ACDC: Predicting Neutron Noise in Heterogeneous Nuclear Reactors

This theoretical work addresses statistical methods in nuclear multiplying systems. We derive an efficient method for calculating the time-dependent deviation from Poisson behavior in neutron detection for a general, spatially heterogeneous subcritical system. Such deviations from Poisson statistics are known to be associated with neutron multiplication due to nuclear fission, and their measurement has important diagnostic implications in the nuclear industry.

 

Using the probability generating function method, we deduce the super-Poissonian deviation of the detector count covariance matrix induced by neutron multiplication due to fissions. The resulting general form coincides with the second moment of an Itō–Langevin process. Essentially, we introduce a novel approach for evaluating the number of pairs of neutron detections (the second moment) from the knowledge of the Green’s function of the neutron transport operator (the first moment), which is considerably more tractable to simulate.

 

Our method, termed Adjoint Calculation of Doubles Contribution (ACDC), has the potential to enable simulations that reduce computational requirements by several orders of magnitude compared to direct simulations of the system’s neutron noise. This approach may assist in the design of subcritical noise experiments for licensing new research reactors, in improving nuclear cross-section libraries, and in non-destructive assay techniques for spent nuclear fuel.