Geometry of Vlasov kinetic moments: a bosonic Fock space for the symmetric Schouten bracket

Higher order Hamiltonian fluid reduction of Vlasov equation

From the Hamiltonian structure of the Vlasov equation, we build a Hamiltonian model for the first three moments of the Vlasov distribution function, namely, the density, the momentum density and the specific internal energy. We derive the Poisson bracket of this model from the Poisson bracket of the Vlasov equation, and we discuss the associated Casimir invariants.

On the use of projectors for Hamiltonian systems and their relationship with Dirac brackets

The role of projectors associated with Poisson brackets of constrained Hamiltonian systems is analyzed. Projectors act in two instances in a bracket: in the explicit dependence on the variables and in the computation of the functional derivatives. The role of these projectors is investigated by using Dirac's theory of constrained Hamiltonian systems. Results are illustrated by three examples taken from plasma physics: magnetohydrodynamics, the Vlasov-Maxwell system, and the linear two-species Vlasov system with quasineutrality.

一维维拉夫方程的哈密顿流体简化

Hamiltonian hydrodynamic reductions of one-dimensional Vlasov equations

本文通过分析一维维拉夫方程的哈密顿闭合形式，揭示了多种模型在参数化上的统一结构，基于μ2的多项式生成，为简化描述维拉夫-泊松动力学提供了新路径。

Magnetic moment type of lifting from particle dynamics to Vlasov-Maxwell dynamics

Techniques for coordinate changes that depend on both dependent and independent variables are developed and applied to the Maxwell-Vlasov Hamiltonian theory. Particle coordinate changes with a new velocity variable dependent on the magnetic field, with spatial coordinates unchanged, are lifted to transform the noncanonical Poisson bracket and, thus, the field Hamiltonian structure of the Vlasov-Maxwell equation. Several examples are given including magnetic coordinates, where the velocity is decomposed into components parallel and perpendicular to the local magnetic field, and the case of sphe…

Hamiltonian structure of reduced fluid models for plasmas obtained from a kinetic description

We consider the Hamiltonian structure of reduced fluid models obtained from a kinetic description of collisionless plasmas by Vlasov-Maxwell equations. We investigate the possibility of finding Poisson subalgebras associated with fluid models starting from the Vlasov-Maxwell Poisson algebra. In this way, we show that the only possible Poisson subalgebra involves the moments of zeroth and first order of the Vlasov distribution, meaning the fluid density and the fluid velocity. We find that the bracket derived in [Phys. Rev. Lett. 93, 175002 (2004)] which involves moments of order 2 is not a Poi…

The Maxwell-Vlasov equations in Euler-Poincare form

Low's well known action principle for the Maxwell-Vlasov equations of ideal plasma dynamics was originally expressed in terms of a mixture of Eulerian and Lagrangian variables. By imposing suitable constraints on the variations and analyzing invariance properties of the Lagrangian, as one does for the Euler equations for the rigid body and ideal fluids, we first transform this action principle into purely Eulerian variables. Hamilton's principle for the Eulerian description of Low's action principle then casts the Maxwell-Vlasov equations into Euler-Poincare form for right invariant motion on …