On the confinement of a tokamak plasma

TL;DR

This paper uses mathematical tools to analyze magnetic confinement in tokamak plasmas, deriving simplified models and identifying stability conditions related to temperature gradients and plasma behavior.

Contribution

It formally derives a gyrokinetic system and a bi-temperature fluid model for tokamak plasmas, providing insights into stability thresholds and plasma behavior.

Findings

Existence of a temperature gradient threshold for stability

Derivation of a simplified bi-temperature fluid system

Identification of stability and instability regimes

Abstract

The goal of this paper is to understand from a mathematical point of view the magnetic confinement of plasmas for fusion. Following Fr\'enod and Sonnendr\"ucker \cite{FS2}, we first use two-scale convergence tools to derive a gyrokinetic system for a plasma submitted to a large magnetic field with a slowly spatially varying intensity. We formally derive from this system a simplified bi-temperature fluid system. We then investigate the behaviour of the plasma in such a regime and we prove nonlinear stability or instability depending on which side of the tokamak we are looking at. In our analysis, we will also point out that there exists a temperature gradient threshold beyond which one can expect stability, even in the "bad" side : this corresponds to the so-called H-mode.