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V. V. Syshchenko

Publications and source records attributed to V. V. Syshchenko.

14 recordsLinked to original sources
arXiv2024

Mixed (Regular and Chaotic) Dynamics under the Channeling of the High Energy Positrons in [100] Direction of the Silicon Crystal and Podolskiy-Narimanov Distribution

The character of motion (regular or chaotic) on the quantum level manifests itself in the statistics of the set of the system's energy levels. The completely regular case generates the sequence of the levels with exponential (Poisson) level spacing distribution; the completely chaotic one -- with Wigner distribution. The most interesting case is the co-existence of the regular and chaotic motion domains in the phase space of the system under consideration. The assumption of independent generation of two level sequencies by one chaotic domain and by all regular domains leads to Berry--Robnik distribution. However, the presence of the chaotic motion domain in the phase space affects the levels produced by the regular domains via the so-called chaos-assisted tunneling (CAT) that leads to Podolskiy--Narimanov distribution of the level spacings. This distribution needs the mean amplitude of the tunnel transition and the relative contribution of the regular domains to the mean level density as the parameters. Using their estimations for the transverse motion of the high energy positrons channeling near [100] direction in the silicon crystal we found that Podolskiy--Narimanov distribution demonstrates the best agreement with the level spacing distribution.

physics.acc-ph↗
arXiv2024

Dynamical Chaos and Level Splitting under the Channeling of the High Energy Positrons in [100] Direction of the Silicon Crystal

The motion of charged particles in a crystal in the axial channeling regime can be both regular and chaotic. The chaos in quantum case manifests itself in the statistical properties of the energy levels set. These properties have been studied previously for the electrons channeling along [110] direction of the silicon crystal, in the case when the classical motion was completely chaotic, as well as for the ones channeling along [100] direction, when the classical motion can be both regular and chaotic for the same energy depending on the initial conditions. Here we study the positrons channeling in [100] direction. This case is of special interest due to the substantial tunneling probability between dynamically isolated regular motion domains in the phase space. The interaction of the energy levels via tunneling distinctly changes the level spacing statistics. All transverse motion energy levels as well as corresponding stationary wave functions are computed numerically for the 30 GeV positrons channeling in [100] direction of the silicon crystal. The values of the matrix elements for the tunnel transitions are extractad from these data. These results confirm the chaos assistance for the tunneling and the level splitting. These values will be used in the further researches of the quantum chaos manifestations in the channeling phenomenon.

physics.acc-ph↗
arXiv2019

Regular and Chaotic Motion Domains in the Channeling Electron's Phase Space and Mean Level Density for Its Transverse Motion Energy

The motion of charged particles in a crystal in the axial channeling regime can be both regular and chaotic. The chaos in quantum case manifests itself in the statistical properties of the energy levels set. These properties have been studied previously for the electrons channeling along [110] direction of the silicon crystal, in the case when the classical motion was completely chaotic. The case of channeling along [100] direction is of special interest because the classical motion here can be both regular and chaotic for the same energy depending on the initial conditions. The semiclassical energy level density (as well as its part that corresponds to the regular motion domains in the phase space) is computed for the 10 GeV channeling electrons and positrons. It is demonstrated that the level spacing distribution for both electrons and positrons can be better described by Berry--Robnik distribution than by both Wigner (completely chaotic case) or Poisson (completely regular case) distributions.

physics.acc-ph↗
arXiv2019

Eikonal Approximation and the Conical Effect in Smith-Purcell Radiation

The diffraction and transition radiation under normal incidence of a particle to the semi-infinite dielectric plate had been considered previously using the eikonal approximation in the transition radiation theory. This approach is valid for the high radiation frequencies domain (where the dielectric permittivity of the plate material is close to unit), including X-ray domain. In the present report this method is applied to the case of oblique incidence of the particle on the plate (but parallel to the plate's edge) as well as to the periodic set of such plates (Smith-Purcell radiation). The oblique incidence of the particle (both in the case of the single plate and in the case of the periodic grating of such plates) leads to the so called conical effect in the radiation angular distribution observed recently. We outline that the origin of this effect lies in the superluminal motion along the plate's edge of the disturbance produced by the incident particle's field in the plates. The analogous effects arise in various physical situations. Also we compare our results to ones obtained using different technique.

physics.acc-ph↗
arXiv2017

Diffraction and Smith-Purcell radiation on the hemispherical bulges in a metal plate

The radiation resulting from the uniform motion of a charged particle near a hemispheric bulge in a metal plane is considered. The description of the radiation process based on the method of images is developed for the case of non-relativistic particle and perfectly conducting target. The spectral-angular and spectral densities of the diffraction radiation on the single bulge (as well as the Smith-Purcell radiation on the periodic string of bulges) are computed. The possibility of application of the developed approach to the case of relativistic incident particle is discussed.

physics.acc-ph↗
arXiv2017

Positrons vs electrons channeling in silicon crystal: energy levels, wave functions and quantum chaos manifestations

