Diffracted transition radiation as a new diagnostic tool for relativistic electron beam emittance

Influence of the reflectivity of a crystal on the angular distribution of diffracted transition radiation of relativistic electrons

“…As shown in [7], for electron energies greater than 10 GeV, and a beam divergence less than 𝛾 −1 , the scatter in the energies of reflected photons relative to the Bragg energy 𝜔 B does not exceed fractions of a percent. Therefore, from here forward, rather than discussing the spectral-angular distribution, we will instead discuss the DTR angular distribution 𝐽 DTR (𝜔 B , 𝜗 ′ 𝑥 , 𝜗 ′ 𝑦 ).…”

“…Therefore, the influence of beam size on the observed radiation distribution is small and we consider and analyze only the angular radiation distribution and the beam divergence. In this case, the angular distribution of DTR can be written as [7]:…”

“…where 𝐺 𝑒 (𝜗 ′ 𝑥 → 𝜗 𝑥 , 𝜗 ′ 𝑦 → 𝜗 𝑦 ) is a two-dimensional Gaussian distribution describing a diverging electron beam [6,7].…”

“…Recently, researchers have proposed using the angular distributions of DTR to determine the divergence of beams of relativistic electrons [6] and estimate their emittance (i.e., to simultaneously measure the transverse sizes and divergence of the beam) [7]. In both cases, the researchers proposed determining the beam divergence by fitting the measured angular distribution by convolving the model angular distribution of the DTR with a two-dimensional Gaussian one describing the diverging electron beam.…”

“…This value is comparable to the characteristic angle 𝛾 −1 for relativistic particles. The presence of this effect leads to differences in the angular distributions of TR and DTR [10]; that is, it changes the model angular distribution of DTR [6,7]. Therefore, the influence of the reflectivity of a crystal on the accuracy of determining the divergence of electron beams, as evaluated from measurements of the angular distributions of DTR, should be considered.…”