Asymptotic-Preserving scheme for a strongly anisotropic vorticity equation arising in fusion plasma modelling

The electric potential is an essential quantity for the confinement process of tokamak plasmas, with important impact on the performances of fusion reactors. Understanding its evolution in the peripheral region - the part of the plasma interacting with the wall of the device - is of crucial importance, since it governs the boundary conditions for the burning core plasma. The aim of the present paper is to study numerically the evolution of the electric potential in this peripheral plasma region. In particular, we are interested in introducing an efficient Asymptotic-Preserving numerical scheme capable to cope with the strong anisotropy of the problem as well as the non-linear boundary conditions, and this with no huge computational costs. This work constitutes the numerical follow-up of the more mathematical paper by C. Negulescu, A. Nouri, Ph. Ghendrih, Y. Sarazin, "Existence and uniqueness of the electric potential profile in the edge of tokamak plasmas when constrained by the plasma-wall boundary physics".