Some Features of Spatial Neutron Kinetics for Multiplying Systems

Recursive solutions for multi-group neutron kinetics diffusion equations in homogeneous three-dimensional rectangular domains with time dependent perturbations

In the present work we solve in analytical representation the three dimensional neutron kinetic diffusion problem in rectangular Cartesian geometry for homogeneous and bounded domains for any number of energy groups and precursor concentrations. The solution in analytical representation is constructed using a hierarchical procedure, i. e. the original problem is reduced to a problem previously solved by the authors making use of a combination of the spectral method and a recursive decomposition approach. Time dependent absorption cross sections of the thermal energy group are considered with step, ramp and Chebyshev polynomial variations. For these three cases, we present numerical results and discuss convergence properties and compare our results to those available in the literature.

Interpretation of Local Flux Measurements in Subcritical Systems and Reactivity Determination

The determination of the subcriticality level constitutes an important issue in the assessment of the accelerator-driven system technology. For this purpose, the interpretation of flux measurements requires a lumped-parameter model employed in an inverse fashion. This papers addresses the drawbacks of point kinetics in performing such a task. In particular, the problem of the generation of integral parameters is considered, in connection with the use of a shape function and of a projection weight tailored to the neutron flux detector. Furthermore, the question of the generation of the effective source is analysed, and some proposals to modify the time dependence of such a function to account for the time delay at the flux detector are presented and discussed.

Comparative assessment of methods for the reactivity measurement in subcritical systems by pulsed experiments

The determination of the subcriticality level for source-driven systems is an important problem that can be handled by several deterministic methods developed for the interpretation of flux signals in pulsed experiments. The paper compares the performance of several methods for different physical characteristics of the system considered and for different durations of the source pulse. The effects of the subcriticality level and of the experimental uncertainty are also investigated. Furthermore, an analysis of the influence of spatial effects is carried out. The study gives some indications on the most suitable method in a specific experimental configuration pointing out at the situations where non-conservative evaluations of the reactivity can be expected, i.e. when the system effective multiplication constant is underestimated.