Abstract
A refined equation for channeling particle diffusion in transverse energy taking into consideration large-angle scattering by nuclei is suggested. This equation is reduced to the Sturm–Liouville problem, allowing one to reveal both the origin and the limitations of the dechanneling length notion. The values of the latter are evaluated for both positively and negatively charged particles of various energies. New features of the dechanneling dynamics of positively charged particles are also revealed. First, it is demonstrated that the dechanneling length notion is completely inapplicable for their nuclear dechanneling process. Second, the effective electron dechanneling length of positively charged particle varies more than twice converging to a constant asymptotic value only at the depth exceeding the latter.
Highlights
Channeling effect in crystals delivers unique possibilities of both high energy charged particle radiation and control
Proton and ion planar channeling in bent crystals is a promising tool for both extraction and collimation of the beams of the large hadron collider (LHC) and future circular collider (FCC) [4,5,6]
Planar channeling of charmed and beauty baryons in bent crystals makes it possible to study the effects of both CP- and CPT violation [7]
Summary
Channeling effect in crystals delivers unique possibilities of both high energy charged particle radiation and control. Since the critical channeling angle of low energy ions of mass M considerably exceeds the maximal angle θmax = m/M of their scattering by electrons with mass m, the electron dechanneling of non-relativistic ions can be correctly described in neglect of both large-angle catastrophic scattering and the scattering angle fourth power contribution to the mean square variation of transverse energy These assumptions lose their applicability in many other cases. To provide a correct evaluation of the dechanneling length in the presence of nuclear scattering, a refined diffusion equation, which takes into consideration both the scattering angle fourth power contribution to the mean square variation of transverse energy and large-angle catastrophic scattering, is introduced in this paper This equation is used to evaluate dechanneling length for the largest accelerator energies as well as to reveal the peculiarities of the dechanneling process introduced by both nuclear and electron scattering of both positively and negatively charged particles
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