Superfocusing of channeled protons and crystal rainbows

This study is devoted to the effect of superfocusing of protons having the energy of 2 MeV in a 〈1 0 0〉 channel of a Si crystal. The analysis is performed by the theory of crystal rainbows. We analyze the superfocusing effect in the first rainbow cycle. The evolution of the spatial distribution of channeled protons is examined by the numerical solution of the proton equations of motion in the transverse position plane. We demonstrate that the superfocusing effect is a reduced crystal rainbow effect, in which the rainbow line comes to a point.