Multiscale numerical methods for isothermal fluid models of confined plasmas

TL;DR

This work develops an asymptotic-preserving numerical framework for multiscale, isothermal fluid models of magnetized confined plasmas, where strong magnetic fields induce anisotropy and possible quasi-neutrality breakdowns. The proposed method remains stable and accurate across regimes, including the drift limit, by carefully treating the small parameter $\epsilon$ and deriving reduced models as $\epsilon \to 0$. The paper provides theoretical guarantees of well-posedness and AP convergence, and demonstrates numerical performance through tables and figures illustrating anisotropy and cross-field dynamics. The approach offers robust, scalable simulations for magnetized confinement devices, enabling reliable prediction of plasma behavior across disparate spatial and temporal scales.

Abstract

The aim of this work is to introduce a numerical method to cope with the multiscale nature of confined plasma physics. These investigations are focused on fluid plasma description under large magnetic field. The difficulties in this context stem from intense magnetization of the plasma, inducing a severe anisotropy, possible quasi-neutrality breakdowns, which may occur locally in the plasma and, eventually, the drift regime which prevails for the description of the electrons. These characteristics bring small parameters compared to the scale of the studied device. This work is therefore devoted to highlighting the difficulties specific to this context and to developing numerical methods efficient to cope with this multiscale nature of the physics within the framework of asymptotic-preserving methods.

Figures (2)

• Figure 1: Example figure using external image files.
• Figure 2: Example PGFPLOTS figure.

Theorems & Definitions (5)

• Theorem 6.1: Mean Value Theorem
• Corollary 6.2
• Proof 1
• Claim 6.3
• Proof 2: Proof of main theorem