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 n(l, L) of the free flight path 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 chi = (Inl)(InL) (where L is the system size) and a distinct value of the fractal dimension phi(chi). The mechanism for multifractality based on an underlying multiplicative process is illustrated on a simple geometrical model. The multiscaling structure of the function n(l, L) is discussed.