires solving for the time evolution of the parallel current density $j_{\parallel }$ in the generalized Ohm's law. This term can be analytically included with little computational overhead in the system on $\Phi$ and $A_{\parallel }$ and improves its numerical condition, facilitating the iterative solving procedure. Simulations on a periodic slab case let us observe the predicted bifurcation of the wave propagation speed between the Alfvén wave and the electron thermal wave speeds for varying perpendicular wavenumbers. The first results on a circular geometry with a limiter attest to the feasibility of turbulent electromagnetic scenarios.