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Long Time Behavior of the Two-Dimensional Vlasov Equation with a Strong External Magnetic Field

Abstract : When charged particles are submitted to a large external magnetic field, their movement in first approximation occurs along the magnetic field lines and obeys a one dimensional Vlasov equation along these field lines. However, when observing the particles on a sufficiently long time time scale, a drift phenomenon perpendicular to the magnetic field lines superposes to this first movement. In this report, we present a rigorous asymptotic analysis of the two-dimensional Vlasov equation when the magnetic field tends to infinity, the observation time scale growing accordingly. Techniques based on the two-scale convergence and the introduction of a second problem enable us to find an equation verified by the weak limit of the distribution function.
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Submitted on : Wednesday, May 24, 2006 - 12:22:10 PM
Last modification on : Friday, February 4, 2022 - 3:24:45 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:40:13 PM

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  • HAL Id : inria-00073262, version 1

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Emmanuel Frénod, Eric Sonnendrücker. Long Time Behavior of the Two-Dimensional Vlasov Equation with a Strong External Magnetic Field. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2000, 10 (4), pp.539--553. ⟨inria-00073262⟩

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