Abstract
A low order expansion in k-eigenmodes of a supercritical medium is shown to yield accurate results for the time dependent neutron chain survival probability as well as its steady state limit, the divergence probability. Numerical results for a 1D nonhomogeneous planar medium, when compared against an established nonlinear eigenvalue solution method, show the eigenmode expansion approach to be remarkably efficient under both weakly and strongly supercritical conditions. Specifically, two to three modes typically suffice to capture the temporal variation of the survival probability and one mode adequately describes the divergence probability for a weakly supercritical medium. Moreover, the dependence of the survival probability on the initiating neutron spatial and angular coordinates stabilizes within a fraction of a neutron lifetime of the chain starting, although the magnitude continues to change with time. Accuracy and numerical performance of the eigenmode expansion method are quantitatively assessed by comparison with the established technique, which itself is first benchmarked using the method of manufactured solutions.
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