Diffraction of Radiation from Channelled Charged Particles

Abstract

An explicit expression for cross-section and radiation spectrum at diffraction is calculated. It is shown that photons emitted by channelled particles form a typical diffraction pattern which contains information about the crystal structure. It is also shown that the change of the longitudinal energy of the particle caused by the radiation braking becomes important when the particle energy is increesed.

Diffraction phenomena in spontaneous and stimulated radiation by relativistic particles in crystals (Review)

“…Due to the dependence of the refractive index under diffraction on a frequency and a particle motion direction, the relation (1) and (2) determining the radiated photon spectrum are the equations with several solutions [13,17,19,27].…”

“…In the dipole approximation, that is true for the X-ray radiation, we have ~ in an arbitrary nondipole case gnf is defined in [17,18],…”

“…Let us follow below the theoretical consideration of PXR derived in [34][35][36][37][42][43][44][45][46]56], According to (2.9), for the calculation of the differential number of emitted photons we need know the solution ~-) (r,ro) which was given, for example, in [2,17] for an arbitrary geometry of two-beam diffraction (Bragg and Laue, see Fig. 3).…”

“…The description of channeled particle motion by the help of one-or two-dimensional Bloch functions was given in [125]. The expressions for spectral-angular DRO distribution for different cases of photon dynamical diffraction were obtained in [17][18][19]. For example, in the case of two-wave Laue diffraction the spectral-angular distribution of DRO can be written in the following way [ 17 -19]": (3.1) where…”

“…<f>nk and <f>ik are the two-dimensional Bloch-functions satisfying the equation like Schrodinger's one (see [17][18][19], L is the crystal target length, Qnn is the population probability of a particle transverse energy state n.…”