Probability distribution of internal stresses in parallel straight dislocation systems

The collective behavior of a system of straight parallel dislocations is investigated. It is found by numerical simulation that the internal stress $\tau$ created by the dislocation has a stochastic component. In order to describe this stochastic character the form of the probability distribution function of the internal stress is determined. It is shown that the mean value of the distribution function is the self-consistent field created by the dislocation and the distribution function decays with $1/{\tau }^3.$