Related papers: Weak stability of the plasma-vacuum interface prob…
Starting from the given passive particle equilibrium particle cylindrical profiles, we built self-consistent stationary conditions of the Maxwell-Vlasov equation at thermodynamic equilibrium with non-flat density profiles. The solutions to…
We investigate a two-dimensional transmission model consisting of a wave equation and a Kirchhoff plate equation with dynamical boundary controls under geometric conditions. The two equations are coupled through transmission conditions…
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.…
In this paper the first non-linear force-free Vlasov-Maxwell equilibrium is presented. One component of the equilibrium magnetic field has the same spatial structure as the Harris sheet, but whereas the Harris sheet is kept in force balance…
Stabilizing plasma dynamics through externally applied electric and magnetic fields is a fundamental control problem. We study this question for a plasma evolving under a uniform external magnetic field. Although the governing dynamics are…
We study the energy stability of pressure-driven laminar magnetohydrodynamic flow in a rectangular duct with transverse homogeneous magnetic field and electrically insulating walls. For sufficiently strong fields, the laminar velocity…
The tangential layers are characterized by a bulk plasma velocity and a magnetic field that are perpendicular to the gradient direction. They have been extensively described in the frame of the Magneto-Hydro-Dynamic (MHD) theory. But the…
The variational principle for linear stability of three-dimensional, inhomogenious, compressible, moving magnetized plasma is suggested. The principle is ``softer'' (easier to be satisfied) than all previously known variational stability…
We consider the relativistic Vlasov-Maxwell system (RVM) on a general axisymmetric spatial domain with perfect conducting boundary which reflects particles specularly, assuming axisymmetry in the problem. We construct continuous global…
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…
We study the finite Larmor radius regime for the Vlasov-Poisson system. The magnetic field is assumed to be uniform. We investigate this non linear problem in the two dimensional setting. We derive the limit model by appealing to…
We study the possibility of constructing steady magnetic fields satisfying the force balance equation of ideal magnetohydrodynamics with tangential boundary conditions in asymmetric confinement vessels, i.e. bounded regions that are not…
We analyze from a far field the evolution of an interface that separates ideal incompressible fluids of different densities and has an interfacial mass flux. We develop and apply the general matrix method to rigorously solve the boundary…
A procedure that allows study of unstable stability of a boundary layer between plasma and a magnetic field has been developed. Layer equilibrium for one reason or another is not set but follows from strict solution of kinetic equation with…
In this paper, we study the control properties of the linearized compressible Navier-Stokes system with Maxwell's law around a constant steady state $(\rho_s, u_s, 0), \rho_s>0, u_s>0$ in the interval $(0, 2\pi)$ with periodic boundary…
Equations describing plasma equilibria are derived from the total energy of the system. The MHD equilibrium is shown to hold even for systems where the magnetic field may locally vanish. Through conservation of helicity, confinement is…
We prove the incompressible limit of compressible ideal magnetohydrodynamic(MHD) flows in a reference domain where the magnetic field is tangential to the boundary. Unlike the case of transversal magnetic fields, the linearized problem of…
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…
We study the linear stability of inviscid steady parallel flow of an ideal gas in a channel of finite width. Compressible isothermal two-dimensional monochromatic perturbations are considered. The eigenvalue problem governing density and…
An important physical model describing the dynamics of dilute weakly ionized plasmas in the collisional kinetic theory is the Vlasov-Poisson-Boltzmann system for which the plasma responds strongly to the self-consistent electrostatic force.…