Hierarchical foliation of one-dimensional Vlasov-Poisson system

Abstract

We elucidate the intermediate of the macroscopic fluid model and the microscopic kinetic model by studying the Poisson algebraic structure of the one-dimensional Vlasov-Poisson system. The water-bag model helps formulating the hierarchy of sub-algebras, which interpolates the gap between the fluid and kinetic models. By analyzing the embedding of the sub-manifold of an intermediate hierarchy in a more microscopic hierarchy, we characterize the microscopic effect as the symmetry breaking pertinent to a macroscopic invariant.

References in corpus (4)

• On the use of projectors for Hamiltonian systems and their relationship with Dirac brackets
• Higher order Hamiltonian fluid reduction of Vlasov equation
• Hamiltonian fluid closures of the Vlasov-Amp{è}re equations: from water-bags to N moment models
• The kinetic origin of the fluid helicity -- a symmetry in the kinetic phase space