Diffracted channeling radiation for axial electron channeling

It is shown that, in contrast to diffracted channeling radiation (DCR) in the case of planar channeling, transitions of type 2 → 1, 3 → 2, 4 → 3, and so on make the main contribution to DCR in the case of axial channeling along an isolated axis. The angular DCR distributions for channeling of electrons with the energy corresponding to the Lorentz factor γ = 100 are calculated for an isolated axis using the Coulomb-type potential.     

Toward a three-dimensional treatment of channeling radiation

Abstract

Many authors have studied channeling radiation theoretically by means of the so called many beam approach. For axial channeling this approach tends to involve rather large eigenvalue problems if high accuracy is desired. With the extension to three-dimensional problems in mind we have therefore investigated the possibilities for a more efficient solution of these eigenvalue problems. The Lanczos algorithm [2] used in the preparation of Fig. 1 provides a substantial reduction of the numerical effort. We have also obtained some preliminary results for three-dimensional corrections to the tranverse problem. These corrections were found to be three-dimensional rather than longitudinal in character and tend to reduce the photon energy. The corrections are smaller than 1 percent for 4 MeV electrons in silicon. A more thorough investigation of these effects for the low energy part of the spectrum and a study of their impact on the high energy radiation [3] is now in progress. The conventional transverse many beam approach based on the Lindhard continuum approximation does not describe the latter effect.     

Chaotic behavior of channeling particles

Channeling describes the collimated motion of energetic charged particles along the lattice plane or axis in a crystal. The energetic particles are steered through the channels formed by strings of atomic constituents in the lattice. In the case of planar channeling, the motion of a charged particle between the atomic planes can be periodic or quasiperiodic, such as a simple oscillatory motion in the transverse direction. In practice, however, the periodic motion of the channeling particles can be accompanied by an irregular, chaotic behavior. In this paper, the Moliere potential, which is considered as a good analytical approximation for the interaction of channeling particles with the rows of atoms in the lattice, is used to simulate the channeling behavior of positively charged particles in a tungsten (100) crystal plane. By appropriate selection of channeling parameters, such as the projectile energy E(0) and incident angle psi(0), the transition of channeling particles from regular to chaotic motion is demonstrated. It is argued that the fine structures that appear in the angular scan channeling experiments are due to the particles' chaotic motion.     

Nonlinear theory of channeling of radiation by a ribbon-shaped stream of cyclotron oscillators

The features of the nonlinear stage of radiation from transversely bounded, magnetically steered helical and rectilinear electron streams in a homogeneous medium and in vacuum are investigated theoretically under conditions of the normal and anomalous Doppler effects. The evolution of the transverse distribution of the radiated field is investigated, and the channeling effect of the electron stream is demonstrated. It is shown that in the radiation from a helical stream in a plasmalike medium a practically complete conversion of the energy of gyrational motion of the electrons into energy of electromagnetic oscillations can occur on account of the automatic fine tuning of the radiation angle. Zh. Tekh. Fiz. 69, 9–14 (January 1999)     

Spectral method in axial channeling theory

The energy quantization of transverse particle motion in continuous potentials of atomic chains and planes can occur when fast charged particles travel in crystals. In the proposed paper, the energy levels of electrons moving in the mode of axial channeling in a system of parallel atomic chains have been found (Si crystal [110] chains have been used as an example). The energy eigenvalues were determined numerically using the so-called spectral method, which shows itself to good advantage in the problem of the plane channeling of charged particles in crystals.     

Quantum effects for parametric X-ray radiation during channeling: Theory and first experimental observation

The theory of X-ray radiation from relativistic channeled electrons at the Bragg angles—parametric X-ray radiation (PXR) during channeling (PXRC)—is developed while accounting for two quantum effects: the initial population of bound states of transverse motion and the transverse “form-factor” of channeled electrons. An experiment was conducted using a 255 MeV electron beam from a linac at the SAGA Light Source. We have identified a difference in the angular distributions of PXR and PXRC and obtained a fairly good agreement between the theoretical and experimental results.     

