Rainbows with Crystals and Nanotubes

This review paper is devoted to the crystal rainbow effect, which occurs in ion channeling in crystals and nanotubes. We begin with a description of crystal rainbows. Then, we analyze the evolution of the angular distribution of channeled ions with the crystal thickness. The analysis includes the rainbow cycles, and the effects of spatial focusing and angular focusing of channeled ions. This leads us to the theory of crystal rainbows. It is shown that it is the proper theory of ion channeling. After that, we describe how the effect of spatial focusing of channeled ions can be used for a subatomic microscopy. Further, the rainbow effect occurring with carbon nanotubes is considered. Finally, we demonstrate how an ion beam can be guided by a bent carbon nanotube