A neutron balance approach in critical parameter determination

The determination of a critical parameter, process known also as criticality or eigenvalue search, is one of the major functionalities in neutronics codes. The determination of the critical boron concentration or the critical control rod position are two examples. Classical procedures used to solve this problem are based on the iterative Newton–Raphson method where the value of the parameter is changed until the eigenvalue matches the target. We present here a different approach where an equation, derived from the neutron balance, is set and the critical parameter is the unknown. Solving this equation is equivalent to solve an eigenvalue problem where the critical parameter is the eigenvalue. It is also shown that this approach can be seen as an application of inverse perturbation theory. This method reduces considerably the computation time in situations where changes on the critical parameter make a high distortion on the flux distribution, as it is the case of the control rods. Some numerical examples illustrate the performances and the gain in stability in cases of simultaneous control of criticality and axial offset of the power distribution. The application to the determination of the critical uranium enrichment in a transport code is also presented. The simplicity of the method makes its implementation in fuel bundle lattice and reactor codes very easy.