Neutron fluctuations in accelerator driven and power reactors via backward master equations

The transport of neutrons in a reactor is a random process, and thus the number of neutrons in a reactor is a random variable. Fluctuations in the number of neutrons in a reactor can be divided into two categories, namely zero noise and power reactor noise. As the name indicates, they dominate (i.e. are observable) at different power levels. The reasons for their occurrences and utilization are also different. In addition, they are described via different mathematical tools, namely master equations and the Langevin equation, respectively. Zero noise carries information about some nuclear properties such as reactor reactivity. Hence methods such as Feynman- and Rossi-alpha methods have been established to determine the subcritical reactivity of a subcritical system. Such methods received a renewed interest recently with the advent of the so-called accelerator driven systems (ADS). Such systems, intended to be used either for energy production or transuranium transmutation, will use a subcritical core with a strong spallation source. A spallation source has statistical properties that are different from those of the traditionally used radioactive sources which were also assumed in the derivation of the Feynman- and Rossi-alpha formulae. Therefore it is necessary to re-derive the Feynman- and Rossi-alpha formulae. Such formulae for ADS have been derived recently but in simpler neutronic models. One subject of this thesis is the extension of such formulae to a more general case in which six groups of delayed neutron precursors are taken into account, and the full joint statistics of the prompt and all delayed groups is included. The involved complexity problems are solved with a combination of effective analytical techniques and symbolic algebra codes. Power reactor noise carries information about parametric perturbation of the system. Langevin technique has been used to extract such information. In such a treatment, zero noise has been neglected. This is a pragmatic approach that avoids to handle complications that are unimportant for practical applications. However, from the academical point of view, it is highly desirable to establish direct contact between these two branches of neutron fluctuations in form of a unified theory from which the zero noise and the power reactor noise components can be obtained as limiting cases. Then the neglections made when considering the zero and power reactor noise separately can be estimated. Such a unified theory will also illuminate the reason for the advantage of using the Langevin approach to calculate the power reactor noise, and should be able to describe the neutron noise in intermediate cases, where neither the zero noise nor the power reactor noise dominates. The other subject of this thesis is to develop such a theory by assuming the cross section fluctuations to be a simple binary pseudo random process. Via backward master equation approach, a solution is obtained which is significantly more complicated than the cases of zero noise or power reactor noise separately, which are also given in the paper. It is shown that the general solution contains both the zero noise and the power reactor noise in the sense that they can be extracted individually as limiting cases of the general solution