Relationship Between Neutron Flux and Reactor Power

P th _fV 3.12 x 10¹⁰ fissions watt sec Reactor Theory (Neutron Characteristics) DOE-HDBK-1019/1-93 REACTION RATES Rev. 0 Page 21 NP-02 The power released in a reactor can be calculated based on Equation (2-6). Multiplying the reaction rate by the volume of the reactor results in the total fission rate for the entire reactor. Dividing by the number of fissions per watt-sec results in the power released by fission in the reactor in units of watts. This relationship is shown mathematically in Equation (2-7) below. (2-7) where: P = power (watts) = thermal neutron flux (neutrons/cm -sec) th 2 = macroscopic cross section for fission (cm ) f -1 V = volume of core (cm )³ Relationship Between Neutron Flux and Reactor Power In an operating reactor the volume of the reactor is constant. Over a relatively short period of time (days or weeks), the number density of the fuel atoms is also relatively constant. Since the atom density and microscopic cross section are constant, the macroscopic cross section must also be constant. Examining Equation (2-7), it is apparent that if the reactor volume and macroscopic cross section are constant, then the reactor power and the neutron flux are directly proportional. This is true for day-to-day operation. The neutron flux for a given power level will increase very slowly over a period of months due to the burnup of the fuel and resulting decrease in atom density and macroscopic cross section.