# American Institute of Mathematical Sciences

December  2011, 15(3): 513-544. doi: 10.3934/dcdsb.2011.15.513

## Mathematical models for strongly magnetized plasmas with mass disparate particles

 1 Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 16 route de Gray, Besançon, 25030 Cedex 2 CMI/LATP (UMR 6632), Université de Provence, 39, rue Joliot Curie, 13453 Marseille Cedex 13

Received  January 2010 Revised  May 2010 Published  February 2011

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.
Citation: Mihai Bostan, Claudia Negulescu. Mathematical models for strongly magnetized plasmas with mass disparate particles. Discrete & Continuous Dynamical Systems - B, 2011, 15 (3) : 513-544. doi: 10.3934/dcdsb.2011.15.513
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##### References:
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