A stochastic theory of particle transport

Abstract

A probability balance equation is formulated for the number of particles present in a cascade resulting from multiple births at each collision. Janossy’s regeneration point method is used and it leads to an integro differential equation for the generating function from which statistical information can readily be extracted. The technique is applied to the interpretation of radiation damage cascades in a homogeneous, amorphous medium in which two particles are ‘born’ per collision. The history of a single chain is followed and equations for the mean and variance are obtained as well as for individual probabilities. It is further shown how the backward and forward forms of the Boltzmann equation are related via the Green function of the system. Additional study shows that the variance also obeys a forward type of equation although its solution is not obtained as conveniently as that of the corresponding backward equation. Several analogies are made with other branches of particle physics; in particular, cosmic rays and neutron transport.