Contribution of α2\alpha^2-terms to the total interaction cross sections of relativistic elementary atoms with atoms of matter

It is shown that the corrections of $\alpha^2$ order to the total cross sections for interaction of elementary hydrogen-like atoms with target atoms, reported in the previously published paper [S.Mrowczynski, Phys.Rev. D36, 1520 (1987)], do not include some terms of the same order of magnitude. That results in a significant contribution of these corrections in particular cases. The full $\alpha^2$-corrections have been derived and it is shown that they are really small and could be omitted for most practical applications.Comment: 5 page

Theory and computation of covariant Lyapunov vectors

Lyapunov exponents are well-known characteristic numbers that describe growth rates of perturbations applied to a trajectory of a dynamical system in different state space directions. Covariant (or characteristic) Lyapunov vectors indicate these directions. Though the concept of these vectors has been known for a long time, they became practically computable only recently due to algorithms suggested by Ginelli et al. [Phys. Rev. Lett. 99, 2007, 130601] and by Wolfe and Samelson [Tellus 59A, 2007, 355]. In view of the great interest in covariant Lyapunov vectors and their wide range of potential applications, in this article we summarize the available information related to Lyapunov vectors and provide a detailed explanation of both the theoretical basics and numerical algorithms. We introduce the notion of adjoint covariant Lyapunov vectors. The angles between these vectors and the original covariant vectors are norm-independent and can be considered as characteristic numbers. Moreover, we present and study in detail an improved approach for computing covariant Lyapunov vectors. Also we describe, how one can test for hyperbolicity of chaotic dynamics without explicitly computing covariant vectors.Comment: 21 pages, 5 figure

Hyperbolic chaos in self-oscillating systems based on mechanical triple linkage: Testing absence of tangencies of stable and unstable manifolds for phase trajectories

Dynamical equations are formulated and a numerical study is provided for self-oscillatory model systems based on the triple linkage hinge mechanism of Thurston -- Weeks -- Hunt -- MacKay. We consider systems with holonomic mechanical constraint of three rotators as well as systems, where three rotators interact by potential forces. We present and discuss some quantitative characteristics of the chaotic regimes (Lyapunov exponents, power spectrum). Chaotic dynamics of the models we consider are associated with hyperbolic attractors, at least, at relatively small supercriticality of the self-oscillating modes; that follows from numerical analysis of the distribution for angles of intersection of stable and unstable manifolds of phase trajectories on the attractors. In systems based on rotators with interacting potential the hyperbolicity is violated starting from a certain level of excitation.Comment: 30 pages, 18 figure

First experimental results obtained using the highpower free electron laser at the siberian center for photochemical research

The first lasing near the wavelength of 140 µm was achieved in April 2003 using a high-power free electron laser (FEL) constructed at the Siberian Center for Photochemical Research. In this paper we briefly describe the design of the FEL driven by an accelerator–recuperator. Characteristics of the electron beam and terahertz laser radiation, obtained in the first experiments, are also presented in the paper.У Сибірському центрі фотохімічних досліджень навесні 2003 року отримана генерація випромінювання з довжиною хвилі 140 мкм на потужному лазері на вільних електронах (ЛВЕ). У роботі коротко описана конструкція ЛВЕ на базі прискорювача рекуператора і представлені результати вимірювання деяких параметрів електронного пучка і терагерцового випромінювання.В Сибирском центре фотохимических исследований весной 2003 года получена генерация излучения с длиной волны 140 мкм на мощном лазере на свободных электронах (ЛСЭ). В работе кратко описана конструкция ЛСЭ на базе ускорителя рекуператора и представлены результаты измерения некоторых параметров электронного пучка и терагерцового излучения