相关论文: Hamiltonian formulation of reduced Vlasov-Maxwell …
The Hamiltonian formulation of guiding-center Vlasov-Maxwell equations, which contain dipole contributions to the guiding-center polarization and magnetization, is presented in terms of a guiding-center Hamiltonian functional that is…
The Hamiltonian formulations for the perturbed Vlasov-Maxwell equations and the perturbed ideal magnetohydrodynamics (MHD) equations are expressed in terms of the perturbation derivative $\partial{\cal F}/\partial\epsilon \equiv [{\cal F},…
Hamiltonian integration methods for the Vlasov-Maxwell equations are developed by a Hamiltonian splitting technique. The Hamiltonian functional is split into five parts, i.e., the electrical energy, the magnetic energy, and the kinetic…
The Vlasov-Maxwell equations possess a Hamiltonian structure expressed in terms of a Hamiltonian functional and a functional bracket. In the present paper, the transformation ("lift") of the Vlasov-Maxwell bracket induced by the dynamical…
A Hamiltonian field theory for the macroscopic Maxwell equations with fully general polarization and magnetization is stated in the language of differential forms. The precise procedure for translating the vector calculus formulation into…
Extended guiding-center Vlasov-Maxwell equations are derived under the assumption of time-dependent and inhomogeneous electric and magnetic fields that obey the standard guiding-center space-time-scale orderings. The guiding-center…
The covariant Hamilton-Jacobi formulation of Maxwell's equations is derived from the first-order (Palatini-like) Lagrangian using the analysis of constraints within the De~Donder-Weyl covariant Hamiltonian formalism and the corresponding…
The inclusion of spatial smoothing in finite-dimensional particle-based Hamiltonian reductions of the Vlasov equation are considered. In the context of the Vlasov-Poisson equation (and other mean-field Lie-Poisson systems), smoothing…
Reduced equations that describe low-frequency plasma dynamics play an important role in our understanding of plasma behavior over long time scales. One of the oldest paradigms for reduced plasma dynamics involves the ponderomotive…
The Hamiltonian structure of the guiding-center Vlasov-Maxwell equations is presented in terms of a Hamiltonian functional and a guiding-center Vlasov-Maxwell bracket. The bracket, which is shown to satisfy the Jacobi identity exactly, is…
We analyse a reduced 1D Vlasov--Maxwell system introduced recently in the physical literature for studying laser-plasma interaction. This system can be seen as a standard Vlasov equation in which the field is split in two terms: an…
The paper [1] by Crouseilles, Einkemmer, and Faou used an incorrect Poisson bracket for the Vlasov-Maxwell equations. If the correct Poisson bracket is used, the solution of one of the subsystems cannot be computed exactly in general. As a…
The gyrokinetic Vlasov-Maxwell equations are cast as an infinite-dimensional Hamiltonian system. The gyrokinetic Poisson bracket is remarkably simple and similar to the Morrison-Marsden-Weinstein bracket for the Vlasov-Maxwell equations. By…
Three geometric formulations of the Hamiltonian structure of the macroscopic Maxwell equations are given: one in terms of the double de Rham complex, one in terms of L2 duality, and one utilizing an abstract notion of duality. The final of…
We consider the Vlasov-Maxwell equations with one spatial direction and two momenta, one in the longitudinal direction and one in the transverse direction. By solving the Jacobi identity, we derive reduced Hamiltonian fluid models for the…
Stochastic solutions are obtained for the Maxwell-Vlasov equation in the approximation where magnetic field fluctuations are neglected and the electrostatic potential is used to compute the electric field. This is a reasonable approximation…
The elimination of a fast time scale from the Vlasov equation by Lie-transform methods is an important step in deriving a reduced Vlasov equation such as the drift-kinetic Vlasov equation or the gyrokinetic Vlasov equation. It is shown here…
Hamiltonian extended magnetohydrodynamics (XMHD) is restricted to respect helical symmetry by reducing the Poisson bracket for 3D dynamics to a helically symmetric one, as an extension of the previous study for translationally symmetric…
Given a foliation S of a manifold M, a distribution Z in M transveral to S and a Poisson bivector \Pi on M we present a geometric method of reducing this operator on the foliation S along the distribution Z. It encompasses the classical…
The perturbative variational formulation of the Vlasov-Maxwell equations is presented up to third order in the perturbation analysis. From the second and third-order Lagrangian densities, respectively, the first-order and second-order…