Electromagnetic radiation of relativistic channeling particles (the Kumakhov effect)

Detailed investigation of the channeling phenomena involved in bending of high-energy beams by means of crystals

During the latest decade, experiments have been performed at the CERN SPS to investigate the use of high-energy channeled nuclei in bent crystals for extraction, beam splitting and beam bending. An understanding of channeling in a bent crystal with extraction and deflection efficiencies for different energies, crystal types and ions has been developed. Furthermore, the long-standing question of radiation damage has been addressed with encouraging outcome. This makes extrapolations possible for the construction of, e.g., an extraction device for the LHC at CERN, RHIC at Brookhaven or new splitting elements in high-energy beams.We present the main results obtained and discuss existing and future applications of bent crystals in high-energy physics.

Channeling of high-energy particles in bent crystals – Experiments at the CERN SPS

Bending of GeV particle beams by channeling in bent crystal planes

Channeling of a 450 GeV/c proton beam through a bent silicon crystal has found a novel application to the production of simultaneous particle beams. A pair of simultaneous, nearly-collinear beams of long- and short-lived neutral kaons has thereby been derived. These beams form an integral part of an experiment, NA48, at CERN, designed to measure the CP-violation parameter ϵ′ ϵ with high precision.

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A novel application of bent crystal channeling to the production of simultaneous particle beams

Steering of charged particle trajectories by a bent crystal

Steering of charged-particle trajectories by means of a curved single crystal

This paper surveys results concerning the quantization approach to the Jacobian Conjecture and related topics on noncommutative algebras. We start with a brief review of the paper and its motivations. The first section deals with the approximation by tame automorphisms and the Belov–Kontsevich Conjecture. The second section provides quantization proof of Bergman’s centralizer theorem which has not been revisited for almost 50 years and formulates several related centralizer problems. In the third section, we investigate a free algebra analogue of a classical theorem of Białynicki-Birula’s theorem and give a noncommutative version of this famous theorem. Additionally, we consider positive-root torus actions and obtain the linearity property analogous to the Białynicki-Birula theorem. In the last sections, we introduce Feigin’s homomorphisms and we see how they help us in proving our main and fundamental theorems on screening operators and in the construction of our lattice Wn-algebras associated with sln, which is by far the simplest known approach concerning constructing such algebras until now.

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A. F. Elishev

Papers

Steering of charged particle trajectories by a bent crystal

Steering of charged-particle trajectories by means of a curved single crystal

Polynomial Automorphisms, Deformation Quantization and Some Applications on Noncommutative Algebras