Channeling radiation: Past achievements and future prospects

Abstract

When a relativistic charged particle passes through a single crystal very nearly along a major crystalline plane or axis so that it is channeled in that direction, it undergoes periodic motion in the plane transverse to this direction and hence it can radiate. Quantum mechanically, this channeling radiation corresponds to a radiative transition between two eigenstates of the transverse crystalline potential; when the transition occurs between two bound states, a sharp spectral line is emitted. When there are only two bound states (for incident electrons), or when the interplaner potential is nearly harmonic (as for incident positrons), the emitted radiation is nearly monochromatic. Since the discovery of channeling radiation at the LLNL Electron-Positron Linear Accelerator, many of its properties have been delineated, both there and elsewhere. For example, channeling radiation is very intense, forward-directed, easily tunable, and for the planar case, linearly polarized. Channeling radiation has been used as a probe both of the interplanar potentials and other properties of perfect crystals and of the effects of impurities and defects in imperfect crystals. Finally, channeling radiation has great potential use as a photon source for numerous other applications in several fields of science and technology.

This paper is intended to keynote the first International Conference on Coherent Radiation Processes in Strong Fields by recalling some history of the discovery and exploitation to date of channeling radiation. Studies of channeling radiation, in addition to elucidating the physics of the process itself, its application to the determination of properties of perfect and imperfect crystals, and its potential application to a large variety of fields by its use as an intense, monochromatic, forward-directed, tunable, and polarized photon source, have spawned an entire industry of studies of other coherent radiation processes, all consisting of photon production from beams of relativistic charged particles traversing periodic structures, which constitute the principal subject matter of this Conference. This paper will be limited to the discussion of channeling radiation and some of its applications. It will be in the nature of an illustrative exposition, showing many of the features of channeling radiation and its applications in a qualitative way. Several detailed studies of channeling radiation will be presented later in the Conference.     

Linear polarization of channeling radiation from axially channeled electrons

Abstract

The degree of polarization of channeling radiation emitted by axially channeled electrons has been calculated using the many-beam method. The polarization was found to be substantial, and to increase monotonically with the channeling angle. The many-beam results are compared with those obtained from the single-string approximation and are found to be significantly different.     

New approximation for the interaction potential of light channeled particles with crystals

A new approximation for the continuous interaction potentials of atomic planes and strings with channeled electrons and positrons in crystals is proposed. A model in which atomic electron distributions within a certain atomic subshell are assumed to be exponentially decaying is used. Contrary to the Thomas-Fermi (TF) and Thomas-Fermi-Dirac (TFD) models this approach takes into account the shell structure of atoms in reasonably good agreement with the Hartree-Fock method (HF). Simple analytical expressions for the continuous plane (string) potentials are given. Calculations of several planar potentials for positrons channeled in silicon and tungsten are presented. Results are compared with widely known Lindhard and Molière approximations. Some estimates of the Kumakhov spontaneous radiation intensity under positron planar channeling conditions in the classical approximation are also given.     

Large-angle channeling radiation from relativistic electrons in optically transparent crystals

In the work within the frame of quantum electrodynamics are obtained new formulae describing the large-angle photon emission from channeled electrons with taking into account of the dispersion of refractive index. Calculations based on these formulae show that the spectral and angular distributions of large-angle optical and ultraviolet radiation from planar channeled sub-GeV electrons in optically transparent crystal reflect the band structure of transverse energy levels of channeled electrons. Comparison with ordinary Cherenkov radiation spectrum reveals that channeling (depending on the beam energy) leads to sufficient change of the large-angle emission spectrum.     

Diffraction and channeling in nanotubes

A theory of the interaction of fast charged particles and gamma rays with nanotubes with different helicity is developed. Analytical expressions are obtained for the potential and the electron density of a nanotube taking account of the anisotropic thermal vibrations of the atoms. A system of equations determining the quantum states of the transverse motion of relativistic electrons, positrons, and x-ray photons in a superlattice consisting of nanotubes is formulated, and methods for solving this system are developed. Calculations of the soft x-ray Bragg reflection coefficients of a superlattice are performed in the two-wave approximation of the dynamical theory of diffraction.     

Simulation of radiation energy losses by channeled relativistic electrons in a crystal

A computer code is developed to calculate the radiation energy losses (RELs) of electrons during both 〈100〉 axis and (100) plane channeling in a thin Si crystal. A computer simulation of these losses is carried out by taking the initial angular divergence of the beam into account, and the REL dependences on the angle of electron entry into the crystal are obtained for both axial and planar channeling (orientational dependences). The calculations are carried out in connection with experiments on the interaction of 20–255 MeV electrons with crystals conducted at the SAGA Light Source linear accelerator (Tosu, Saga, Japan). The simulation results show the possibility of using the orientational dependence of the RELs of channeled electrons in thin crystals to diagnose the initial angular divergence of the electron beam and to orient crystals.     

