Donut and dynamic polarization effects in proton channeling through carbon nanotubes

TL;DR

This study explores how proton channeling through carbon nanotubes produces donut-shaped and rainbow effects in angular distributions, revealing new insights into proton behavior near the critical channeling angle and potential applications in imaging and nanoscale proton beam creation.

Contribution

It demonstrates the development of donut and rainbow effects in proton channeling distributions and analyzes the influence of incident angle and image force on these phenomena.

Findings

Ring-like donut structure forms near critical angle.

Rainbow effect observed in angular distributions.

Proton incident angle affects distribution maxima and proton rearrangement.

Abstract

We investigate the angular and spatial distributions of protons of the energy of 0.223 MeV after channeling through an (11,~9) single-wall carbon nanotube of the length of 0.2 $\mu$m. The proton incident angle is varied between 0 and 10 mrad, being close to the critical angle for channeling. We show that, as the proton incident angle increases and approaches the critical angle for channeling, a ring-like structure is developed in the angular distribution - donut effect. We demonstrate that it is the rainbow effect. When the proton incident angle is between zero and a half of the critical angle for channeling, the image force affects considerably the number and positions of the maxima of the angular and spatial distributions. However, when the proton incident angle is close to the critical angle for channeling, its influence on the angular and spatial distributions is reduced strongly. We demonstrate that the increase of the proton incident angle can lead to a significant rearrangement of the propagating protons within the nanotube. This effect may be used to locate atomic impurities in nanotubes as well as for creating nanosized proton beams to be used in materials science, biology and medicine.