Emission from relativistic fermions in planar channeling

The radiation power from an electron moving in a focusing electrostatic field is derived for the case of planar channeling, with allowance for the electron spin. It is shown that the radiated power is independent of the initial spin orientation for an oscillator potential in the electrostatic field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 63–66, August, 1984.I am indebted for assistance to professors I. M. Ternov and V. G. Bagrov.     

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.     

Rigorous channeling stability theorems

This letter states the first rigorous results on the stability of channeling trajectories of fast charged particles in crystals within the context of non-trivial two- and three-dimensional non-relativistic classical models. These results were obtained by deriving asymptotic forms of the relevant canonical maps and then applying suitable versions of Moser's twist theorem.     

Critical parameters of channeling

Basic methods for calculating critical channeling parameters that play a decisive role in the problem of dechanneling of ions are reviewed. The analytic expressions derived for the threshold energy of channeling, the critical transverse energy, and the closest approach distance between particles and atomic chains or planes forming the channels, as well as critical angles of axial and planar channeling, are valid in a wide range of particle energies. The dependence of critical parameters of channeling on the temperature of crystals is analyzed.     

Diffusion coefficients in channeling

Making use of the general formula introduced by Ohtsuki, detailed calculations for diffusion coefficients in channeling are performed. The nuclear and single electron excitations are considered separately compared with the plasmon excitation. Some analytic expressions proposed in previous paper are confirmed.     

Fast-ion channeling in fullerene crystals

The motion of H⁺ and He⁺ ions with energies of 230 and 2000 keV in C₆₀ and K₃C₆₀ crystals was calculated by the Monte Carlo method. Ion channeling was shown to occur in the 〈100〉 and 〈111〉 directions. The main parameters characterizing channeling were determined. Medium-energy ions were found to be preferable in the detection of channeling in C₆₀ films.     

On channeling in LiH crystals

The thermal-oscillation-averaged potential of channeling along the charged $(1\bar 11)$ and (111) planes in a LiH crystal is derived. The theoretical value of the energy of an emitted photon that meets the transition between levels of adjacent potential wells is found to agree well with experimental data.     

Modification of the theory of diffracted channeling radiation for axial electron and positron channeling

A new type of combinational channeling radiation induced by subbarrier (interband) transitions for the transverse motion of relativistic electrons (positrons) is studied. It is known as diffracted channeling radiation (DCR). The formula describing the DCR angular distribution in the case of axial channeling is obtained by taking into account the band structure of energy levels for the transverse motion of electrons (positrons). It is shown that, in the two-wave approximation of the wave function A(r) of virtual photons, the DCR matrix elements in the dipole approximation for axial and plane channeling coincide formally (with the dimension of the problem taken into account). However, the formulas for DCR angular distributions in the cases of axial and plane channeling differ considerably.     

Solitons at the electron channeling

The features of electron channeling in single crystals are investigated. The channeling potential at the periodicity interval is shown to be a potential of the soliton type, which should determine new features of electron channeling.     

Alpha channeling in mirror machines

The injection of radio frequency waves can cool charged particles trapped in a magnetic mirror. This cooling effect relies upon waves with azimuthal and axial phase velocities resonating with ions in different axial locations. The ions are then forced to diffuse along highly constrained orbits, such that they can only exit the magnetic trap at low energy. This cooling effect may have application to magnetic fusion mirror machines, where the free energy of the fusion by-products, the alpha particles, might be channeled into the waves that effect the cooling, thereby both extracting the fusion ash quickly and making that energy available in a convenient form for more useful purposes.     

Critical angles for axial channeling

The critical angle for axial proton channeling has been measured as a function of temperature for a number of different crystals. The results are consistently below the values predicted from simple analytical estimates. The magnitude of this discrepancy does not seem to depend on the specific lattice structure. In point of fact, all the results are consistent with a relationship ψ_1/2 = α(p/a). ψ₁, where ψ₁ is Lindhard's characteristic angle, and α(p/a)is a function of the thermal vibrational amplitude p, measured in units of the Thomas-Fermi screening distance a. A formula for α(p/a), derived by Barrett from computer simulations, on the average predicts the magnitude of α quite well, but the observed functional dependence on p/a is considerably stronger than predicted.     

Muon decay channeling in silicon

The angular distribution of positrons from muon decay in an oriented [111] Si wafer shows a symmetric pattern of six lines of minimum counting rate radiating from a central minimum. The pattern results from positron blocking by the (110) planes and [111) axis. The measurement technique and the dependence of the features on positron energy, muon implanation depth and sample temperature are discussed.     

Peculiarities of heavy ion channeling

Abstract

Depth distributions of implanted Mg⁺- and Ca⁺-ions and the corresponding radiation damage were studied for different channeling orientations of silicon crystals. The shape of the implantation profiles is discussed by using simple models for dechanneling and energy loss processes. A correlation between dechanneling, damage production and depth distributions of the channeled ions could be observed. This correlation is seen by the maxima shifts in damage and implanted ion distributions between channel and random incidence.     

Self channeling of whistler waves

Channels of excess plasma density aligned along the magnetic field guide whistler without spatial divergence. If the whistler wave is of sufficient intensity it maintains the channel through its own radiation pressure which pushes the plasma towards regions of increasing wave amplitude.     

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.     

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.     

Temperature effect in antiproton channeling

The temperature dependence of axially channeled antiprotons in a Si crystal is studied using computer simulation. The number of channeled particles and the energy and angular distributions are calculated for antiprotons with an energy of 300 keV in the temperature range of 100 to 1000 K in the 〈100〉, 〈110〉, and 〈111〉 channels. The roles of the potential and atomic thermal vibrations are studied thoroughly. It is found that dechanneling depends on the crystal temperature. There exists an optimal temperature, which is dependent on the axis direction, for which dechanneling is minimal.