Angular distribution of radiation by relativistic electrons in a thin crystal

The results of theoretical investigation of angular distributions of radiation from a relativistic electron passing through a thin crystal at a small angle to the crystal axis are presented. The electron trajectories in crystal were simulated using the binary collision model which takes into account both coherent and incoherent effects at scattering. The angular distribution of radiation was calculated as a sum of radiation from each electron. It is shown that there are nontrivial angular distributions of the emitted photons, which is connected to the superposition of the coherent scattering of electrons by atomic rows (doughnut scattering effect) and the suppression of the radiation due to the multiple scattering effect (similar to the Landau-Pomeranchuk-Migdal effect in an amorphous matter). The orientation dependence of angular distribution of radiation is also analyzed.