Evolution of the stimulated resonance of a channeling electron beam

Abstract

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.