PROBABILISTIC REACTOR DYNAMICS .1. THE THEORY OF CONTINUOUS EVENT TREES

The concept of probabilistic reactor dynamics is formalized in which deterministic reactor dynamics is supplemented by the fact that deterministic trajectories in phase-space switch to other trajectories because of stochastic changes in the structure of the reactor such as a change of state of components as a result of a malfunction, regulation feedback, or human error. A set of partial differential equations is obtained under a Markovian assumption from the Chapman-Kolmogorov equation giving the probability pi(x, i, t) that the reactor is in a state x where vector x describes neutronic and thermohydraulic variables, and in a component state i at time t. The integral form is equivalent to an event tree where branching occurs continuously. A backward Kolmogorov equation allows evaluation of the probability and the average time for x(t) to escape from a given safety domain.