  This book contains a thorough theoretical consideration of the process of
proton channeling through carbon nanotubes. We begin with a very brief summary
of the theoretical and experimental results of studying ion channeling through
nanotubes. Then, the process of ion channeling is described briefly. After
that, the crystal rainbow effect is introduced. We describe how it was
discovered, and present the theory of crystal rainbows, as the proper theory of
ion channeling in crystals and nanotubes. We continue with a description of the
effect of zero-degree focusing of protons channeled through nanotubes. It is
shown that the evolution of the angular distribution of channeled protons with
the nanotube length can be divided in the cycles defined by the rainbow effect.
Further, we analyze the angular distributions and rainbows in proton channeling
through nanotubes. This is done using the theory of crystal rainbows. The
angular distributions are generated by the computer simulation method, and the
corresponding rainbow patterns are obtained in a precise analysis of the
mapping of the impact parameter plane to the transmission angle plane. We
demonstrate that the rainbows enable the full explanation of the angular
distributions. We also investigate how the effect of dynamic polarization of
the carbon atoms valence electrons influences the angular and spatial
distributions of protons transmitted through short nanotubes in vacuum and
embedded in dielectric media. In addition, we explore the channeling star
effect in 1 GeV proton channeling through bundles of nanotubes, which appears
when the proton beam divergence angle is larger than the critical angle for
channeling.
