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

Yves Elskens (1) , D. F. Escande (1) , Fabrice Doveil (1)

1 PIIM - Physique des interactions ioniques et moléculaires

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.

Mots clés: basic plasma physics; Debye shielding; Landau damping; Vlasov equation; N-body dynamics; Liouville equation; statistical ensemble

Domaines: Physique des plasmas [physics.plasm-ph]; Physique mathématique [math-ph]; Physique mathématique [math-ph]; Enseignement de la physique [physics.ed-ph]

Yves Elskens, D. F. Escande, Fabrice Doveil. Vlasov equation and $N$-body dynamics - How central is particle dynamics to our understanding of plasmas ?. The European Physical Journal D : Atomic, molecular, optical and plasma physics, 2014, 68, pp.218. ⟨10.1140/epjd/e2014-500164-9⟩. ⟨hal-00954244v2⟩