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A refined equation for channeling particle diffusion in transverse energy taking into consideration large-angle scattering by nuclei is suggested. This equation is reduced to the Sturm–Liouville problem, allowing one to reveal both the origin and the limitations of the dechanneling length notion. The values of the latter are evaluated for both positively and negatively charged particles of various energies. New features of the dechanneling dynamics of positively charged particles are also revealed. First, it is demonstrated that the dechanneling length notion is completely inapplicable for their nuclear dechanneling process. Second, the effective electron dechanneling length of positively charged particle varies more than twice converging to a constant asymptotic value only at the depth exceeding the latter.

We present the crystalrad simulation code, combining all the features of the crystal simulation code for simulations of charged particles trajectories in a bent crystal and the radcharm++ code for calculation of the radiation spectrum. The crystalrad code is based on Monte Carlo simulations of trajectories in the planar and axial electric field either in a straight, bent, or periodically bent crystal taking into account multiple and single Coulomb scattering on nuclei and electrons, nuclear scattering and ionization energy losses. The trajectories simulated are used for calculation of radiation spectra by the Baier-Katkov method. We compare our simulations with experimental data taken at MAMI (MAinzer MIkrotron) as well as give an example for a possible future study with sub-GeV electrons interacting with Si bent crystals.

We report on the measurements of the spectra of gamma radiation generated by 855 MeV electrons in bent silicon and germanium crystals at MAMI (MAinzer MIkrotron). The crystals were 15 μm thick along the beam direction to ensure high deflection efficiency. Their (111) crystalline planes were bent by means of a piezo-actuated mechanical holder, which allowed to remotely change the crystal curvature. In such a way it was possible to investigate the radiation emitted under planar channeling and volume reflection as a function of the curvature of the crystalline planes. We showed that, using volume reflection, intense gamma radiation can be produced – with intensity comparable to that obtained in channeling but with higher angular acceptance. We studied the trade-off between radiation intensity and angular acceptance at different values of the crystal curvature. The measurements of radiation spectra have been carried out for the first time in bent germanium crystals. In particular, the intensity of radiation in the germanium crystal is higher than in the silicon one due to the higher atomic number, which is important for the development of the X-ray and gamma radiation sources based on higher-Z deformed crystals, such as crystalline undulators.

In the article, computer simulation on the behavior of a ferromagnetic thin film on a non-magnetic substrate by computer simulation is performed. The substrate is described by the two-dimensional Frenkel–Kontorova potential. The Ising model is used to describe the magnetic properties of a two-dimensional ferromagnetic film. The Wolf cluster algorithm is used to model the magnetic behavior of the film. A square lattice is considered for an unperturbed ferromagnetic film. Computer simulations show that mismatch of film and substrate periods results in film splitting into regions with different atomic structures. Magnetic properties for the obtained structure have been investigated. The hysteresis loop is calculated using the Metropolis algorithm. Deformations of the substrate lead to a decrease in the phase transition temperature. The Curie temperature decreases both when the substrate is compressed and when stretched. The change in phase transition temperature depends on the decreasing rate of exchange interaction with distance and the amplitude of interaction with the substrate. When the substrate is compressed, an increase in the amplitude of the interaction between the film and the substrate results in an increase in the phase transition temperature. The opposite effect occurs when the substrate is stretched. The hysteresis loop changes its shape and parameters when the substrate is deformed. Compression and stretching of the substrate results in a decrease in coercive force. The reduction in coercive force when compressing the substrate is greater than when stretching. The magnetization of the film is reduced by deformations at a fixed temperature.

An intense positron sources is a demanding element in the design of future lepton colliders. A crystal-based hybrid positron source could be an alternative to a more conventional scheme based on the electron conversion into positron in a thick amorphous target. The conceptual idea of the hybrid source is to have two separate objects, a photon radiator and a photon-to-positron converter target. In such a scheme an electron beam crosses a thin axially oriented crystal with the emission of a channeling radiation, characterized by a considerably larger amount of photons if compared to Bremsstrahlung. The net result is an increase in the number of produced positrons at the converter target. In this paper we present the results of a beam test conducted at the DESY TB 21 with 5.6 GeV electron beam and a crystalline tungsten radiator. Experimental data clearly highlight an increased production of photons and they are critically compared with the outcomes of novel method to simulate the number of radiated photons, showing a very good agreement. Strong of this, the developed simulation tool has been exploited to design a simple scheme for a positron source based on oriented crystal, demonstrating the advantages in terms of reduction of both deposited energy and the peak energy deposition density if compared to conventional sources. The presented work opens the way for a realistic and detailed design of a hybrid crystal-based positron source for future lepton colliders.

