7,580 research outputs found
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
Theory and applications of the Vlasov equation
Forty articles have been recently published in EPJD as contributions to the
topical issue "Theory and applications of the Vlasov equation". The aim of this
topical issue was to provide a forum for the presentation of a broad variety of
scientific results involving the Vlasov equation. In this editorial, after some
introductory notes, a brief account is given of the main points addressed in
these papers and of the perspectives they open.Comment: Editoria
Vlasov moments, integrable systems and singular solutions
The Vlasov equation for the collisionless evolution of the single-particle
probability distribution function (PDF) is a well-known Lie-Poisson Hamiltonian
system. Remarkably, the operation of taking the moments of the Vlasov PDF
preserves the Lie-Poisson structure. The individual particle motions correspond
to singular solutions of the Vlasov equation. The paper focuses on singular
solutions of the problem of geodesic motion of the Vlasov moments. These
singular solutions recover geodesic motion of the individual particles.Comment: 16 pages, no figures. Submitted to Phys. Lett.
Vlasov Equation In Magnetic Field
The linearized Vlasov equation for a plasma system in a uniform magnetic
field and the corresponding linear Vlasov operator are studied. The spectrum
and the corresponding eigenfunctions of the Vlasov operator are found. The
spectrum of this operator consists of two parts: one is continuous and real;
the other is discrete and complex. Interestingly, the real eigenvalues are
infinitely degenerate, which causes difficulty solving this initial value
problem by using the conventional eigenfunction expansion method. Finally, the
Vlasov equation is solved by the resolvent method.Comment: 15 page
Multiphysics simulations of collisionless plasmas
Collisionless plasmas, mostly present in astrophysical and space
environments, often require a kinetic treatment as given by the Vlasov
equation. Unfortunately, the six-dimensional Vlasov equation can only be solved
on very small parts of the considered spatial domain. However, in some cases,
e.g. magnetic reconnection, it is sufficient to solve the Vlasov equation in a
localized domain and solve the remaining domain by appropriate fluid models. In
this paper, we describe a hierarchical treatment of collisionless plasmas in
the following way. On the finest level of description, the Vlasov equation is
solved both for ions and electrons. The next courser description treats
electrons with a 10-moment fluid model incorporating a simplified treatment of
Landau damping. At the boundary between the electron kinetic and fluid region,
the central question is how the fluid moments influence the electron
distribution function. On the next coarser level of description the ions are
treated by an 10-moment fluid model as well. It may turn out that in some
spatial regions far away from the reconnection zone the temperature tensor in
the 10-moment description is nearly isotopic. In this case it is even possible
to switch to a 5-moment description. This change can be done separately for
ions and electrons. To test this multiphysics approach, we apply this full
physics-adaptive simulations to the Geospace Environmental Modeling (GEM)
challenge of magnetic reconnection.Comment: 13 pages, 5 figure
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