Related papers: Vlasov Equation In Magnetic Field
The efficient numerical solution of many kinetic models in plasma physics is impeded by the stiffness of these systems. Exponential integrators are attractive in this context as they remove the CFL condition induced by the linear part of…
Motivated by the fundamental model of a collisionless plasma, the Vlasov-Maxwell (VM) system, we consider a related, nonlinear system of partial differential equations in one space and one momentum dimension. As little is known regarding…
It is shown that the eigenvalue problem for the hermitian Wilson-Dirac operator of for a uniform magnetic field in two dimensions can be reduced to one-dimensional problem described by a relativistic analog of the Harper equation. An…
The rules to write out any one of the linearly independent functions belonging to the infinite set of those in polynomial form that satisfy the sourceless Grad-Shafranov equation as stated in the toroidal-polar coordinate system are…
We derive the relativistic Vlasov equation from quantum Hartree dynamics for fermions with relativistic dispersion in the mean-field scaling, which is naturally linked with an effective semiclassic limit. Similar results in the…
We consider the Vlasov-Poisson system with initial data a small, radial, absolutely continuous perturbation of a point charge. We show that the solution is global and disperses to infinity via a modified scattering along trajectories of the…
In this paper, we present a rigorous derivation of the mean-field limit for a moderately interacting particle system in $\R^d$ $(d\geq 2)$. For stochastic initial data, we demonstrate that the solution to the interacting particle model,…
When the Vlasov equation is investigated numerically using the method of test particles, the particle-particle interactions that inevitably arise in the simulation (but are not present in the Vlasov equation itself) result in an…
In this paper, we study the Cauchy problem of the magnetic type Zakharov system which describes the pondermotive force and magnetic field generation effects resulting from the non-linear interaction between plasma-wave and particles. By…
In this paper we discuss the dissipative property of near-equilibrium classical solutions to the Cauchy problem of the Vlasov-Maxwell-Boltzmann System in the whole space $\R^3$ when the positive charged ion flow provides a spatially uniform…
The eigenvalue problem for a linear function L centers on solving the eigen-equation Lx = rx. This paper generalizes the eigenvalue problem from a single linear function to an iterated function system F consisting of possibly an infinite…
An application of approximate transformation groups to study dynamics of a system with distinct time scales is discussed. The utilization of the Krylov-Bogoliubov-Mitropolsky method of averaging to find solutions of the Lie equations is…
Following Fr\'enod and Sonnendr\"ucker, we consider the finite Larmor radius regime for a plasma submitted to a large magnetic field and take into account both the quasineutrality and the local thermodynamic equilibrium of the electrons. We…
The Vlasov-Poisson system describes the time evolution of a plasma in the so-called collisionless regime. The investigation of a high-temperature plasma that is influenced by an exterior magnetic field is one of the most significant aspects…
The study of hot plasma expansion in a magnetic field is of interest for many astrophysical applications. In order to observe this process in laboratory, an experiment is proposed in which an ultrashort laser pulse produces a…
We discuss two approaches to solving the parametric (or stochastic) eigenvalue problem. One of them uses a Taylor expansion and the other a Chebyshev expansion. The parametric eigenvalue problem assumes that the matrix $A$ depends on a…
A hybrid model of the Vlasov equation in multiple spatial dimension $D>1$ [H. A. Rose and W. Daughton, Physics of Plasmas v. 18, 122109 (2011)], the Vlasov multi dimensional model (VMD), consists of standard Vlasov dynamics along a…
A starting point for deriving the Vlasov equation is the BBGKY hierarchy that describes the dynamics of coupled marginal distribution functions. With a large value of the plasma parameter one can justify eliminating 2-point correlations in…
We present a new method for solving the relativistic Vlasov--Maxwell system of equations, applicable to a wide range of extreme high-energy-density astrophysical and laboratory environments. The method directly discretizes the kinetic…
In this paper, we propose a moment method to numerically solve the Vlasov equations using the framework of the NRxx method developed in [6, 8, 7] for the Boltzmann equation. Due to the same convection term of the Boltzmann equation and the…