https://doi.org/10.1140/epjd/e2014-50164-9
Regular Article
Vlasov equation and N-body dynamicsa
How central is particle dynamics to our understanding of plasmas?
UMR 7345 CNRS, Aix-Marseille Université, Campus Saint-Jérôme, Case 321, Av. esc. Normandie-Niemen, 13397 Marseille, Cedex 20, France
b
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Received: 28 February 2014
Received in final form: 12 May 2014
Published online: 12 August 2014
Abstract
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 (r,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.
Contribution to the Topical Issue “Theory and Applications of the Vlasov Equation”, edited by Francesco Pegoraro, Francesco Califano, Giovanni Manfredi and Philip J. Morrison.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2014
