Energy loss distributions of relativistic protons axially channeled in a bent silicon crystal

A detailed study of the energy loss distributions of the relativistic protons axially channeled in the bent < 100 > Si crystals is presented in this work. The bending angle was varied from 0 to 20 μrad, while the crystal thickness was equal to 1 mm. The proton energy was chosen to be 7 TeV in accordance with the Large Hadron Collider (LHC) project, at the European Organization for Nuclear Research (CERN), in Geneva, Switzerland. The energy loss distributions of the channeled protons were generated using the numerical solution of the proton equations of motion in the transverse plane and the computer simulation method. An accurate energy loss model was used, which takes into account the trajectory dependence of the energy loss of protons during their motion through the crystal channels. Further, the dispersion of the proton’s scattering angle caused by its collisions with the electrons of the crystal and the divergence of the proton beam were taken into account. The calculated dependence of the number of dechanneled protons on the bending angle was excellently fitted by the Gompertz type dechanneling function.