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The Vlasov-Poisson system with strong magnetic field in quasineutral regime. (English) Zbl 1053.82032

Summary: Consider the motion of a gas of electrons with a background of ions, subject to the self-consistent electric field and to a constant external magnetic field. As the Debye length and the Larmor radius vanish at the same rate, the asymptotic current density is governed by the 2D1/2 incompressible Euler equation. Establishing limit requires to overcome various difficulties: compactness with respect to the space variable, control of large velocities, oscillations in the time variable. Yet, for particular initial data, the simultaneous gyrokinetic and quasineutral approximation is completely justified.

MSC:

82D10 Statistical mechanics of plasmas
35F25 Initial value problems for nonlinear first-order PDEs
35L60 First-order nonlinear hyperbolic equations
35Q60 PDEs in connection with optics and electromagnetic theory
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
35Q99 Partial differential equations of mathematical physics and other areas of application
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