Reactor Kinetics Using Partial Equations

This paper proposes partial neutron transport equations for stationary and transient calculations. The partial equations of neutron transport are based on separately following neutrons born from external source, prompt fission neutrons, and delayed neutrons. The delayed neutrons are described by a system of equations containing one equation for each group. The paper defines the parameters of these equations and presents the results of fast neutron reactor benchmark calculations.

Determination of the field of the external source neutrons in the system of partial equations provides a natural transfer of the source power (in units of neutrons per second) to the core power of energy release from the interaction of the external source neutrons in the reactor core (in units of watt). Thus, an external source neutron is used for the initial normalization of the neutron field based on the required reactor power. Operating with the field of delayed neutrons, in contrast to the field of concentrations of delayed neutron precursors, provides a quantitative assessment of the interaction of these neutrons with the reactor environment, and thus, assesses their contribution to the reactivity effects in fast reactors.

Partial neutron transport equations allow us to extract additional information about the time behavior of the fast neutron reactor.