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In this work we investigate the rainbows appearing in channeling of 1 GeVprotons through the long (11, 9) single-wall carbon nanotubes. The nanotubelength is varied from 10 to 500 micrometers. The angular distributions ofchanneled protons are computed using the numerical solution of the protonequations of motion in the transverse plane and the Monte Carlo method. Eachrainbow is characterized by a sharp decrease of the proton yield on its largeangle side. As the nanotube length increases, the number of rainbows increasesand the average distance between them decreases in an easily predictable way.When the average distance between the rainbows becomes smaller than theresolution of the angular distribution, one cannot distinguish between theadjacent rainbows, and the angular distribution becomes equilibrated. We callthis route to equilibration the rainbow route to equilibration. This work is ademonstration of how a simple one-dimensional bound dynamic system can exhibita complex collective behavior.

Proton channeling through long chiral carbon nanotubes: the rainbow route to equilibration