The motion of fast electrons through the crystal during axial channeling could be regular and chaotic. The dynamical chaos in quantum systems manifests itself in both statistical properties of energy spectra and morphology of wave functions of the individual stationary states. In this report, we investigate the axial channeling of high and low energy electrons and positrons near [100] direction of a silicon crystal. This case is particularly interesting because of the fact that the chaotic motion domain occupies only a small part of the phase space for the channeling electrons whereas the motion of the channeling positrons is substantially chaotic for the almost all initial conditions. The energy levels of transverse motion, as well as the wave functions of the stationary states, have been computed numerically by the method presented at previous RREPS. Note that the potential of the elementary cell in (100) plane of silicon crystal possesses the symmetry of the square. The group theory methods had been used for classification of the computed eigenfunctions and identification of the non-degenerate and doubly degenerate energy levels. The channeling radiation spectrum for the low energy electrons has been also computed.

physics.acc-ph↗
arXiv2015

Structure of the channeling electrons wave functions under dynamical chaos conditions

The stationary wave functions of fast electrons axially channeling in the silicon crystal near [110] direction have been found numerically for integrable and non-integrable cases, for which the classical motion is regular and chaotic, respectively. The nodal structure of the wave functions in the quasi-classical region, where the energy levels density is high, is agreed with quantum chaos theory predictions.

physics.acc-ph↗
arXiv2013

On spectral method in the axial channeling theory

The quantization of the transverse motion energy in the continuous potentials of atomic strings and planes can take place under passage of fast charged particles through crystals. The energy levels for electron moving in axial channeling regime in a system of parallel atomic strings (for instance, [110] strings of a silicon crystal) are found in this work for the electron energy of order of several tens of MeV, when a total number of energy levels becomes large (up to several hundreds). High resolution of the spectral method used for energy level search has been demonstrated. Hence this method could be useful for investigation of quantum chaos problem.

physics.acc-ph↗
arXiv2011

Incoherent bremsstrahlung in flat and bent crystals

Incoherent bremsstrahlung by high-energy particles in crystal is due to the thermal spread of atoms in relation to their equilibrium positions in the lattice. The simulation procedure developed earlier for the incoherent radiation is applied to the case of the electrons and positrons motion in the sinusoidally bent crystal. The results of simulation are in agreement with the data of recent experiments carried out at the Mainz Microtron MAMI. The possibility of use of the sinusoidally bent crystals as undulators is discussed.

physics.acc-ph↗
arXiv2010

Contribution of incoherent effects to the orientation dependence of bremsstrahlung from rapid electrons in crystal

The bremsstrahlung cross section for relativistic electrons in a crystal is split into the sum of coherent and incoherent parts (the last is due to a thermal motion of atoms in the crystal). Although the spectrum of incoherent radiation in crystal is similar to one in amorphous medium, the incoherent radiation intensity could demonstrate substantial dependence on the crystal orientation due to the electrons' flux redistribution in the crystal. In the present paper we apply our method of the incoherent bremsstrahlung simulation developed earlier to interpretation of some recent experimental results obtained at the Mainz Microtron MAMI.

physics.acc-ph↗
arXiv2010

On the motion of high-energy wave packets and the transition radiation by "half-bare'' electron

The problem of the motion of high-energy wave packets combined of free electromagnetic waves is considered. It is demonstrated that the transformation of such packets to the packet of spherically diverging waves happens on long distances along the packet's motion direction, that substantially exceed the radiated wavelength. The transition radiation by the ``half-bare'' ultrarelativistic electron is considered. It is demonstrated that the transition radiation by such an electron on the targets located inside and outside the coherence length of the radiation process would be substantially different.

physics.acc-ph↗
arXiv2010

Transition radiation on semi-infinite plate and Smith-Purcell effect

The Smith-Purcell radiation is usually measured when an electron passes over the grating of metallic stripes. However, for high frequencies (exceeding the plasma frequency of the grating material) none material could be treated as a conductor, but ought to be considered as a dielectric with plasma-like permittivity. So for describing Smith-Purcell radiation in the range of high frequencies new theoretical approaches are needed. In the present paper we apply the simple variant of eikonal approximation developed earlier to the case of radiation on the set of parallel semi-infinite dielectric plates. The formulae obtained describe the radiation generated by the particles both passing through the plates (traditionally referred as "transition radiation") and moving in vacuum over the grating formed by the edges of the plates (traditionally referred as "diffraction radiation", and, taking into account the periodicity of the plates arrangement, as Smith-Purcell radiation).

physics.acc-ph↗
arXiv2010

Incoherent bremsstrahlung in flat and bent crystal

The bremsstrahlung cross section for relativistic electrons in a crystal is split into the sum of coherent and incoherent parts (the last is due to a thermal motion of atoms in the crystal). Although the spectrum of incoherent radiation in crystal is similar to one in amorphous medium, the incoherent radiation intensity could demonstrate substantial dependence on the crystal orientation due to the electrons' flux redistribution in the crystal. In the present paper we apply our method of the incoherent bremsstrahlung simulation developed earlier to interpretation of some recent experimental results obtained at the Mainz Microtron MAMI.

physics.acc-ph↗