A SIMPLE DERIVATION OF THE NEUTRON-TRANSPORT EQUATION

A new and simple derivation of the neutron transport equation is given. The approach is similar to that used in the Liouville equation and its applications to the Boltzmann equation in that it is formulated in terms of the one-particle or one-point density function, as opposed to the traditional reactor physics approach of counting neutrons in a volume of the phase-space. It makes use of the recognition that the expected number of particles in a phase cell dV is the same as the probability of finding one particle in dV. A novelty of the derivation here is that because of the linear Markovian property of the process, it is possible to derive a master (Chapman-Kolmogorov) equation for the one-particle density, that is, for the neutron density or neutron flux of the traditional transport equation. This way, the forward and the backward (adjoint) equations of neutron transport can be derived from a single master equation. The variance of the one-point distribution function is also derived, and an explicit solution is given.