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Power Reactor Noise Studies and Applications

Doctoral thesis, 2002

The present thesis deals with the neutron noise arising in power reactor systems. Generally, it can be divided into two major parts: first, neutron noise diagnostics, or more specifically, novel methods and algorithms to monitor nuclear industrial reactors; and second, contributions to neutron noise theory as applied to power reactor systems.
Neutron noise diagnostics is presented by two topics. The first one is a theoretical study on the possibility to use a newly proposed current-flux (C/F) detector in Pressurised Water Reactors (PWR) for the localisation of anomalies. The second topic concerns various methods to detect guide tube impacting in Boiling Water Reactors (BWR). The significance of these problems comes from the operational experience. The thesis describes a novel method to localise vibrating control rods in a PWR by using only one C/F detector. Another novel method, based on wavelet analysis, is put forward to detect impacting guide tubes in a BWR.
Neutron noise theory is developed for both Accelerator Driven Systems (ADS) and traditional reactors. By design the accelerator-driven systems would operate in a subcritical mode with a strong external source. This calls for a revision of many concepts and methods that have been developed for traditional reactors and also it poses a number of new problems. As for the latter, the thesis investigates the space-dependent neutron noise caused by a fluctuating source. It is shown that the frequency-dependent spatial behaviour exhibits some new properties that are different from those known in traditional critical systems. On the other hand, various reactor physics approximations (point kinetic, adiabatic etc.) have not been defined yet for the subcritical systems. In this respect the thesis presents a systematic formulation of the above mentioned approximations as well as investigations of their properties.
Another important problem in neutron noise theory is the treatment of moving boundaries. In this case one needs to redefine such common methods in reactor physics as point kinetic and adiabatic approximations because various functions involved have different regions of definition. The thesis presents one possible line of developing the general theory of linear kinetics as applied to systems with varying size. It also develops further the Green's function technique in two ways. First, the Green's function method is used to obtain an analytical solution for the one-group model with constant parameters. Mathematically, the model is described by an equation with inhomogeneous boundary condition. In addition, the absorber model is proposed, which happens to be very useful in deriving, for example, the point reactor and adiabatic approximation for the neutron noise due to oscillating boundaries. Second, the Green's function method is developed to derive another analytical solution for the general multi-group model with space-dependent parameters. This leads further to the generalised multi-group absorber model, which, in turn, gives a generalisation of the point reactor and adiabatic approximation for the multi-group model. Moreover, the general absober model allows to develop further the adjoint function method to represent the neutron noise induced by fluctuating boundaries in the multi-group diffusion theory.
Finally, the thesis investigates monotonicity properties of the effective multiplication factor, keff, in particular it gives a formal proof to the nesting hypothesis, which states that keff can only increase (or stay constant) in case of nesting, i.e. when adding extra volume to the system.

power spectra

control rod vibrations

Green's function

nesting hypothesis

adjoint function

fluctuating boundary

noise diagnostics

Accelerator Driven System

localisation algorithm

point reactor and adiabatic approximation