Electron. J. Diff. Eqns., Vol. 2002(2002), No. 06, pp. 1-20.

The Vlasov equation with strong magnetic field and oscillating electric field as a model for isotop resonant separation

Emmanuel Frenod & Frederique Watbled

Abstract:
We study the qualitative behavior of solutions to the Vlasov equation with strong external magnetic field and oscillating electric field. This model is relevant to the understanding of isotop resonant separation. We show that the effective equation is a kinetic equation with a memory term. This memory term involves a pseudo-differential operator whose kernel is characterized by an integral equation involving Bessel functions. The kernel is explicitly given in some particular cases.

Submitted November 24, 2001. Published January 10, 2002.
Math Subject Classifications: 82D10, 35B27, 35Q99, 76X05, 47G10, 47G20.
Key Words: Vlasov equation, Homogenization, Two-scale convergence, Memory effects, Pseudo-differential equations, Isotop separation.

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Emmanuel Frenod
LMAM, Universite de Bretagne Sud
Campus de Tohannic, F-56000, Vannes, France
e-mail: Emmanuel.Frenod@univ-ubs.fr
Frederique Watbled
LMAM, Universite de Bretagne Sud
Campus de Tohannic, F-56000, Vannes, France
and
IRMAR, Universite Rennes 1, Campus de Beaulieu
35042 Rennes cedex
e-mail: watbled@maths.univ-rennes1.fr

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