Breaking of two-dimensional relativistic electron oscillations under small deviations from axial symmetry

A numerical asymptotic model for the breaking of two-dimensional plane relativistic electron oscillations under a small deviation from axial symmetry is developed. The asymptotic theory makes use of the construction of time-uniformly applicable solutions to weakly nonlinear equations. A special finite-difference algorithm on staggered grids is used for numerical simulation. The numerical solutions of axially symmetric one-dimensional relativistic problems yield two-sided estimates for the breaking time. Some of the computations were performed on the “Chebyshev” supercomputer (Moscow State University).     

Iterative solution of matrix games using grid variational inequalities

A new approach to the approximate solution of matrix games is proposed. It is based on the reduction of the original problem to a variational inequality of a special form. In particular, this makes it possible to design preconditioned iterative methods, which proved to be effective as a tool for the numerical solution of large and ill-conditioned systems of linear algebraic equations.     

A difference scheme for plasma wakefield simulation

The paper presents a scheme implemented by the finite difference method for solving a system of nonlinear partial differential equations describing a three-dimensional axially symmetric plasma wakefield. The results of wakefield dynamics calculation until breaking are also presented.     

Numerical solution of some unstable problem

While modeling nonlinear wakefield excited by a short laser pulse in a plasma channel, the pulse group speed is normally less than the speed of light, whereas they are usually considered to be equal. This paper shows that consideration of the speed difference leads to an exponential instability of the model. It is also proved that this unstable problem is equivalent to a specific stable problem. This feature allows us to develop stable numerical schemes for their solution.     

On the Existence of a Global Solution of a Hyperbolic Problem

Doklady Mathematics - A quasilinear system of hyperbolic equations describing plane one-dimensional relativistic oscillations of electrons in a cold plasma is considered. For a simplified...     

Application of the Energy Conservation Law in the Cold Plasma Model

Computational Mathematics and Mathematical Physics - For the two-fluid hydrodynamic cold plasma model, differential relations characterizing the energy conservation law are derived. The case when...     

Iteration in a subspace for solving matrix games

A new method for solving symmetric matrix games is proposed and justified. It is based on iterating vectors in the null space of a specially constructed matrix. According to the numerical tests performed, the efficiency of the proposed method is comparable with that of the available iterative algorithms having about the same computational complexity. This approach is also applicable to more complicated problems than the calculation of particular optimal strategies. For instance, it can be used for finding the unique minimum length solution.     

To the question of large-amplitude electron oscillations in a plasma slab

A new approach is proposed for constructing and analyzing piecewise smooth exact solutions of the system of quasilinear hyperbolic equations that models the simplest electron oscillations in a plasma slab. A necessary and sufficient condition for their existence and uniqueness is established. An approximate numerical-analytical solution method is constructed for smooth initial data.     

On the best constant in the inf-sup-condition for elongated rectangular domains

The Ladyzhenskaya-Babushka-Brezzi inequality (inf-sup-condition) is often used in the analysis of convergence of approximate solutions of hydrodynamic equations to exact ones. The constant involved in it depends on the shape of the domain and determines the efficiency of different algorithms. In this paper, its asymptotics and two-sided estimates for rectangular domains are obtained. To this end, a new method for estimating eigenvalues of a certain spectral problem with Stokes’ saddle operator is used. Translated fromMatematicheskie Zametki, Vol. 67, No. 3, pp. 387–396, March, 2000.     

The theory of recombination X-ray lasers

Theoretical models and main numerical results concerning the pumping of H- and He-like ions in an expanding plasma are presented. The following types of short-wavelength schemes are considered: recombination in a freely expanding plasma fiber; recombination connected with photoionization of the ionic ground state by external radiation; photo-pumping of ionic levels by a Planck spectrum with a cut-off long-wave wing; and some modifications of the above schemes.