A proof-of-principle experimental setup for the extraction of 6 GeV electrons from the DESY II Booster Synchrotron using the channeling effect in a bent crystal is elaborated. Various aspects of the experimental setup were investigated in detail, such as the particle beam dynamics during the extraction process, the manufacturing and characterization of bent crystals, and the detection of the extracted beam. In order to optimize the crystal geometry, the overall process of beam extraction was simulated, taking into account the influence of radiation energy losses. As result it is concluded that the multi-turn electron beam extraction efficiency can reach up to 16%. In principle this crystal-based beam extraction technique can be applied at any electron synchrotron in order to provide multi-GeV electron beams in a parasitic mode. This technique will allow to supply fixed-target experiments by intense high-quality monoenergetic electron beams. Furthermore, electron/positron crystal-based extraction from future lepton colliders may provide an access to unique experimental conditions for ultra-high energy fixed-target experiments including searches for new physics beyond the Standard Model.

We report the observation of the steering of 855 MeV electrons by bent silicon and germanium crystals at the MAinzer MIkrotron. Crystals with 15 μ m of length, bent along (111) planes, were exploited to investigate orientational coherent effects. By using a piezo-actuated mechanical holder, which allowed to remotely change the crystal curvature, it was possible to study the steering capability of planar channeling and volume reflection vs. the curvature radius and the atomic number, Z. For silicon, the channeling efficiency exceeds 35%, a record for negatively charged particles. This was possible due to the realization of a crystal with a thickness of the order of the dechanneling length. On the other hand, for germanium the efficiency is slightly below 10% due to the stronger contribution of multiple scattering for a higher-Z material. Nevertheless this is the first evidence of negative beam steering by planar channeling in a Ge crystal. Having determined for the first time the dechanneling length, one may design a Ge crystal based on such knowledge providing nearly the same channeling efficiency of silicon. The presented results are relevant for crystal-based beam manipulation as well as for the generation of e.m. radiation in bent and periodically bent crystals.

The article developed a mathematical model describing the deformation of reinforced concrete, taking into account its adhesion to reinforcement. The model consists of three layers: concrete, contact layer, reinforcement. The contact layer surrounding the reinforcement takes into account the complex deformation of the concrete when interacting with the profiled reinforcement. Arguments are presented for criteria that determine the transition of concrete, reinforcement and contact layer to limit states. A diagram of testing of reinforced concrete specimen has been proposed and a procedure for processing experimental data, which allow you to determine the bond parameters. Equations that bind the mechanical characteristics of the contact layer with two the bond parameters of concrete with reinforcement are obtained. The developed model was used in the numerical solution of the problem of static pull-out of reinforcement from concrete. The calculation of the finite element method showed a good correspondence with the experimental data, including during plastic deformation of the reinforcement. This shows the correctness of theoretical provisions and developed mathematical algorithms used to model the deformation of reinforced concrete.

We observed reduction of multiple Coulomb scattering of 855 MeV electrons within a Si crystalline plate w.r.t. an amorphous plate with the same mass thickness. The reduction owed to complete or partial suppression of the coherent part of multiple scattering in a crystal vs crystal orientation with the beam. Experimental data were collected at Mainz Mikrotron and critically compared to theoretical predictions and Monte Carlo simulations. Our results highlighted maximal 7% reduction of the r.m.s. scattering angle at certain beam alignment with the [100] crystal axes. However, partial reduction was recorded over a wide range of alignment of the electron beam with the crystal up to 15 ∘ . This evidence may be relevant to refine the modelling of multiple scattering in crystals for currently used software, which is interesting for detectors in nuclear, medical, high energy physics.

The paper investigates the stability of the Lotka — Volterra dynamic system ≪predator — two preys≫ with the help of variational method. This method is applicable for studying equilibrium stability non-linear dynamical systems of any kind and in any dimension. It approves its effectiveness even in cases where the use of the Lyapunov function causes great difficulties (for example, when solving tasks of large dimension). The proposed method is based on a variation method for estimating the rate of phase-state metric change for the perturbed system when the variable t → ∞. The disadvantage of the variation method is the fact that this method provides only the necessary conditions of stability. However, its it forms the first step in studying the stability of non-linear dynamical systems of any kind and any dimension.