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

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 $(\mathbf{r},\mathbf{v})$-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.

arXiv commentrevTeX, 15 pp

References in corpus (7)

• On Landau damping
• Nonequilibrium Statistical Mechanics of Systems with Long-Range Interactions: Ubiquity of Core-Halo Distributions
• A new approach to quantitative propagation of chaos for drift, diffusion and jump processes
• Landau damping
• Kinetic limit of N-body description of wave-particle self- consistent interaction
• Long-time discrete particle effects versus kinetic theory in the self-consistent single-wave model
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• From conformal invariance towards dynamical symmetries of the collisionless Boltzmann equation
• Direct path from microscopic mechanics to Debye shielding, Landau damping, and wave-particle interaction
• Infinite-dimensional meta-conformal Lie algebras in one and two spatial dimensions
• Boundedness of meta-conformal two-point functions in one and two spatial dimensions
• Phase mixing importance for both Landau instability and damping
• Low-dimensional chaos in the single wave model for self-consistent wave-particle Hamiltonian
• Meta-conformal algebras in $d$ spatial dimensions