Angular distributions of 7 TeV protons axially channeled through the thin bent 〈1 0 0〉 Si crystal

Abstract

We have studied theoretically angular distributions of relativistic protons axially channeled through the thin bent 〈1 0 0〉 Si crystal. The proton energy is 7 TeV, the thickness of the crystal is 1 mm, which corresponds to the reduced crystal thickness, Λ, equal to 2.1, while the bending angle, α, is varied from 0.002 to 0.020 mrad. The angular distributions of axially channeled protons are generated by the computer simulation method using the numerical solution of the ion equations of motion, with the Lindhard’s expression for the continuum interaction potential of the ion and the crystal. Uncertainness of the scattering angle of the proton caused by its collisions with the electrons of the crystal and proton (electronic) energy loss are taken into account. The results of the analysis show that the two additional maxima appear in the angular distributions, for the bending angles α ⩽ 0.006 mrad. They originate from four areas in the impact parameter plane located in between atomic strings defining the channel that correspond to the saddle points of the continuum potential. The obtained deflection efficiency curve has an inflection point, which can be attributed to the disappearing of the two additional maxima in the angular distribution. We have also studied the dependence of the deflection efficiency on the length of the crystal when the deflection angle is equal to 0.1 mrad, regarding the possible application of the crystal channeling for halo collimation of the proton beam in the Large Hadron Collider (LHC) project, at the European Organization for Nuclear Research (CERN).