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[en] Calculations concerning the betatron oscillations in a storage ring lattice comprising a lumped element sextupole field are presented. The method used is based on the second order approximation of the averaging method. The existence of singular points inside the region of the phase space defined by the separatrix is assumed. Formula are given permitting the calculations of the size of the corresponding intersecting invariant curves and a simple expression is deduced for the betatron tune shift. Numerical application is made, the results are compared to those obtained by a tracking program. A good agreement between them is noticed
[en] Current researches on beam dynamics in synchrotrons with digital wideband transverse feedback systems are reviewed. Particular attention is given to quantitative and qualitative regularities in frequency shifts and decrements of coherent betatron oscillation damping when feedback loop signals are digitally processed. Theoretical predictions are compared with the experimental data obtained at the Large Hadron Collider.
[en] The betatron difference resonance, Qx - 2Qz = -6, where Qx,z are the number of betatron oscillations per turn, was studied at the Indiana University Cyclotron Facility (IUCF) cooler ring. The position of the beam was measured in both the horizontal and vertical planes of oscillation after a pulsed kicker magnet was fired to produce coherent motion. The effect of the coupling resonance was clearly observed and it was found that the subsequent particle motion could be described by a simple Hamiltonian. The resonance strength and tune shift as a function of betatron amplitude were measured
[en] We describe theoretically and numerically the interaction of a laser- or LINAC-accelerated beam of relativistic electrons with a high intensity optical lattice, resulting from the superposition of two transverse laser pulses. The bunch is trapped and guided within the potential channels of the optical lattice, leading to betatron oscillations. We describe the emission from individual particles and from the bunch, and analyze its spectrum, considering the dominant incoherent radiation as well as possible effects of partial coherency. Analysis of the emitted radiation should provide useful information on the characteristics of the electron beam, and its interaction with the optical lattice. (authors)
[en] The invention is aimed at the increase of secondary particle yield regularity. To achieve the aim in the suggested method of gradual radiation obtaining in cyclic accelerators with a rigid focusing at the end of each acceleration cycle, after exposure time of the object irradiated using the method of resonance excitation of circulating beam ends, the amplitude of vertical betatron oscillations is increased. On reaching the set degree of discordance between emittance of secondary beam and acceptance of its transport systems its accelerating voltage is switched off. Application of the method suggested facilitates regime selection of primary beam guidance to the internal target, increases the degree of secondary particle yield regularity during exposition of experimental device, simplifies processing of counting statistics during event recording in the experiments with counting technique, prevents from premature degradation of detecting equipment and thus increases operational efficiency of cyclic accelerators with rigid focusing and the quality of physical studies conducted using them