Mathematical models for strongly magnetized plasmas with mass disparate particles

Pages: 513 - 544, Volume 15, Issue 3, May 2011

doi:10.3934/dcdsb.2011.15.513       Abstract        References        Full Text (371.7K)       Related Articles

Mihai Bostan - Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 16 route de Gray, Besançon, 25030 Cedex, France (email)
Claudia Negulescu - CMI/LATP (UMR 6632), Université de Provence, 39, rue Joliot Curie, 13453 Marseille Cedex 13, France (email)

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.

Keywords:  Vlasov equation, multi-scale analysis, average operator.
Mathematics Subject Classification:  Primary: 35Q75, 78A35; Secondary: 82D10.

Received: January 2010;      Revised: May 2010;      Published: February 2011.

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