Flux distribution calculations in planar channeling

Abstract

A technique has been developed to calculate the spatial and velocity distributions of channeled ions in planar channeling as a function of the depth in a crystal. The continuum plane approximation is assumed but no assumptions about statistical equilibrium are made. At fixed depths, the distributions are found to exhibit both jump discontinuities and infinities, so an integral of the distributions over small intervals around various positions across the channel is calculated. Also, the distributions are found to change considerably with depth and the integrals as a function of depth give a clear picture of the flux-peaking phenomenon. The key idea in this technique is an examination of the motion of the ions in the phase plane; this turns out to be a very systematic way of ordering the particles and thereby gaining insight into the structure of the distributions. The technique is illustrated by examining the evolution of the spatial distribution with depth for channeling of 1-MeV helium ions along the {110} planes of silicon.