Motion Of Particles In Channels Research Articles

Evolution of the stimulated resonance of a channeling electron beam

The motion of channeled particles in the co-moving coordinate system can be considered as a onedimensional oscillator (in the case of planar channeling) or as a two-dimensional atom (in the case of axial channeling). The transverse motion of channeled particles is characterized by the discrete spectrum; in this case, the probability of occupation of transverse-motion levels depends on the entrance angle of the charged particle with respect to the crystallographic axes of a single crystal. A charged channeled particle passing through a single crystal experiences the periodic action of lattice atoms. If the frequency of the external periodic action of the crystal lattice coincides with that of the transition of the channeled particle from one quantum state of transverse motion to another, then resonance excitation of the channeled particle can occur; it is similar to the excitation of atomic electrons by the periodic field of a monochromatic electromagnetic wave. In this paper, the resonance conditions are discussed and the dependence of the probability of the occupation of transverse-motion levels of channeled particles (electrons) on the single-crystal thickness is analyzed.

Resonance capture of electrons and positrons in the axial channeling mode at a crystal surface

The motion of channeled particles in a single crystal is determined by the continuous potential of the crystallographic axes. The transverse motion of particles in the axial channeling mode is characterized by a discrete energy spectrum. In this paper, the criteria for selection of the continuous potential and the conditions for quantization of the transverse energy for axially channeled particles are discussed, and the criterion for the resonance capture of particles in the axial channeling mode during particle entrance into a single crystal is formulated; it requires that the particle’s angular momentum with respect to the channel axis coincides with a quantity that is a multiple of Planck’s constant. The effect of resonance capture can be observed, for example, via an increase in the intensity of electromagnetic radiation of the beam of channeled particles in the optical range at frequencies corresponding to transitions between the allowed levels of transverse motion.

A computational study of trajectories of micro- and nano-particles with different shapes in flow through small channels

Transport of small particles, of micrometer and sub-micrometer size, by fluid occurs in many technological and biological systems. The channels through which the fluid flows are often with cross-sectional dimensions on the order of several to tens of micrometers. The aim of this study was to investigate effects of shape of micro- and nano-particles on particle trajectories when particles are transported within small channels as blood vessels. Efficiency of therapeutics by particles as the drug carriers is significantly dependent on particle trajectories. It is desirable to have particle trajectories approaching the vessel walls in order to increase therapeutic efficacy. We studied motion of particles in channels (pipes) for two physical conditions: Poiseuille flow, which is characteristic in pipe flow, and shear flow. Shear flow conditions are analyzed since the character of fluid flow near the wall in these systems can be approximated as shear, with a linear change of velocity with the distance from the wall. We here investigated trajectories of particles of different shapes in 2D flow using the finite element (FE) method, with a strong coupling approach for solid-fluid interaction and a remeshing procedure. The results give insight into the characteristics of the particle motion, e.g. trajectories and rotations, under various flow conditions in micron size channels, including flow in the presence of moving deformable discs. We demonstrate that the particle trajectories are essentially parallel to the wall for various conditions and that particle size and shape do not considerably alter the parallel nature of the trajectories.

A Mathematica package for calculation of planar channeling radiation spectra of relativistic electrons channeled in a diamond-structure single crystal (quantum approach)

The presented Mathematica code is an efficient tool for simulation of planar channeling radiation spectra of relativistic electrons channeled along major crystallographic planes of a diamond-structure single crystal. The program is based on the quantum theory of channeling radiation which has been successfully applied to study planar channeling at electron energies between 10 and 100 MeV. Continuum potentials for different planes of diamond, silicon and germanium single crystals are calculated using the Doyle–Turner approximation to the atomic scattering factor and taking thermal vibrations of the crystal atoms into account. Numerical methods are applied to solve the one-dimensional Schrödinger equation. The code is designed to calculate the electron wave functions, transverse electron states in the planar continuum potential, transition energies, line widths of channeling radiation and depth dependencies of the population of quantum states. Finally the spectral distribution of spontaneously emitted channeling radiation is obtained. The simulation of radiation spectra considerably facilitates the interpretation of experimental data. Program summaryProgram title: PCRCatalog identifier: AEOH_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOH_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 446No. of bytes in distributed program, including test data, etc.: 209805Distribution format: tar.gzProgramming language: Mathematica.Computer: Platforms on which Mathematica is available.Operating system: Operating systems on which Mathematica is available.RAM: 1 MBClassification: 7.10.Nature of problem:Planar channeling radiation is emitted by relativistic charged particles during traversing a single crystal in direction parallel to a crystallographic plane. Channeling is modeled as the motion of charged particles in a continuous planar potential which is formed by the spatially and thermally averaged action of the individual electrostatic potentials of the crystal atoms of the corresponding plane. Classically, the motion of channeled particles through the crystal resembles transverse oscillations being the source of radiation emission. For electrons of energy less than 100 MeV considered here, planar channeling has to be treated quantum mechanically by a one-dimensional Schrödinger equation for the transverse motion. Hence, this motion of the channeled electrons is restricted to a number of discrete (bound) channeling states in the planar continuum potential, and the emission of channeling radiation is caused by spontaneous electron transitions between these eigenstates. Due to relativistic and Doppler effects, the energy of the emitted photons directed into a narrow forward cone is typically shifted up by about three to five orders of magnitude. Consequently, the observed energy spectrum of channeling radiation is characterized by a number of radiation lines in the energy domain of hard X-rays. Channeling radiation may, therefore, be applied as an intense, tunable, quasi-monochromatic X-ray source.Solution method:The problem consists in finding the electron wave function for the planar continuum potential. Both the wave functions and corresponding energies of channeling states solve the Schrödinger equation of transverse electron motion. In the framework of the so-called many-beam formalism, solving the Schrödinger equation reduces to a eigenvector–eigenvalue problem of a Hermitian matrix. For that the program employs the mathematical tools allocated in the commercial computation software Mathematica. The electric field of the atomic planes in the crystal forces dipole oscillations of the channeled charged particles. In the quantum mechanical approach, the dipole approximation is also valid for spontaneous transitions between bound states. The transition strength for dedicated states depends on the magnitude of the corresponding dipole matrix element. The photon energy correlates with the particle energy, and the spectral width of radiation lines is a function of the life times of the channeling states.Running time:The program has been tested on a PC AMD Athlon X2 245 processor 2.9 GHz with 2 GB RAM. Depending on electron energy and crystal thickness, the running time of the program amounts to 5–10 min.

A theory of the bulk trapping of particles into a channeled transport mode

A theory describing the bulk trapping of heavy relativistic particles into a channeled transport mode is constructed. It is demonstrated that a discrete character of the atomic plane potential in a bent crystal explains the elastic energy losses for the transverse motion of channeled particles, which exceed the inelastic losses for the same motion by a factor of 107.