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arXiv · 1809.00827

Multi-species neutron transport equation

Alex M. G. Cox·Simon C. Harris·Emma Horton·Andreas E. Kyprianou
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Abstract

The Neutron Transport Equation (NTE) describes the flux of neutrons through inhomogeneous fissile medium. Whilst well treated in the nuclear physics literature (cf. [9, 27]), the NTE has had a somewhat scattered treatment in mathematical literature with a variety of different approaches (cf. [8, 25]). Within a probabilistic framework it has somewhat undeservingly received little attention in recent years; nonetheless, probabilistic treatments can be found see for example [19, 26, 24, 29, 4, 3]. In this article our aim is threefold. First we want to introduce a slightly more general setting for the NTE, which gives a more complete picture of the different species of particle and radioactive fluxes that are involved in fission. Second we consolidate the classical c0-semigroup approach to solving the NTE with the method of stochastic representation which involves expectation semigroups. Third we provide the leading asymptotic of our multi-species NTE, which will turn out to be crucial for further stochastic analysis of the NTE in forthcoming work [6, 5]. The methodology used in this paper harmonises the culture of expectation semigroup analysis from the theory of stochastic processes against c0-semigroup theory from functional analysis. In this respect, our presentation is thus part review of existing theory and part presentation of new research results based on generalisation of existing results.

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Alex M. G. Cox, Simon C. Harris, Emma Horton, Andreas E. Kyprianou. 2019-01-03. Multi-species neutron transport equation. https://doi.org/10.1007/s10955-019-02307-2

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