The extinction probabilities of nuclear assemblies: A sensitivity study.

摘要

For certain operating regimes, deterministic analysis methods traditionally applied to the theoretical analysis of nuclear reactors may fail to accurately predict quantities and behaviors that are functionals of the characteristics of a time-dependent neutron population. When such situations arise, it often becomes necessary to employ stochastic analysis models that are analogous to more traditional deterministic models (such as neutron diffusion or transport theories). The fundamental difference between these models and their deterministic counterparts lies in the fact that they are formulated in terms of neutron population probabilities that may be regarded as functions of space, angle, time, and energy. When these probability distribution functions are determined, a variety of useful quantities may be extracted from them, including the probability that at any time, the neutron population contained within the assembly under investigation is exactly zero. This probability is of particular importance in the stochastic analysis of nuclear reactors, and is referred to as the extinction probability of an assembly.;It may be shown that the extinction probability of a nuclear assembly is dependent upon a potentially large number of input quantities that are additional to any space, angular, time, and energy dependence already included through the development of the governing mathematical model. In many contexts these input quantities (for example, the prompt multiplication factor or cross section data) may be regarded as static or dynamic during the time evolution of the nuclear assembly, and in any case may be subject to small, inherent variations. These variations are typically of a fundamentally different nature than their evolution-induced counterparts and may represent theoretical constructs such as measurement uncertainties or errors. The existence of these inherent variations may affect the predictions that the stochastic model of the nuclear assembly is capable of delivering, in particular various extinction probabilities that may be defined. To the knowledge of the author, no such investigation of these implications has been conducted to date.;It is thus the purpose of this work to investigate the nature of input parameter variation-induced effects on the extinction probabilities of certain types of nuclear assemblies. A broadly defined class of mathematical analysis techniques known as sensitivity analysis (and in particular, a theoretical construct known as the Gateaux-variation) will be employed to calculate these effects. The analysis will be left as general as possible within the context of a clean, stochastic point model, though examples of interest to the consideration of fast reactors near start-up time will also be considered. In addition to providing situation-specific information regarding input parameter influence on the start-up behavior of fast reactors, the primary goal of this work is to maximize the usefulness of the generalized developments as applied to other potential problem classes of interest.