Related papers: A Hamiltonian splitting for the Vlasov-Maxwell sys…
The hybrid Vlasov-Maxwell system of equations is suitable to describe a magnetized plasma at scales of the order of or larger than proton kinetic scales. An exact stationary solution is presented by revisiting previous results with a…
High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…
The relativistic Vlasov-Maxwell system describes the evolution of a collisionless plasma. The problem of linear instability of this system is considered in two physical settings: the so-called "one and one-half" dimensional case, and the…
This paper formulates a new particle-in-cell method for the Vlasov-Maxwell system. Under the Lorenz gauge condition, Maxwell's equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The…
The Numerical Flow Iteration (NuFI) method has recently been proposed as a memory-slim solution method for the Vlasov--Poisson system. It stores the temporal evolution of the electric field, instead of the distribution functions, and…
Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithm conserves a discrete non-canonical symplectic structure…
In the presence of an inhomogeneous oscillatory electric field, charged particles experience a net force, averaged over the oscillatory timescale, known as the ponderomotive force. We derive a one-dimensional Hamiltonian model which…
The Vlasov-Poisson-Boltzmann system is often used to govern the motion of plasmas consisting of electrons and ions with disparate masses when collisions of charged particles are described by the two-component Boltzmann collision operator.…
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 simple Hamiltonian modeling framework for general models in nonlinear optics is given. This framework is specialized to describe the Hamiltonian structure of electromagnetic phenomena in cubicly nonlinear optical media. The model has a…
We consider the linear stability problem for a 3D cylindrically symmetric equilibrium of the relativistic Vlasov-Maxwell system that describes a collisionless plasma. For an equilibrium whose distribution function decreases monotonically…
The Vlasov--Maxwell equations are used for the kinetic description of magnetized plasmas. As they are posed in an up to 3+3 dimensional phase space, solving this problem is extremely expensive from a computational point of view. In this…
A new scheme for numerical integration of the 1D2V relativistic Vlasov-Maxwell system is proposed. Assuming that all particles in a cell of the phase space move with the same velocity as that of the particle located at the center of the…
We present a Hamiltonian formulation for the linearized Vlasov-Maxwell system with a Maxwellian background distribution function. We discuss the geometric properties of the model at the continuous level, and how to discretize the model in…
In this paper we present a novel particle method for the Vlasov--Poisson equation. Unlike in conventional particle methods, the particles are not interpreted as point charges, but as point values of the distribution function. In between the…
The standard approach for integrating the multidimensional Vlasov equation using grid based, conservative schemes is based on a time splitting approach. Here, we show that although the truncation error is of second order, time splitting can…
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…
We show that nonrelativsitic scaling of the collisionless Vlasov-Maxwell system implies the existence of a formal invariant slow manifold in the infinite-dimensional Vlasov-Maxwell phase space. Vlasov-Maxwell dynamics restricted to the slow…
The time evolution of a two-component collisionless plasma is modeled by the Vlasov-Poisson system. In this work, the setting is two and one-half dimensional, that is, the distribution functions of the particles species are independent of…
We present a novel framework for Finite Element Particle-in-Cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov-Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining…