Abstract
The controlled fusion is achieved by magnetic confinement : the plasma is confined into toroidal devices called tokamaks, under the action of strong magnetic fields. The particle motion reduces to advection along the magnetic lines combined to rotation around the magnetic lines. The rotation around the magnetic lines is much faster than the parallel motion and efficient numerical resolution requires homogenization procedures. Moreover the rotation period, being proportional to the particle mass, introduces very different time scales in the case when the plasma contains disparate particles; the electrons turn much faster than the ions, the ratio between their cyclotronic periods being the mass ratio of the electrons with respect to the ions. The subject matter of this paper concerns the mathematical study of such plasmas, under the action of strong magnetic fields. In particular, we are interested in the limit models when the small parameter, representing the mass ratio as we ll as the fast cyclotronic motion, tends to zero.
Highlights
Many research programs in plasma physics are devoted to magnetic confinement
It concerns the dynamics of a population of charged particles under the action of strong magnetic fields, let say Bε(x) depending on some parameter ε > 0
M is the particle mass, q is the particle charge and v is the velocity in the plane perpendicular to the magnetic field lines
Summary
Many research programs in plasma physics are devoted to magnetic confinement. It concerns the dynamics of a population of charged particles under the action of strong magnetic fields, let say Bε(x) depending on some parameter ε > 0. Notice that in the case of a gaz, consisting of distinct particles (let us say ions/electrons), the cyclotronic motion introduces several small time scales, for example when the particle masses are disparate. The goal of this paper is how to generalize this method when two different small time scales appear in the model, as for example in the electron Vlasov equation (8). The method can be adapted straightforwardly to any linear transport equation involving multiple scales ε, ε2, ..., εp with p ∈ N⋆, but the explicit derivation of the limit model may become very complex since, in general, it requires p averaging processes.
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