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A new splitting is proposed for solving the Vlasov-Maxwell system. This splitting is based on a decomposition of the Hamiltonian of the Vlasov-Maxwell system and allows for the construction of arbitrary high order methods by composition…

Numerical Analysis · Mathematics 2017-01-06 Nicolas Crouseilles , Lukas Einkemmer , Erwan Faou

The time evolution of a collisionless plasma is modeled by the relativistic Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. We consider the case that the plasma…

Mathematical Physics · Physics 2021-03-23 Jörg Weber

Energy conserving particle-in-cell schemes are constructed for a class of reduced relativistic Vlasov--Maxwell equations of laser-plasma interaction. Discrete Poisson equation is also satisfied by the numerical solution. Specifically,…

Numerical Analysis · Mathematics 2022-11-30 Yingzhe Li

The super simple Vlasov (ssV) code was developed to study instabilities, turbulence, and reconnection in weakly magnetized plasmas, such as the solar wind in the dissipation range and the edge of fusion plasmas. The ssV code overcomes the…

High-intensity laser plasma interactions create complex computational problems because they involve both fluid and kinetic regimes, which need models that maintain physical precision while keeping computational speed. The research…

Plasma Physics · Physics 2025-10-14 Sadra Saremi , Amirhossein Ahmadkhan Kordbacheh

This article is concerned with the kinetic modeling, by means of the Vlasov equation, of charged particles under the influence of a strong external electromagnetic field, i.e. when epsilon^2, the dimensionless cyclotron period, tends to…

Mathematical Physics · Physics 2009-05-15 Pierre Degond , Sever Hirstoaga , Marie-Hélène Vignal

We present the first plasma simulations obtained with the code dHybridR, a hybrid particle-in-cell code with fluid electrons and both thermal and energetic ions that retain relativistic dynamics. dHybridR is constructed to study…

High Energy Astrophysical Phenomena · Physics 2020-01-08 Colby C. Haggerty , Damiano Caprioli

Recent experimental results from the Trident laser confirm the importance of kinetic effects in determining laser reflectivities at high intensities. Examples observed include scattering from low frequency electron acoustic waves (EAWs),…

Plasma Physics · Physics 2015-06-26 N. J. Sircombe , T. D. Arber , R. O. Dendy

We present an explicit temporal discretization of particle-in-cell schemes for the Vlasov equation that results in exact energy conservation when combined with an appropriate spatial discretization. The scheme is inspired by a simple,…

Numerical Analysis · Mathematics 2024-11-15 Lee F. Ricketson , Jingwei Hu

Many problems encountered in plasma physics require a description by kinetic equations, which are posed in an up to six-dimensional phase space. A direct discretization of this phase space, often called the Eulerian approach, has many…

Numerical Analysis · Mathematics 2018-06-12 Lukas Einkemmer , Christian Lubich

Electromagnetic waves are an inherent part of all plasmas -- laboratory fusion plasmas or astrophysical plasmas. The conventional methods for studying properties of electromagnetic waves rely on discretization of Maxwell equations suitable…

The motion of a collisionless plasma - a high-temperature, low-density, ionized gas - is described by the Vlasov-Maxwell system. In the presence of large velocities, relativistic corrections are meaningful, and when symmetry of the particle…

Analysis of PDEs · Mathematics 2009-12-31 Robert Glassey , Stephen Pankavich , Jack Schaeffer

The nonlinear propagation of dust-acoustic (DA) waves in a magnetized dusty plasma with a pair of trapped ions is investigated. Starting from a set of hydrodynamic equations for massive dust fluids as well as kinetic Vlasov equations for…

Plasma Physics · Physics 2017-11-20 A. P. Misra

This paper proposes an adaptive hyper-reduction method to reduce the computational cost associated with the simulation of parametric particle-based kinetic plasma models, specifically focusing on the Vlasov-Poisson equation. Conventional…

Numerical Analysis · Mathematics 2026-02-05 Cecilia Pagliantini , Federico Vismara

We present a new numerical scheme for solving the advection equation and its application to Vlasov simulations. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent…

Computational Physics · Physics 2011-07-06 Takashi Minoshima , Yosuke Matsumoto , Takanobu Amano

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…

Plasma Physics · Physics 2015-05-13 Alain J Brizard

We present a review of recent developments of simulations of the Vlasov-Maxwell system of equations using a Fourier transform method in velocity space. In this method, the distribution functions for electrons and ions are Fourier…

Plasma Physics · Physics 2011-07-26 Bengt Eliasson

A semi-implicit finite difference time domain (FDTD) numerical Maxwell solver is developed for full electromagnetic Particle-in-Cell (PIC) codes for the simulations of plasma-based acceleration. The solver projects the volumetric Yee…

Plasma Physics · Physics 2020-08-26 Alexander Pukhov

For simulating laser-plasma interactions, we developed a parallel, multi-dimensional, fully relativistically particle-in-cell (PIC) code, named YUNIC. The core algorithm is introduced, including field solver, particle pusher, field…

Plasma Physics · Physics 2021-04-02 Huai-Hang Song , Wei-Min Wang , Yu-Tong Li

The particle-in-cell (PIC) method is successfully used to study magnetized plasmas. However, this requires large computational costs and limits simulations to short physical run-times and often to setups in less than three spatial…

High Energy Astrophysical Phenomena · Physics 2023-01-24 Rouven Lemmerz , Mohamad Shalaby , Timon Thomas , Christoph Pfrommer