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This paper studies the nonlinear Landau damping on the torus T 3 for the Vlasov–Poisson system with radiation damping. We show that even under the influence of the radiation damping effects, the plasma still has the remarkable property of Landau damping. The corresponding density and force field decay exponentially fast as time goes to infinity. [ABSTRACT FROM AUTHOR]

This paper develops and analyses a semi-discrete numerical method for the two-dimensional Vlasov–Stokes system with periodic boundary condition. The method is based on the coupling of the semi-discrete discontinuous Galerkin method for the Vlasov equation with discontinuous Galerkin scheme for the stationary incompressible Stokes equation. The proposed method is both mass and momentum conservative. Since it is difficult to establish non-negativity of the discrete local density, the generalized discrete Stokes operator become non-coercive and indefinite, and under the smallness condition on the discretization parameter, optimal error estimates are established with help of a modified the Stokes projection to deal with the Stokes part and, with the help of a special projection, to tackle the Vlasov part. Finally, numerical experiments based on the dG method combined with a splitting algorithm are performed. [ABSTRACT FROM AUTHOR]

Dynamical low-rank approximation (DLRA) for the numerical simulation of Vlasov–Poisson equations is based on separation of space and velocity variables, as proposed in several recent works. The standard approach for the time integration in the DLRA model uses a splitting of the tangent space projector for the low-rank manifold according to the separated variables. It can also be modified to allow for rank-adaptivity. A less studied aspect is the incorporation of boundary conditions in the DLRA model. In this work, a variational formulation of the projector splitting is proposed which allows to handle inflow boundary conditions on spatial domains with piecewise linear boundary. Numerical experiments demonstrate the principle feasibility of this approach. [ABSTRACT FROM AUTHOR]

The Vlasov–Poisson–Fokker–Planck (VPFP) system is a fundamental model in plasma physics that describes the Brownian motion of a large ensemble of particles within a surrounding bath. Under the high-field scaling, both collision and field are dominant. This paper introduces two Asymptotic-Preserving Neural Network (APNN) methods within a physics-informed neural network (PINN) framework for solving the VPFP system in the high-field regime. These methods aim to overcome the computational challenges posed by high dimensionality and multiple scales of the system. The first APNN method leverages the micro–macro decomposition model of the original VPFP system, while the second is based on the mass conservation law. Both methods ensure that the loss function of the neural networks transitions naturally from the kinetic model to the high-field limit model, thereby preserving the correct asymptotic behavior. Through extensive numerical experiments, these APNN methods demonstrate their effectiveness in solving multiscale and high dimensional uncertain problems, as well as their broader applicability for problems with long time duration and non-equilibrium initial data. [ABSTRACT FROM AUTHOR]

In the upper atmosphere (ionosphere), plasma with two electron populations is very common. The cold electrons ( T e ∼ 1 eV) usually originate in the ionosphere, while the hot electrons ( T e ∼ 100 eV) come from the magnetosphere. In addition to these two electron populations, there may be a beam of electrons streaming along the magnetic field lines. These electrons are responsible for exciting various electrostatic wave modes. In this article, we provide a systematic insight in the evolution of the system, based on the beam energy. With an increase in beam velocity, the beam temporarily recovers a portion of its initial energy as well as a higher saturation energy. The wave energy is lost significantly before saturation and after linear growth at a relatively modest beam velocity. In addition, the low beam velocity generates BGK electron holes in the phase space, which are missing at higher beam velocities. We also present the analysis of the condition of sustained electron holes in the phasespace. [ABSTRACT FROM AUTHOR]

A test problem for the 'particle-in-cell' method is proposed which allows one to check individual errors on each stage of numerical implementation of the method. General testing usually controls only total (final) error. Using the test problem, we analyze errors of a difference method of MacCormack type and the CIC method being the most popular version of the 'particle-in-cell' method. It is shown that the CIC method having also the second formal order of accuracy is seriously inferior to the difference method under the same given error and same grid parameters. In particular, the results of the particle method lose their sense after approximately one calculation period, although the time interval of confidence in simulation data for the difference method is practically unlimited. The testing method proposed here is suitable for an arbitrary one-dimensional version of the 'particle-in-cell' method, and it allows one not only to compare numerical implementations of individual stages with each other, but also to verify available theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigated the two-dimensional, four-field reduced magnetohydrodynamics equations that are used to examine the tearing instability and magnetic reconnection of phenomena in plasmas. The generalized Ohm's law is used in the derivation of the 2D four-field RMHD equations. We established the existence and uniqueness of a strong solution for the 2D four-field RMHD equations under periodic boundary conditions during some time interval in Sobolev-Slobodetskiĭ space with the help of successive approximations and a p r i o r i estimates. [ABSTRACT FROM AUTHOR]

This article is devoted to the study of the relativistic Vlasov–Klein–Gordon system in space dimension three. The dynamical model describes a collisionless ensemble of classical particles coupled with a Klein–Gordon field. By combining the Fourier method and smoothing effect of low velocity particles, we prove a higher regularity of the field, which is widely used for the study of Vlasov equation. [ABSTRACT FROM AUTHOR]

