Multifractality and multiscaling in collision cascades

It is shown that self-ion collisional cascades exhibit multifractality. The structure of the cascades was studied by analyzing the length distribution [ital n]([ital l],[ital L]) of the free flight path [ital l] traveled by particles during the cascade evolution. It was found that the collisional cascade can be partitioned into an infinity of subsets, each one characterized by a fixed value of [ital x]=ln[ital l]/ln[ital L] (where [ital L] is the system size) and a distinct value of the fractal dimension [phi]([ital x]). The mechanism for multifractality based on an underlying multiplicative process is illustrated on a simple geometrical model. The multiscaling structure of the function [ital n]([ital l],[ital L]) is discussed.