2009/10/22 by Daniel Han-Kwan, Han-Kwan, Daniel
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Navier-Stokes equation solutions #Plasma Physics (physics.plasm-ph) #Quantum chaos and dynamical systems
paper · doi:10.48550/arxiv.0910.4226
openalex publication_date 2009/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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 \citeFS2, 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.