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
Received: 28 February 2014
Received in final form: 12 May 2014
Published online: 12 August 2014
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.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2014