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

Yves Elskens; Dominique F. Escande; Fabrice Doveil

doi:10.1140/epjd/e2014-50164-9

EPJ

Vlasov equation and N-body dynamics^a

How central is particle dynamics to our understanding of plasmas?

Yves Elskens^b, Dominique F. Escande and Fabrice Doveil

UMR 7345 CNRS, Aix-Marseille Université, Campus Saint-Jérôme, Case 321, Av. esc. Normandie-Niemen, 13397 Marseille, Cedex 20, France

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.

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Vlasov equation and N-body dynamicsa

How central is particle dynamics to our understanding of plasmas?

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Vlasov equation and N-body dynamics^a