Parametric channeling and collapse of beams of charged particles with internal structure in crystals: 2. Parametric processes during channeling of atomic ions, nuclei, and relativistic electrons in crystals

Features of parametric effects during channeling of atomic ions, nuclei, and relativistic electrons (positrons) in crystals were considered. It was shown that parametric coupling between ion channeling states in the field of crystal axes and planes and electronic states in the ion volume leads to the possibility of “parametric collapse” of the beam, i.e., a decrease in the oscillation amplitude of the atomic ion in the channel due to periodic transfer of the ion oscillation energy to the inner electron of the atom. The same effect can be used to cool beams due to energy transfer to intrinsic nuclear states with low energy levels. It was shown that parametric cooling of beams with a decrease in the transverse energy can also occur during axial channeling of relativistic electron beams. This process results from the parametric coupling between channeling states, which are caused by the particle charge and electron spin states in an effective magnetic field induced in the moving coordinate system.     

Frequency-angular characteristics of quasicharacteristic radiation in the case of plane channeling of relativistic electrons in crystals

In this paper, a theoretical study of the frequency-angular characteristics of short-wavelength quasicharacteristic radiation is presented. This radiation is produced as a result of transitions between the energy levels of transverse motion in the case of plane channeling of relativistic electrons in various crystals. Detailed numerical analysis shows that short-wavelength radiation, the parameters of which remain unchanged in a broad range of particle energies, exists at small angles in the domain of existence of the normal complex Doppler effect.     

Temperature dependence of the efficiency at which electrons are captured into axial channeling

A procedure for calculating the efficiency at which electrons are captured into axial channeling with a realistic axis potential is discussed. That region in the space of the electron's total transverse energy E and angular momentum L (integrals of motion) which corresponds to stable bound states of the electron with an atomic row is found. The temperature dependence of the capture coefficient is analyzed. As the crystal temperature is increased, the capture coefficient decreases, to a particularly noticeable extent for beams making a small angle with the crystallographic axis and for crystals having a high atomic number z.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 69–74, May, 1988.     

Proton channeling studies in thin crystals with a supercollimated beam

Abstract

A supercollimated beam of 4 MeV H^? ions with an angular spread of 1.5 × 10^?3 degrees, a diameter of 25 μ and a current of 10 picoamps was used to study the axial and planar channeling characteristics of single crystal silicon samples ranging in thickness from 0.5 to 1.0 μ. Since the angular spread of the beam is much smaller than most of the gross angular phenomena associated with channeling, it is possible to study the detailed characteristics of both planar and axial channeling with greater precision than before. Preliminary results indicate that this technique will allow a direct study of interatomic or continuum potential distributions and will also be useful for studying nuclear multiple scattering as a function of the tranverse energy of channeled particles relative to atomic rows and planar directions.     

Orbital angular momentum of channeling radiation from relativistic electrons in thin Si crystal

We propose to use channeling radiation (CR) from relativistic electrons as a source of high energy twisted photons in the MeV range. We calculate numerically the orbital angular momentum (OAM) of radiation produced by electrons with the energies $155÷2500$ MeV for the axial and planar channeling in the thin Si crystal. We obtain that the average OAM of CR in this case is approximately $1÷6?$ per photon with the photon energies about $1÷2$ MeV.     

Radiation from 39 and 45 MeV electrons channeled in Lithium Niobate

Abstract

Channeling radiation from 39 and 45 MeV electrons channeled along the <0001> axis, the (0110) plane and the (1210) plane of a 30 μm thick LiNbO ₃ crystal has been measured. Calculations of the planar crystal potentials were performed by means of the many-beam formalism. Good agreement between theory and experiment is obtained for the planar channeling radiation. Associated with channeling additional radiation lines have been observed, which may be explained by a periodic perturbation of the continuum potential.     

Temperature dependence of muon-decay positron channeling in semiconductors

Planar channeling data ofμ ⁺-decay positrons in various semiconductors are reported. Together with the extensive spectroscopic data supplied by transverse μSR, the location of the different states of the hydrogen pseudo-isotopeμ ⁺ e⁻ (muonium) can be identified by means of planar simulations. In high purity silicon as well as in gallium arsenide a thermally activated site transition is observed which can be assigned to a transition between different muonium states.