The donut and dynamic polarization effects in proton channeling through carbon nanotubes

We investigate the angular and spatial distributions of protons with an energy of 0.223 MeV after channeling them through an (11, 9) single-wall carbon nanotube of 0.2 mu m length. 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-the donut effect. We demonstrate that it is the rainbow effect. If the proton incident angle is between zero and 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, if the proton incident angle is close to the critical angle for channeling, its influence on the angular and spatial distributions is considerably decreased. We demonstrate that an 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.