Related papers: A one-dimensional Vlasov-Maxwell equilibrium for t…
Plasma kinetics, for both flat and curved spacetime, is conventionally performed on the mass shell, a 7--dimensional time-phase space with a Vlasov vector field, also known as the Liouville vector field. The choice of this time-phase space…
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…
In this paper we provide sharp criteria for linear stability or instability of equilibria of collisionless plasmas in the presence of boundaries. Specifically, we consider the relativistic Vlasov-Maxwell system with specular reflection at…
Generic equilibria are derived for turbulent relaxing plasmas via an entropy-maximization procedure that accounts for the short-time conservation of certain collisionless invariants. The conservation of these collisionless invariants endows…
We present, for the first time, the structure of the axisymmetric force-free magnetosphere of an aligned rotating magnetic dipole, in the case in which there exists a sufficiently large charge density (whose origin we do not question) to…
We consider the periodic problem for two-fluid non-isentropic Euler-Maxwell systems in plasmas. By means of suitable choices of symmetrizers and an induction argument on the order of the time-space derivatives of solutions in energy…
We prove the existence of piecewise smooth MHD equilibria in three-dimensional toroidal domains of $\mathbf{R}^3$ where the pressure is constant on the boundary but not in the interior. The pressure is piecewise constant and the plasma…
The physical mechanism responsible for driving accretion flows in astrophysical accretion disks is commonly thought to be related to the development of plasma instabilities and turbulence. A key question is therefore the determination of…
We study the plasma-vacuum interface problem in relativistic magnetohydrodynamics for the case when the plasma density does not go to zero continuously, but jumps. In the vacuum region we consider the Maxwell equations for electric and…
In this paper, we consider the three dimensional Vlasov equation with an inhomogeneous, varying direction, strong magnetic field. Whenever the magnetic field has constant intensity, the oscillations generated by the stiff term are periodic.…
A family of mixed finite elements is proposed for solving the first order system of linear elasticity equations in any space dimension, where the stress field is approximated by symmetric finite element tensors. This family of elements has…
It is found that the ideal magnetohydrodynamic equilibrium of an axisymmetric gravitating magnetically confined plasma with incompressible flows is governed by a second-order elliptic differential equation for the poloidal magnetic flux…
We investigate the general plasma-vacuum interface problems for the ideal incompressible MHD equations with or without surface tension and prove their nonlinear local well-posedness in standard Sobolev spaces under either non-zero surface…
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…
We construct fully three-dimensional (3D) equilibria with pressure anisotropy and closed, nested toroidal magnetic surfaces that are strongly asymmetric in the toroidal direction by applying a sinusoidal perturbation to the axisymmetric…
We propose a novel reformulation of the Vlasov-Amp{\`e}re equations for plasmas. This reformulation exposes discrete symmetries to achieve simultaneous conservation of mass, momentum, and energy; preservation of Gauss's law involution;…
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…
We present a new fast solver to calculate fixed-boundary plasma equilibria in toroidally axisymmetric geometries. By combining conformal mapping with Fourier and integral equation methods on the unit disk, we show that high-order accuracy…
Stochastic solutions are obtained for the Maxwell-Vlasov equation in the approximation where magnetic field fluctuations are neglected and the electrostatic potential is used to compute the electric field. This is a reasonable approximation…
We present a new Vlasov code for collisionless plasmas in the nonrelativistic regime. A Darwin approximation is used for suppressing electromagnetic vacuum modes. The spatial integration is based on an extension of the flux-conservative…