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Pré-Publication, Document De Travail Année : 2009

On the confinement of a tokamak plasma

Résumé

The goal of this paper is to understand from a mathematical point of view the magnetic confinement of plasmas for fusion. Following Frénod and Sonnendrücker \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.
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Dates et versions

hal-00425375 , version 1 (21-10-2009)
hal-00425375 , version 2 (22-10-2009)
hal-00425375 , version 3 (19-07-2010)

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Daniel Han-Kwan. On the confinement of a tokamak plasma. 2009. ⟨hal-00425375v3⟩
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