The Vlasov-Poisson system with strong magnetic field. (English) Zbl 0977.35108

Golse, François; Saint-Raymond, Laure

J. Math. Pures Appl., IX. Sér. 78, No. 8, 791-817 (1999).

The motion of a gas of a mixture of light and heavy particles of opposite charge (a plasma) is governed by a Vlasov-Poisson type system. The presence of an external magnetic field is included in the model by introduction of an additional Lorentz force term in the Vlasov equation. The authors are concerned with the limiting behavior of this system for large magnetic fields. Various time scales are taken into account and their limiting behavior is discussed. The so-called ‘guiding center’ dynamics of the axis of a helical motion of the particles is studied in the 2-dimensional case. The 3-dimensional case is investigated in the time scale of the particle motion along field lines. Whereas in the 2-dimensional case the magnetic field is assumed to be constant, in the 3-dimensional situation two cases of variable magnetic fields are discussed. Some of the asymptotic limit results presented here have been previously announced in [the authors, C. R. Acad. Sci. Paris, Sér. I, Math. 327, No. 10, 865-870 (1998; Zbl 0921.76196)].

Reviewer: Rainer Picard (Dresden)

MSC:

35Q35	PDEs in connection with fluid mechanics
76X05	Ionized gas flow in electromagnetic fields; plasmic flow
82C21	Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics

Keywords:

Vlasov equation; Poisson equation; guiding center dynamics

Citations:

Zbl 0921.76196