Hamiltonian formulation of the quasineutral Vlasov-Poisson system

TL;DR

This paper derives a Hamiltonian formulation for the quasineutral limit of the Vlasov-Poisson system, capturing plasma dynamics without fast oscillations and ensuring incompressible flow through a novel synthesis of fluid and kinetic Poisson brackets.

Contribution

It introduces a Hamiltonian framework for the quasineutral Vlasov-Poisson system using slow manifold reduction and Poisson-Dirac theory, unifying fluid and kinetic structures.

Findings

Hamiltonian structure for quasineutral plasma dynamics

Incompressible bulk plasma flow in the model

Electric field balances plasma stresses

Abstract

Slow manifold reduction and the theory of Poisson-Dirac submanifolds are used to deduce a Hamiltonian formulation for a quasineutral limit of the planar, collisionless, magnetized Vlasov-Poisson system. Motion on the slow manifold models plasma dynamics free of fast Langmuir oscillations. Preservation of quasineutrality requires the bulk plasma flow is incompressible. The electric field is determined by counterbalancing plasma stresses that would otherwise produce compression. The Hamiltonian structure for the quasineutral model synthesizes well-known Poisson brackets for incompressible fluids and collisionless kinetic equations.