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

## TL;DR

This paper develops an efficient asymptotic-preserving numerical scheme to accurately simulate the evolution of electric potential in the highly anisotropic peripheral region of tokamak plasmas, crucial for fusion reactor performance.

## Contribution

It introduces a novel asymptotic-preserving method tailored for strongly anisotropic vorticity equations in plasma physics, addressing computational challenges without high costs.

## Key findings

- Successfully handles strong anisotropy and non-linear boundary conditions
- Maintains accuracy across different asymptotic regimes
- Reduces computational costs compared to traditional methods

## Abstract

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".