STOCHASTIC NEUTRONICS WITH PANDA DETERMINISTIC CODE

The master equation for the neutron probability distribution induced by one initial neutron in a multiplicative medium is a Kolmogorov Backward equation. From this equation, the generating function methodology is used to derive the rst two moments and survival probability equations. They are time dependent adjoint transport equations. The rst moment or mean number equation is the classic linear adjoint transport equation. The second moment and survival probability equations present an additional term. Nevertheless, they can be solved with standard numerical methods used in deterministic transport theory. A neutron source can be taken into account using the same methodology. The generating function method is applied to the master equation derived for the source induced neutron population probability distribution. By this way, the source induced mean number, variance and initiation probability expressions are derived. For nuclear safety applications, the deterministic 2D code PANDA has been adapted to solve these linear and nonlinear time dependent adjoint multigroup transport equations and to take into account a neutron source. A numerical application is presented. This space and energy dependent numerical test will be used in the validation process for intercode comparison.