On the Asymptotic Limit of the Three Dimensional Vlasov–Poisson System for Large Magnetic Field: Formal Derivation

In this paper we establish the asymptotic limit of the three dimensional Vlasov–Poisson equation with strong external magnetic field. The guiding center approximation is investigated in the three dimensional case with a non-constant magnetic field. In the long time asymptotic limit, the motion can b...

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Bibliographic Details
Published in:Journal of statistical physics 2016-11, Vol.165 (4), p.765-784
Main Authors: Degond, Pierre, Filbet, Francis
Format: Article
Language:English
Subjects:
Asymptotic properties
Electric fields
Magnetic fields
Magnetic moments
Mathematical and Computational Physics
Mathematics
Numerical Analysis
Orthogonality
Physical Chemistry
Physics
Physics and Astronomy
Poisson equation
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
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Summary:In this paper we establish the asymptotic limit of the three dimensional Vlasov–Poisson equation with strong external magnetic field. The guiding center approximation is investigated in the three dimensional case with a non-constant magnetic field. In the long time asymptotic limit, the motion can be split in two parts: one stationary flow along the lines of the magnetic field and the guiding center motion in the orthogonal plane of the magnetic field where classical drift velocities and invariants (magnetic moment) are recovered.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-016-1645-2