Convergence and acceleration of fission source simulations

One of the most important calculations in reactor physics is determining when a reactor is critical, subcritical, or supercritical. Mathematically, the computation amounts to solving an eigenvalue problem: eigenvalue k = 1 corresponds to criticality, k < 1 to subcriticality, and k > 1 to supercriticality. In order to compute the eigenvalue, it is crucial to first calculate the so-called fission source distribution, often denoted by S, which describes the long-run average distribution of fission events in the reactor.


Solving for the fission source distribution S and the eigenvalue k exactly is impossible even in very simple cases. Hence, approximating k and S in an efficient and accurate manner is fundamental to reactor physics. One of the primary tools in use is Monte Carlo simulation.


Various approaches for improving the speed and efficiency of simulation codes were presented and discussed. For example, Valeria Raffuzzi discussed the application of multi-group methods to the nuclear data, where complex nuclear cross-sections are approximated by grouping similar energies into one category to drastically increase efficiency.


The question “Has the simulation converged to the stationary state?” is key to any Monte Carlo simulation. Alex Cox presented a collection of so-called exact simulation methods, such as coupling from the past and debiasing. These methods can answer questions of convergence exactly, but can only be applied directly in simple, low-dimensional settings. Paul Smith presented the many testing methods that are applied in industrial-scale reactor codes, such as Shannon entropy, the Kolmogorov-Smirnov test, and the Kullback-Leibler divergence.

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