Related papers: Stability in Quasineutral Plasmas with Thermalized…
We investigate the formation of a plasma boundary layer (sheath) by considering the Vlasov--Poisson system on a half-line with the completely absorbing boundary condition. In an earlier paper by the first two authors, the solvability of the…
We investigate the dynamical stability of a fully-coupled system of $N$ inertial rotators, the so-called Hamiltonian Mean Field model. In the limit $N \to \infty$, and after proper scaling of the interactions, the $\mu$-space dynamics is…
The stability of static solutions of the spherically symmetric, asymptotically flat Einstein-Vlasov system is studied using a Hamiltonian approach based on energy-Casimir functionals. The main result is a coercivity estimate for the…
The present paper completes our earlier results on nonlinear stability of stationary solutions of the Vlasov-Poisson system in the stellar dynamics case. By minimizing the energy under a mass-Casimir constraint we construct a large class of…
We construct a mean-field model that describes the nonlinear dynamics of a spin-polarized electron gas interacting with fixed, positively-charged ions possessing a magnetic moment that evolves in time. The mobile electrons are modeled by a…
It is shown that in perfectly quasi-isodynamic stellarators, trapped particles with a bounce frequency much higher than the frequency of the instability are stabilizing in the electrostatic and collisionless limit. The collisionless…
Starting from the Vlasov-Maxwell equations describing the dynamics of various species in a quasi-neutral plasma, an exact relativistic hydrodynamic closure for a special type of water-bag distributions satisfying the Vlasov equation has…
We construct the approximate solutions to the Vlasov--Poisson system in a half-space, which arises in the study of the quasi-neutral limit problem in the presence of a sharp boundary layer, referred as to the plasma sheath in the context of…
In this paper, we study an asymptotic preserving (AP), energy stable and positivity preserving semi-implicit finite volume scheme for the Euler-Poisson-Boltzmann (EPB) system in the quasineutral limit. The key to energy stability is the…
The mathematical description of laboratory fusion plasmas produced in Tokamaks is still challenging. Complete models for electrons and ions, as Vlasov-Maxwell systems, are computationally too expensive because they take into account all…
This paper deals with the numerical resolution of the Vlasov-Poissonsystem with a strong external magnetic field by Particle-In-Cell(PIC) methods. In this regime, classical PIC methods are subject tostability constraints on the time and…
In this paper we characterize the stabilization for some thermo-elastic type system with Cattaneo law and we prove that the exponential or polynomial stability of this system implies a polynomial stability of the correspond thermoelastic…
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…
In this paper, we develop a framework for the discretization of a mixed formulation of quasi-reversibility solutions to ill-posed problems with respect to Poisson's equations. By carefully choosing test and trial spaces a formulation that…
We consider the 1/2-dimensional relativistic Vlasov-Maxwell system that describes the time-evolution of a plasma. We find a relatively simple criterion for spectral instability of a wide class of equilibria. This class includes…
Motivated by the stellar wind ejected from the upper atmosphere (Corona) of a star, we explore a boundary problem of the two-species nonlinear relativistic Vlasov-Poisson systems in the 3D half space in the presence of a constant vertical…
We review stability and instability results for self-gravitating matter distributions, where the matter model is a collisionless gas as described by the Vlasov equation. The focus is on the general relativistic situation, i.e., on steady…
We prove the existence and nonlinear stability of steady states of the Vlasov-Poisson system in the stellar dynamics case. The steady states are obtained as minimizers of an energy-Casimir functional from which fact their dynamical…
This review presents an upgraded wave theory adapted to the high fluctuation level of driven realistic i.e. non-idealized plasmas. Above all, this means giving up the well-known concept of a linear wave theory in favor of a thoroughly…
The dynamics of dilute plasma particles such as electrons and ions can be modeled by the fundamental two species Vlasov-Poisson-Boltzmann equations, which describes mutual interactions of plasma particles through collisions in the…