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arXiv · 1403.0056

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

Yves Elskens·D. F. Escande·Fabrice Doveil
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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.

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Yves Elskens, D. F. Escande, Fabrice Doveil. 2014-05-12. Vlasov equation and $N$-body dynamics - How central is particle dynamics to our understanding of plasmas?. https://doi.org/10.1140/epjd%2Fe2014-50164-9

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