Related papers: Optimal Control of the Two-Dimensional Vlasov-Maxw…
The problem posed by the possible existence/non-existence of spatially non-symmetric kinetic equilibria has remained unsolved in plasma theory. For collisionless magnetized plasmas this involves the construction of stationary solutions of…
We consider the theory and application of a solution method for the inverse problem in collisionless equilibria, namely that of calculating a Vlasov-Maxwell equilibrium for a given macroscopic (fluid) equilibrium. Using Jeans' Theorem, the…
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…
The Vlasov--Maxwell equations are used for the kinetic description of magnetized plasmas. As they are posed in an up to 3+3 dimensional phase space, solving this problem is extremely expensive from a computational point of view. In this…
Modern Tokamaks have evolved from the initial axisymmetric circular plasma shape to an elongated axisymmetric plasma shape that improves the energy confinement time and the triple product, which is a generally used figure of merit for 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…
We study the permanent regimes of the reduced Vlasov-Maxwell system for laser-plasma interaction. A non-relativistic and two different relativistic models are investigated. We prove the existence of solutions where the distribution function…
Dynamical symmetries of the collisionless Boltzmann transport equation, or Vlasov equation, but under the influence of an external driving force, are derived from non-standard representations of the $2D$ conformal algebra. In the case…
Spectral approximation based on Hermite-Fourier expansion of the Vlasov-Poisson model for a collisionless plasma in the electro-static limit is provided, by including high-order artificial collision operators of Lenard-Bernstein type. These…
The Vlasov-Poisson system with massless electrons (VPME) is widely used in plasma physics to model the evolution of ions in a plasma. It differs from the Vlasov-Poisson system (VP) for electrons in that the Poisson coupling has an…
Validity of fluid models breaks down for non-thermal or weakly collisional plasmas which often occur e.g. in the solar wind. In these regimes one has to resort to modelling through the first-principle Vlasov-Maxwell system, but its…
We present a new numerical scheme for solving the advection equation and its application to the Vlasov simulation. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent…
This paper is a first step toward understanding the effect of toroidal geometry on the rigorous stability theory of plasmas. We consider a collisionless plasma inside a torus, modeled by the relativistic Vlasov-Maxwell system. The surface…
A collisionless plasma is modeled by the Vlasov-Poisson system in three space dimensions. A fixed background of positive charge, which is independent of time and space, is assumed. The situation in which mobile negative ions balance the…
We present a Vlasov-DArwin numerical code (ViDA) specifically designed to address plasma physics problems, where small-scale high accuracy is requested even during the non linear regime to guarantee a clean description of the plasma…
1.5D Vlasov-Maxwell simulations are employed to model electromagnetic emission generation in a fully self-consistent plasma kinetic model for the first time in the solar physics context. The simulations mimic the plasma emission mechanism…
The Euler-Maxwell system as a hydrodynamic model for plasma physics to describe the dynamics of the compressible electrons in a constant charged non-moving ion background is studied. The global smooth flow with small amplitude is…
We prove cyclotron damping for the collisionless Vlasov-Maxwell equations on $\mathbb{T}_{x}^{3}\times\mathbb{R}_{v}^{3}$ under the assumptions that the electric induction is zero and $(\mathcal{\mathbf{PSC}})$ holds. It is a crucial step…
We present an extension of the multi-moment advection scheme (Minoshima et al., 2011, J. Comput. Phys.) to the three-dimensional case, for full electromagnetic Vlasov simulations of magnetized plasma. The scheme treats not only point values…
The Radiative Vlasov-Maxwell equations model the radiative kinetics of collisionless relativistic plasma. In them the Lorentz force is modified by the addition of radiation reaction forces. The radiation forces produce damping of particle…