On the quantum theory of radiation by channeling particles

On the basis of the Dirac equation the intensity of the spontaneous γ-radiation by relativistic channeling particles has been calculated. In the ultrarelativistic limit the quantum treatment gives a result close to that of the classic calculation.     

Production of hypothetical,light neutral particles in high-energy channeling

The rates forX ^° creation by photons and electrons channeling along a crystal axis are estimated. The process is found to depend strongly on the parameters of the crystal fields. PromisingX ^° production rates can therefore be obtained for germanium rather than for lighter elements.     

Electromagnetic radiation of relativistic channeling particles (the Kumakhov effect)

A new type of electromagnetic radiation characteristic for channeling in single crystals relativistic particles which has been recently predicted by Kumakhov and proved experimentally is reviewed. It is observed as one or several strong peaks in the soft part of the Bremsstrahlung, surpassing it by a factor of nearly one hundred. At moderate electron energies sharp peaks corresponding to spontaneous transitions between quantum eigenstates of the channeling particles were detected. But for high energy channeling electrons these peaks merge into one broad classical peak with the frequency determined by the collective potential of an atomic row or plane. This radiation also strongly depends on the charge sign, velocity and mass of the particle.     

Chaotic behavior in stellar dynamos

Slowly rotating main-sequence stars with deep convective zones have activity cycles like the sun's. The solar cycle is aperiodic and modulated to give intervals of reduced activity. A simple sixth-order system, obtained by truncating the dynamo equations, has solutions that mimic this behavior. The transition to chaos is analyzed and the astrophysical significance of these results is discussed.     

Chaotic motion of dust particles in planetary magnetospheres

We numerically investigate the motion of a charged particle in a planetary magnetosphere using several kinds of equatorial plane phase portraits determined by two dynamical parameters: the charge-to-mass ratio and the z-component of the angular momentum. The dependence of chaos on any of the three factors including the two parameters and the energy is mainly discussed. It is found that increasing the energy or the absolute value of the ratio always causes the extent of chaos. However, chaos is weaker for larger angular momentum. Qualitative interpretations to the results obtained are also given.     

Chaotic behavior learning of Chua's circuit

Least-square support vector machines(LS-SVM) are applied for learning the chaotic behavior of Chua’s circuit.The system is divided into three multiple-input single-output(MISO) structures and the LS-SVM are trained individually.Comparing with classical approaches,the proposed one reduces the structural complexity and the selection of parameters is avoided.Some parameters of the attractor are used to compare the chaotic behavior of the reconstructed and the original systems for model validation.Results show that the LS-SVM combined with the MISO can be trained to identify the underlying link among Chua’s circuit state variables,and exhibit the chaotic attractors under the autonomous working mode.     

Chaotic scattering and acceleration of particles by waves

Relativistic charged particles in a uniform magnetic field and traveling waves of large amplitude can be accelerated limitlessly. Since much of phase space is chaotic the process can be viewed as chaotic scattering on waves. For multiple waves an explicit map arises with unusual properties. It contains infinite island chains around nonperiodic orbits and it is also an example of transient chaos in a Hamiltonian system.     

Chaotic phenomena of charged particles in crystal lattices

In this article, we have applied the methods of chaos theory to channeling phenomena of positive charged particles in crystal lattices. In particular, we studied the transition between two ordered types of motion; i.e., motion parallel to a crystal axis (axial channeling) and to a crystal plane (planar channeling), respectively. The transition between these two regimes turns out to occur through an angular range in which the particle motion is highly disordered and the region of phase space spanned by the particle is much larger than the one swept in the two ordered motions. We have evaluated the maximum Lyapunov exponent with the method put forward by Rosenstein et al. [Physica D 65, 117 (1993)] and by Kantz [Phys. Lett. A 185, 77 (1994)]. Moreover, we estimated the correlation dimension by using the Grassberger-Procaccia method. We found that at the transition the system exhibits a very complex behavior showing an exponential divergence of the trajectories corresponding to a positive Lyapunov exponent and a noninteger value of the correlation dimension. These results turn out to be linked to a physical interpretation. The Lyapunov exponents are in agreement with the model by Akhiezer et al. [Phys. Rep. 203, 289 (1991)], based on the equivalence between the ion motion along the crystal plane described as a "string of strings" and the "kicked" rotator. The nonintegral value of the correlation dimension can be explained by the nonconservation of transverse energy at the transition.     

