On some exceptional cases in the integrability of the three-body problem

We consider the Newtonian planar three--body problem with positive masses $m_1$, $m_2$, $m_3$. We prove that it does not have an additional first integral meromorphic in the complex neighborhood of the parabolic Lagrangian orbit besides three exceptional cases $\sum m_i m_j/(\sum m_k)^2= 1/3$, $2^3/3^3$, $2/3^2$ where the linearized equations are shown to be partially integrable. This result completes the non-integrability analysis of the three-body problem started in our previous papers and based of the Morales-Ramis-Ziglin approach.Comment: 7 page

THz transition radiation of electron bunch laser-accelerated in long-scale near-critical density plasmas

Direct laser electron acceleration in near-critical density plasma produces collimated electron beams with high charge $Q$ (up to $\mu$C). This regime could be of interest for high energy THz radiation generation, as many of the mechanisms have a scaling $\propto Q^2$. In this work we focused specifically on challenges that arise during numerical investigation of transition radiation in such interaction. Detailed analytical calculations that include both diffraction and decoherence effects of characteristics of transition radiation in the THz range were conducted with the input parameters obtained from 3D PIC and hydrodynamic simulations. The calculated characteristics of THz radiation are in good agreement with the experimentally measured ones. Therefore, this approach can be used both to optimize properties of THz radiation and distinguish the transition radiation contribution if several mechanisms of THz radiation generation are considered

On the algebraic invariant curves of plane polynomial differential systems

We consider a plane polynomial vector field $P(x,y)dx+Q(x,y)dy$ of degree $m>1$. To each algebraic invariant curve of such a field we associate a compact Riemann surface with the meromorphic differential $\omega=dx/P=dy/Q$. The asymptotic estimate of the degree of an arbitrary algebraic invariant curve is found. In the smooth case this estimate was already found by D. Cerveau and A. Lins Neto [Ann. Inst. Fourier Grenoble 41, 883-903] in a different way.Comment: 10 pages, Latex, to appear in J.Phys.A:Math.Ge

Laser-driven pointed acceleration of electrons with preformed plasma lens

The simultaneous laser-driven acceleration and angular manipulation of the fast electron beam is experimentally demonstrated. The bunch of multi-MeV energy charged particles is generated during the propagation of the femtosecond laser pulse through the near-critical plasma slab accompanied by plasma channeling. Plasma is formed by the controlled breakdown of a thin-tape target by a powerful nanosecond prepulse. The electron beam pointing approach is based on the refraction of a laser pulse in the presence of a strong radial density gradient in the breakdown of the tape with a small displacement of the femtosecond laser beam relative to the breakdown symmetry axis. A shift of several micrometers makes it possible to achieve beam deflection by an angle up to 10 degrees with acceptable beam charge and spectrum conservation. This opens up opportunities for in-situ applications for scanning objects with an electron beam and the multistage electron beam energy gain in consecutive laser accelerators without bulk magnetic optics for particles. Experimental findings are supported by numerical Particle-In-Cell calculations of laser-plasma acceleration and hydrodynamic simulations.Comment: Submitted to PPC

REASONS FOR THE INCREASED DISPERSION IN THE MECHANICAL CHARACTERISTIC OF THE REACTOR PRODUCT MADE FROM Zr-2,5% Nb

Methods of electronic microscopy, tensile testing, X-ray analysis on samples of a product made of Zr-2.5% Nb have been used to determine the reasons for properties dispersion of structural behavior during tensile testing. The process of sample preparation before testing is optimized.Благодарность выражается Евсееву М.В. за помощь в проведении исследований и обсуждении результатов

On the convergence of continued fractions at Runckel’s points

International audienc

Kovalevskaya exponents and integrable systems of classical dynamics I, II

International audienc