The Vlasov equation with strong magnetic field and oscillating electric field as a model of isotope resonant separation

Emmanuel Frenod (1, 2) , Frederique Watbled (1)

1 LMAM - Laboratoire de Mathématiques et Applications des Mathématiques, EA 3885
2 CALVI - Scientific computation and visualization

We study qualitative behavior of the Vlasov equation with strong external magnetic field and oscillating electric field. This model is relevant in order to understand 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. In some particular cases, the kernel is explicitly given.

Mots clés: Vlasov equation; Homogenization; Two-scale convergence; Memory effects; Pseudo-differential equations; Isotop separation

Domaines: Analyse fonctionnelle [math.FA]; Physique des plasmas [physics.plasm-ph]

Emmanuel Frenod, Frederique Watbled. The Vlasov equation with strong magnetic field and oscillating electric field as a model of isotope resonant separation. Electronic Journal of Differential Equations, 2002, 2000, pp.1--20. ⟨hal-00133420⟩