Focusing of atomic and molecular particles upon channeling in chiral carbon nanotubes

The focusing of atomic and molecular particles near the nanotube axis using a model of a carbon nanotube (CNT) with discrete arrangement of atoms in its wall is studied. The degree of focusing of channeling particles in CNTs depends not only on the diameter of the CNTs, but also on its chirality. It is shown that the concentration of channeling particles in the tube’s central part is higher for chiral nanotubes.     

Chaotic behavior in transverse-mode laser dynamics

We analyze chaotic behavior found in numerical simulations of the transverse pattern dynamics of a laser demonstrating that in some cases chaos originates in phase dynamics and is of low dimension. Investigations of both a Ginzburg-Landau equation for the complex field amplitude of the laser output and a Kuramoto-Sivashinsky-type equation for only the phase of that complex field equation find the same behavior. Both equations can be expanded in terms of spatial modes and in the chaotic regime the behavior of the modal amplitudes seems relatively independent. However, the fluctuations of the modal amplitudes are sufficiently correlated so that the spatiotemporal dynamics is a form of low dimensional chaos rather than a more complex turbulent behavior or even one that might merit the term spatiotemporal chaos.     

Chaotic motion of test particles in the Ernst space-time

Trajectories of test particles in the Ernst space-time are studied. The Poincaré surfaces of section are constructed and Lyapunov characteristic exponents are evaluated for a selected set of trajectories. This approach indicates that the number of isolating integrals is not sufficient to separate equations of motion and the particle trajectories are not integrable.     

Observation of channeling and volume reflection in bent crystals for high-energy negative particles

Deflection due to planar channeling and volume reflection in short bent silicon crystals was observed for the first time for 150 GeV/c negative particles, π⁻ mesons, at one of the secondary beams of the CERN SPS. The deflection efficiency was about 30% for channeling and higher than 80% for volume reflection. Volume reflection occurs, in spite of the attractive character of the forces acting between the particles and the crystal planes, in a wide angular range of the crystal orientations determined by the crystal bend angle.     

Spectral method in quantum theory of channeling phenomena of fast charged particles in crystals

We show the possibility of using the spectral method to determine the quantum characteristics of interaction between fast charged particles and crystal when the channeling occurs. Basing on this method, we have developed the procedure for calculation of particles transversal motions eigenlevels for plane channeling. We considered origin of new levels with increasing of particle's energy and zone structure forming from these levels with increasing number of potential wells. We discuss also the possibility of using the spectral method in number of other problems of quantum theory of channeling.     

Role of vacancies and adsorbed atoms in the channeling of molecular particles in CNTs

The channeling of atomic and molecular particles in carbon nanotubes is considered in the presence of vacancies on the walls and of adsorbed atoms inside them. It is shown that the significant influence of the indicated disturbance of nanotube structures greatly affects channeling, which makes it possible to use beams of atomic and molecular particles to probe nanotubes.     

Chaotic behavior in noninteger-order cellular neural networks

In this paper, a simple system showing chaotic behavior is introduced. It is based on the well-known concept of cellular neural networks (CNNs), which have already given good results in generating complex dynamics. The peculiarity of the CNN model consists in the fact that it replaces the traditional first-order cell with a noninteger-order one. The introduction of the fractional cell, with a suitable choice of the coupling parameters, leads to the onset of chaos in a simple two-cell system. A theoretical approach, based on the harmonic balance theory, has been used to investigate the existence of chaos. A circuit realization of the proposed fractional two-cell chaotic CNN is reported and the corresponding strange attractor is also shown.