Related papers: Asymptotic-Preserving methods and multiscale model…
The method of matched asymptotic expansions is applied to the problem of a collisionless plasma generated by UV illumination localized in a central part of the plasma in the limiting case of small Debye length ${\lambda}_D$. A…
A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the…
We present a six-moment multi-fluid model, which solves the governing equations for both ions and electrons, with pressure anisotropy along and perpendicular to the magnetic field direction, as well as the complete set of Maxwell equations.…
We present a new method for solving the relativistic Vlasov--Maxwell system of equations, applicable to a wide range of extreme high-energy-density astrophysical and laboratory environments. The method directly discretizes the kinetic…
A conservative formulation of the drift-reduced fluid plasma model is constructed by analytically inverting the implicit relation defining the polarisation velocity as a function of the time-derivative of the electric field. The obtained…
We study the hyperbolic approximation of the Benjamin-Bona-Mahony (BBM) equation proposed recently by Gavrilyuk and Shyue (2022). We develop asymptotic-preserving numerical methods using implicit-explicit (additive) Runge-Kutta methods that…
In magnetized plasma, the magnetic field confines particles around field lines. The ratio between the intensity of the parallel and perpendicular viscosity or heat conduction may reach the order of $10^{12}$. When the magnetic fields have…
In this paper we derive three new asymptotic models for an hyperbolic-hyperbolicelliptic system of PDEs describing the motion of a collision-free plasma in a magnetic field. The first of these models takes the form of a non-linear and…
The evolution of quasi-isentropic magnetohydrodynamic waves of small but finite amplitude in an optically thin plasma is analyzed. The plasma is assumed to be initially homogeneous, in thermal equilibrium and with a straight and homogeneous…
The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal…
We consider a linearized Euler--Maxwell model for the propagation and absorption of electromagnetic waves in a magnetized plasma. We present the derivation of the model, and we show its well-posedeness, its strong and polynomial stability…
We prove the existence of strong time-periodic solutions and their asymptotic stability with the total energy of the perturbations decaying to zero at an exponential decay rate as $t \rightarrow \infty$ for a semilinear (nonlinearly…
The recently developed energy conserving semi-implicit method (ECsim) for PIC simulation is applied to multiple scale problems where the electron-scale physics needs to be only partially retained and the interest is on the macroscopic or…
Gyrocenter dynamics of charged particles plays a fundamental role in plasma physics. In particular, accuracy and conservation of energy are important features for correctly performing long-time simulations. For this purpose, we here propose…
This paper studies the nonlinear evolution of magnetic field turbulence in proximity of steady ideal MHD configurations characterized by a small electric current, a small plasma flow, and approximate flux surfaces, a physical setting that…
We consider the Riemann problem for relativistic flows of polytropic fluids and find relations for the flow characteristics. Evolution of physical quantities take especially simple form for the case of cold magnetized plasmas. We find…
We consider the relativistic Vlasov--Maxwell (RVM) equations in the limit when the light velocity $c$ goes to infinity. In this regime, the RVM system converges towards the Vlasov--Poisson system and the aim of this paper is to construct…
We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial…
The thermal stability of a weakly magnetized, rotating, stratified, optically thin plasma is studied by means of linear-perturbation analysis. We derive dispersion relations and criteria for stability against axisymmetric perturbations that…
The energy production through thermo-nuclear fusion requires the confinement of the plasma into a bounded domain. In most of the cases, such configurations are obtained by using strong magnetic fields. Several models exist for describing…