2019/10/31 by Y. Elskens, Michael K. -H. Kiessling, Yves Elskens +2 · 15 citations
Engineering · Mathematics · Physics and Astronomy · #BBGKY hierarchy #Classical mechanics #Distribution function #Empirical measure #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Kinetic energy #Kinetic theory #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Maxwell's equations #Measure (data warehouse) #Physics #Plasma #Plasma modeling #Quantum mechanics #Statistical Mechanics and Entropy #Theoretical physics #Vlasov equation #math-ph #math.MP #msc:82C03 #msc:82C40 #msc:83A05 #physics.plasm-ph
paper · pdf · doi:10.1007/s10955-020-02519-x
published in Journal of Statistical Physics 180(1-6), 749-772 (Springer Science+Business Media) · Revised version, 33 pages, accepted for publication (w/o Appendix B) in J. Stat. Phys
openalex created_date 2019/11/01 · arxiv created 2020/02/21 · openalex publication_date 2020/03/20 · arxiv updated 2020/08/12 · openalex updated_date 2026/08/05
It is argued that the relativistic Vlasov--Maxwell equations of the kinetic theory of plasma approximately describe a relativistic system of N charged point particles interacting with the electromagnetic Maxwell fields in a Bopp--Landé--Thomas--Podolsky (BLTP) vacuum, provided the microscopic dynamics lasts long enough.The purpose of this work is not to supply an entirely rigorous vindication, but to lay down a conceptual road map for the microscopic foundations of the kinetic theory of special-relativistic plasma, and to emphasize that a rigorous derivation seems feasible. Rather than working with a BBGKY-type hierarchy of n-point marginal probability measures, the approach proposed in this paper works with the distributional PDE of the actual empirical 1-point measure, which involves the actual empirical 2-point measure in a convolution term.The approximation of the empirical 1-point measure by a continuum density, and of the empirical 2-point measure by a (tensor) product of this continuum density with itself, yields a finite-N Vlasov-like set of kinetic equations which includes radiation-reaction and nontrivial finite-N corrections to the Vlasov--Maxwell-BLTP model. The finite-N corrections formally vanish in a mathematical scaling limit N→∞ in which charges ∝ 1/\surdN. The radiation-reaction term vanishes in this limit, too. The subsequent formal limit sending Bopp's parameter \varkappa→∞ yields the Vlasov--Maxwell model.