GLOBAL WEAK SOLUTIONS OF THE RELATIVISTIC VLASOV-KLEIN-GORDON SYSTEM IN TWO DIMENSIONS

In this paper we consider the system of classical particles coupled with a Klein-Gordon field in two dimensions.We establish a-priori-bounds on the solutions of this system with initial data satisfying a size restriction derived from conservation of energy.This result,together with the smoothing of"velocity averaging",yields the existence of global weak solutions to the corresponding restricted initial value problem.The size restriction is necessary since energy of the system is indefinite.Finally,we show that the weak solutions preserve the total mass.     

Global weak solutions to the Nordström-Vlasov system

The Nordström-Vlasov system is a Lorentz invariant model for a self-gravitating collisionless gas. We establish suitable a priori bounds on the solutions of this system, which together with energy estimates and the smoothing effect of “momentum averaging” yield the existence of global weak solutions to the corresponding initial value problem. In the process we improve the continuation criterion for classical solutions which was derived recently. The weak solutions are shown to preserve mass.     

Long-time simulation of a highly oscillatory Vlasov equation with an exponential integrator

We change a previous time-stepping algorithm for solving a multi-scale Vlasov–Poisson system within a Particle-In-Cell method, in order to perform accurate long-time simulations. As an exponential integrator, the new scheme allows us to use large time steps compared to the size of the oscillations in the solution.     

WENO schemes applied to the quasi-relativistic Vlasov–Maxwell model for laser–plasma interaction

In this paper we focus on WENO-based methods for the simulation of the 1D Quasi-Relativistic Vlasov–Maxwell (QRVM) model used to describe how a laser wave interacts with and heats a plasma by penetrating into it. We propose several non-oscillatory methods based on either Runge–Kutta (explicit) or Time-Splitting (implicit) time discretizations. We then show preliminary numerical experiments.     

Theoretical investigation of a backward wave oscillator

From the linear Vlasov equation,the theoretical investigation on relativistic backward wave osciUator is performed.The relationship between the microwave power and the guiding magnetic field,which accords with the results of the particle simulation and experiments,is deduced.     

Poisson-Vlasov: stochastic representation and numerical codes

In this paper, we examine the effects of the gravitational field on the dynamical evolution of the cavity-field entropy and the creation of the Schr?dinger-cat state in the Jaynes-Cummings model. We consider a moving two-level atom interacting with a single mode quantized cavity-field in the presence of a classical homogeneous gravitational field. Based on an su(2) algebra, as the dynamical symmetry group of the model, we derive the reduced density operator of the cavity-field which includes the effects of the atomic motion and the gravitational field. Also, we obtain the exact solution and the approximate solution for the system-state vector, and examine the atomic dynamics. By considering the temporal evolution of the cavity-field entropy as well as the dynamics of the Q-function of the cavity-field we study the effects of the gravitational field on the generation of the Schr?dinger-cat states of the cavity-field by using the Q-function, field entropy and approximate solution for the system-state vector. The results show that the gravitational field destroys the generation of the Schr?dinger-cat state of the cavity-field.     

Solutions of the Vlasov equation in Lagrange coordinates

We show that the method of “finite-size” particles is a discrete model of the Vlasov equation but in a different (effective) interaction potential. We calculate the effective potential explicitly in the most interesting case of the Coulomb interaction. We find the equations of motion of particles of “finite size” for the Gaussian form factor. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 1, pp. 138–148, April, 2007.     

Effect of quantization and positron concentration on shielding potentials in electron-positron-ion plasma

The kinetic theory of plasma has been employed to compute the test-charge potential distributions accounting for quantization effects in magnetized electron-positron-ion (EPI) plasmas. In this regard, the degenerate positrons and electrons are assumed to follow the Fermi-Dirac distribution, while inertial ions are modelled by Maxwellian velocity distribution. By solving the Fourier-transformed Vlasov–Poisson equations, a modified dielectric function and electrostatic potential is obtained. By imposing various constraints on the test-charge speed, the potential profile has been analysed in terms of Debye–Hückel (DH), far-field (FF), and wake-field (WF) potentials. It has been found that the amplitude of DH and FF potentials increases by the inclusion of quantization effects, and it becomes the opposite for the WF potential profile. Furthermore, the variation of positron concentration significantly affects the DH, FF, and WF potentials. The present findings are important to understand the shielding phenomenon in degenerate multi-species plasmas.     

Multi-moment advection scheme for Vlasov simulations

We present a new numerical scheme for solving the advection equation and its application to Vlasov simulations. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent variables, for better conservation of the information entropy. We have developed one-and two-dimensional schemes and show that they provide quite accurate solutions within reasonable usage of computational resources compared to other existing schemes. The two-dimensional scheme can accurately solve the solid body rotation problem of a gaussian profile for more than hundred rotation periods with little numerical diffusion. This is crucially important for Vlasov simulations of magnetized plasmas. Applications of the one- and two-dimensional schemes to electrostatic and electromagnetic Vlasov simulations are presented with some benchmark tests.