Analytical solution to the nordheim-fuchs model

A model of nuclear reactor dynamics is considered which describes its behavior when the positive perturbation in reactivity is produced to transfer the reactor to the prompt supercritical state. The model presents a system of two differential equations, i.e., the Nordheim-Fuchs model. The analytical solution to the model is derived which enables the basic parameters such that neutron density, reactivity, and temperature to be changed with time. The analytical expression is deduced for determination of the time it takes the neutron density to reach its maximal value. An approximate relationship obtained from physical considerations is given forfinding this parameter. It is shown that the error of this approximate relationship used to determine the time ofachieving the maximal neutron density with respect to results obtained analytically does not exceed several percent. The results from calculations using both analytical and approximate relations are compared with the results obtained by means of six-group model of nuclear reactor kinetics and their good agreement is shown.