In this paper, we prove the global existence and moment propagation of weak solutions for the repulsive plasma-charge model with a time-varying magnetic field. Multi-point charges are allowed according to an improved mechanism to compensate the asymmetry caused by the point charges, which brings us back to the standard Lions-Perthame’s argument. To deal with two type singularities induced by the point charges and the magnetic field, we combine the ideas from Desvillettes et al. (Ann Inst H Poincaré Anal Non Linéaire 32(2):373–400, 2015) and Rege (SIAM J Math Anal 53(2):2452–2475, 2021). The density of the plasma is allowed to be constant around the point charges, by applying the moment lemma established in Perthame (Math Methods Appl Sci 13(5):41–452, 1990) and careful compactness argument. The result answers two questions raised in Desvillettes et al. (Ann Inst H Poincaré Anal Non Linéaire 32(2):373–400, 2015). [ABSTRACT FROM AUTHOR]

In this paper, we consider a Vlasov–Poisson system in the presence of radiation damping, which is a two-species Vlasov–Poisson system for electrons and ions with additional terms to describe the effect of accelerated charged particles. We obtain the global-in-time and optimal decay estimates of classical solutions to it for small initial data in the whole space R 3 . Compared to the previous results, no compact support assumptions on initial data is needed in our paper. And we obtain the optimal L x ∞ decay estimates of the charge densities and the electrostatic field, which was not reported in previous literature. For the proofs of our results, we adapt the modified vector field method which was introduced initially by Smulevici for the classical Vlasov–Poisson system for electrons. [ABSTRACT FROM AUTHOR]

In this paper, we provide sufficient conditions for the energy conservation of the DiPerna–Lions solutions given in DiPerna and Lions (Commun Pure Appl Math 42:729–757, 1989), Rein (Commun Math Sci 2:145–158, 2004) to Vlasov–Maxwell systems in R 3 , which requires only macroscopic density ρ ∈ L t 2 L loc 2 for the relativistic case and | ξ | f ∈ L t , x 2 L ξ 1 for the non-relativistic case, improving the results in Sospedra–Alfonso (Commun Math Sci 8:901–908, 2010), Bardos et al. (Q Appl Math 78:193–217, 2020). Next, by mollification in time twice with different parameters and the weak formulations containing t = 0 , we obtain the same results for solutions given in Guo (Commun Math Phys 154:245–263, 1993) with low temporal regularity to the Vlasov–Maxwell systems in bounded domains under some boundary-layer conditions. [ABSTRACT FROM AUTHOR]

In this paper, semi-discrete numerical scheme for the approximation of the periodic Vlasov-viscous Burgers’ system is developed and analyzed. The scheme is based on the coupling of discontinuous Galerkin approximations for the Vlasov equation and local discontinuous Galerkin approximations for the viscous Burgers’ equation. Both these methods use generalized numerical fluxes. The proposed scheme is both mass and momentum conservative. Based on generalized Gauss–Radau projections, optimal rates of convergence in the case of smooth compactly supported initial data are derived. Finally, computational results confirm our theoretical findings. [ABSTRACT FROM AUTHOR]

The kinetic formulation of the model problem of plasma waves excitation by a powerful short laser pulse is numerically studied for the first time. Kinetic and simplest hydrodynamic plasma models are also compared for the problem under consideration. It is shown that the considered hydrodynamic models do not provide good approximations to the solution to the Vlasov kinetic equation, namely, one leads to discontinuous solutions and the other has a significant qualitative distinction. At a low plasma temperature, the effect of non-isothermicity of the process is small, but it can lead to significant distortions of the solution during further heating. The results obtained here imply that the first two moments of the distribution function are not enough to describe the plasma hydrodynamics; higher-order moments should be used. [ABSTRACT FROM AUTHOR]

In this article, we study microscopic properties of a two-dimensional Coulomb gas ensemble near a conical singularity arising from insertion of a point charge in the bulk of the droplet. In the determinantal case, we characterize all rotationally symmetric scaling limits ("Mittag-Leffler fields") and obtain universality of them when the underlying potential is algebraic. Applications include a central limit theorem for log | p n (ζ) | where pn is the characteristic polynomial of an n:th order random normal matrix. [ABSTRACT FROM AUTHOR]

We consider a two-dimensional determinantal Coulomb gas confined by a class of radial external potentials. In the limit of large number of particles, the Coulomb particles tend to accumulate on a compact set S, the support of the equilibrium measure associated with a given external potential. If the particles are forced to be completely confined in a disk D due to a hard-wall constraint on ∂ D ⊂ Int S , then the equilibrium configuration changes and the equilibrium measure acquires a singular component at the hard wall. We study the local statistics of Coulomb particles in the vicinity of the hard wall and prove that their local correlations are expressed in terms of "Laplace-type" integrals, which appear in the context of truncated unitary matrices in the regime of weak non-unitarity. [ABSTRACT FROM AUTHOR]

We are concerned with the properties of weak solutions for the relativistic Vlasov–Klein–Gordon system. Under some suitable regularity hypotheses on the density of particles and field, we show the renormalization property and global (local) entropy conservation laws. In addition, by virtue of the additional integrability condition ∫ R 3 1 + | v | 2 f d v ∈ L ∞ ((0 , T) ; L 2 (R x 3)) , we prove that global (local) energy for the weak solutions are conserved. [ABSTRACT FROM AUTHOR]