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Abstract
The Neutron Transport Equation (NTE) describes the flux of neutrons over time through an inhomogeneous fissile medium. In the recent articles [5, 10], a probabilistic solution of the NTE is considered in order to demonstrate a PerronFrobenius type growth of the solution via its projection onto an associated leading eigenfunction. In [9, 4], further analysis is performed to understand the implications of this growth both in the stochastic sense, as well as from the perspective of MonteCarlo simulation. Such MonteCarlo simulations are prevalent in industrial applications, in particular where regulatory checks are needed in the process of reactor core design. In that setting, however, it turns out that a different notion of growth takes centre stage, which is otherwise characterised by another eigenvalue problem. In that setting, the eigenvalue, sometimes called keffective (written k횎횏횏), has the physical interpretation as being the ratio of neutrons produced (during fission events) to the number lost (due to absorption in the reactor or leakage at the boundary) per typical fission event. In this article, we aim to supplement [5, 10, 9, 4], by developing the stochastic analysis of the NTE further to the setting where a rigorous probabilistic interpretation of keff is given, both in terms of a PerronFrobenius type analysis as well as via classical operator analysis. To our knowledge, despite the fact that an extensive engineering literature and industrial MonteCarlo software is concentrated around the estimation of keff and its associated eigenfunction, we believe that our work is the first rigorous treatment in the probabilistic sense (which underpins some of the aforesaid MonteCarlo simulations).
Original language  English 

Pages (fromto)  9821001 
Number of pages  20 
Journal  SIAM Journal on Applied Mathematics 
Volume  81 
Issue number  3 
Early online date  27 May 2021 
DOIs  
Publication status  Published  31 Dec 2021 
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 1 Finished

Stochastic Analysis of the Neutron Transport Equation and Applications to Nuclear Safety
Kyprianou, A., Cox, A. & Harris, S.
Engineering and Physical Sciences Research Council
16/05/17 → 31/12/21
Project: Research council