On the confinement of a tokamak plasma
Résumé
The goal of this paper is to understand from a mathematical viewpoint the magnetic confinement of plasmas for fusion. Following Frénod and Sonnendrücker \cite{FS2}, we first use $2$-scale convergence tools to derive a gyrokinetic system for a plasma submitted to a large magnetic field with a slowly spatially varying intensity. We finally investigate the behaviour of the plasma in such a regime and we prove non-linear stability or instability depending on which side of the tokamak we are looking at. In our analysis we will also show that there exists a temperature gradient threshold beyond which one can expect stability, even in the ``bad'' side : this is the so-called H-mode.
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