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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…

Plasma Physics · Physics 2023-05-03 Simon Lautenbach , Rainer Grauer

A collisionless plasma is modeled by the Vlasov-Poisson system in three space dimensions. A fixed background of positive charge - dependant upon only velocity - is assumed. The situation in which mobile negative ions balance the positive…

Analysis of PDEs · Mathematics 2010-01-06 Stephen Pankavich

The Euler-Maxwell system describes the evolution of a plasma when the collisions are important enough that each species is in a hydrodynamic equilibrium. In this paper we prove global existence of small solutions to this system set in the…

Analysis of PDEs · Mathematics 2011-07-11 Pierre Germain , Nader Masmoudi

The relativistic Vlasov-Maxwell system is a kinetic model for collisionless plasmas. For the two-dimensional model, global well-posedness of this model is known and was proven by deriving global bounds on the momentum support of the…

Analysis of PDEs · Mathematics 2024-11-28 Matthew Hernandez , Neel Patel , Elena Salguero

We consider the free boundary problem for the plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region, the flow is governed by the usual compressible MHD equations, while in the vacuum region we…

Analysis of PDEs · Mathematics 2014-07-22 Davide Catania , Marcello D'Abbicco , Paolo Secchi

This paper is concerned with the asymptotic behavior of small data solutions to the three-dimensional Vlasov-Maxwell system in the exterior of a light cone. The plasma does not have to be neutral and no compact support assumptions are…

Analysis of PDEs · Mathematics 2020-12-14 Léo Bigorgne

We study the free boundary problem for a plasma-vacuum interface in ideal incompressible magnetohydrodynamics. Unlike the classical statement when the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, to better…

Analysis of PDEs · Mathematics 2020-07-15 Alessandro Morando , Paolo Secchi , Yuri Trakhinin , Paola Trebeschi

We consider the free boundary problem for relativistic plasma--vacuum interfaces in two and three spatial dimensions. The plasma flow is governed by the equations of ideal relativistic magnetohydrodynamics, while the vacuum magnetic and…

Analysis of PDEs · Mathematics 2026-04-30 Paolo Secchi , Yuri Trakhinin , Tao Wang

Vlasov-Maxwell equilibria are described by the self-consistent solutions of the time-independent Maxwell equations for the real-space dynamics of electromagnetic fields, and the Vlasov equation for the phase-space dynamics of particle…

Plasma Physics · Physics 2017-10-16 O. Allanson , S. Troscheit , T. Neukirch

This paper presents a grid-free simulation algorithm for the fully three-dimensional Vlasov--Poisson system for collisionless electron plasmas. We employ a standard particle method for the numerical approximation of the distribution…

Numerical Analysis · Mathematics 2020-03-06 Torsten Keßler , Sergej Rjasanow , Steffen Weißer

We consider relativistic plasma particles subjected to an external gravitation force in a $3$D half space whose boundary is a perfect conductor. When the mean free path is much bigger than the variation of electromagnetic fields, the…

Analysis of PDEs · Mathematics 2022-03-04 Yunbai Cao , Chanwoo Kim

A basic model for describing plasma dynamics is given by the Euler-Maxwell system, in which compressible ion and electron fluids interact with their own self-consistent electromagnetic field. In this paper we consider the "one-fluid"…

Analysis of PDEs · Mathematics 2017-05-24 Yu Deng , Alexandru D. Ionescu , Benoit Pausader

The asymptotic properties at future null infinity of the solutions of the relativistic Vlasov-Maxwell system whose global existence for small data has been established by the author in a previous work are investigated. These solutions…

Mathematical Physics · Physics 2015-06-26 Simone Calogero

We consider the two-dimensional Vlasov-Poisson system to model a two-component plasma whose distribution function is constant with respect to the third space dimension. First, we show how this two-dimensional Vlasov-Poisson system can be…

Mathematical Physics · Physics 2021-10-12 Patrik Knopf

Collisionless plasmas, such as those encountered in tokamaks, exhibit a rich variety of instabilities. The physical origin, triggering mechanisms and fundamental understanding of many plasma instabilities, however, are still open problems.…

Plasma Physics · Physics 2015-06-22 Valeria Ratushnaya , Ravi Samtaney

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…

Plasma Physics · Physics 2009-11-13 Zhiwu Lin , Walter Strauss

In this paper, we study the controllability of the two-dimensional relativistic Vlasov-Maxwell system in a torus, by means of an interior control. We give two types of results. With the geometric control condition on the control set, we…

Analysis of PDEs · Mathematics 2012-12-03 Olivier Glass , Daniel Han-Kwan

The low-frequency limit of Maxwell equations is considered in the Maxwell-Vlasov system. This limit produces a neutral Vlasov system that captures essential features of plasma dynamics, while neglecting radiation effects. Euler-Poincar\'e…

Plasma Physics · Physics 2015-02-03 Cesare Tronci , Enrico Camporeale

We consider linear stability of steady states of 1(1/2) and 3D Vlasov-Maxwell systems for collisionless plasmas. The linearized systems can be written as separable Hamiltonian systems with constraints. By using a general theory for…

Analysis of PDEs · Mathematics 2021-07-28 Zhiwu Lin

Full self-consistent stationary Vlasov-Maxwell solutions of magnetically confined plasmas are built for systems with cylindrical symmetries. The stationary solutions are thermodynamic equilibrium solutions. These are obtained by computing…

Plasma Physics · Physics 2023-01-04 Aurélien Cordonnier , Xavier Leoncini , Guilhem Dif-Pradalier , Xavier Garbet