How central is particle dynamics to our understanding of plasmas

UMR 7345 CNRS, Aix-Marseille Universit´e, Campus Saint-J´erˆome, Case 321, Av. esc. Normandie-Niemen,13397 Marseille, Cedex 20, FranceReceived 28 February 2014 / Received in final form 12 May 2014Published online 12 August 2014 – ⃝c EDP Sciences, Societ`aItalianadiFisica,Springer-Verlag2014Abstract. Difficulties in founding microscopically the Vlasov equation for Coulomb-interacting particlesare 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 particletrajectories (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 behaviouris sketched.