Hamiltonian field description of the one-dimensional Poisson-Vlasov equations (original) (raw)

The paper presents a Hamiltonian field description of the one-dimensional Poisson-Vlasov equations, offering a framework that connects these equations to classical Hamiltonian dynamics. Emphasis is placed on the introduction of noncanonical Poisson brackets that facilitate the transformation to a canonical formulation through the use of Clebsch potentials. The discussion includes the quadratic and quartic terms in the Hamiltonian, the implications of charge neutrality, and the relationship between the Poisson-Vlasov equations and the dynamics of fluid-like systems.