Vlasov equation and $N$-body dynamics - How central is particle dynamics to our understanding of plasmas ?

Vlasov equation and $N$-body dynamics - How central is particle dynamics to our understanding of plasmas ?

Difficulties in founding microscopically the Vlasov equation for Coulomb-interacting particles are recalled for both the statistical approach (BBGKY hierarchy and Liouville equation on phase space) and the dynamical approach (single empirical measure on one-particle $(\mathbf{r},\mathbf{v})$-space)....

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Bibliographic Details
Published in:The European physical journal. D, Atomic, molecular, and optical physics Vol. 68
Main Authors: Elskens, Yves, Escande, D. F., Doveil, Fabrice
Format: Journal Article
Language:English
Published: EDP Sciences 12-05-2014
Subjects:
Mathematical Physics
Mathematics
Physics
Physics Education
Plasma Physics
Landau damping
N-body dynamics
Debye shielding
Liouville equation
basic plasma physics
Vlasov equation
statistical ensemble
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Summary:Difficulties in founding microscopically the Vlasov equation for Coulomb-interacting particles are recalled for both the statistical approach (BBGKY hierarchy and Liouville equation on phase space) and the dynamical approach (single empirical measure on one-particle $(\mathbf{r},\mathbf{v})$-space). The role of particle trajectories (characteristics) in the analysis of the partial differential Vlasov--Poisson system is stressed. Starting from many-body dynamics, a direct derivation of both Debye shielding and collective behaviour is sketched.
ISSN:1434-6060
1434-6079
DOI:10.1140/epjd/e2014-500164-9