Theory of Neutron Fluctuations in Multiplying Media with Applications in Nuclear Safeguards and Reactor Diagnostics

The number of neutrons in a multiplying (fissile) medium, or its measurable quantities (number of detector pulses in a given time interval, or the instantaneous value of the detector current) exhibits small, random fluctuations around the mean value even in a stationary medium (e.g. a reactor). There are two main reasons for such fluctuations (“neutron noise”), due to different physical processes, and consequently having different characteristics and application areas. Both types of neutron fluctuations carry a wealth of information on the properties of the multiplying medium, and hence can be used to characterize the parameters of a steady (constant in time) system, or monitor changes in the status of a stationary time-dependent system.

One reason of the fluctuations is the branching property of the chain reaction (the multiplication process), which leads to inherent, non-trivial (non-Poisson) fluctuations of the neutron population (similarly to the development of family trees). The “branching noise” dominates in low power (low neutron density) systems, therefore it is often termed as “zero power reactor noise”. The statistical properties of the detection signals are described by probability balance equations (master equations or Chapman-Kolmogorov equations). Although the equations for the full probability distribution (or its generating function) cannot be solved in general, the few lowest order moments can usually be given in simple models of the system. The knowledge of the dependence of the moments on the system properties can be used in detecting, identifying and quantifying hidden fissile material (nuclear safeguards), or determining the margins to criticality of a subcritical system (traditional reactor or accelerator driven subcritical system).

The second reason for neutron fluctuations is the fluctuations of the medium itself in which the neutron multiplication and transport takes place. This is the case of high power nuclear reactors, in which many random changes in the system occur. Examples are random vibrations of the fuel assemblies and control rods and random temperature fluctuations of the coolant in pressurized water reactors, or boiling of the coolant in boiling water reactors etc. In contrast to the zero power reactor noise, this type of neutron fluctuations dominates in high neutron density system, and is called “power reactor noise”. Mathematically, it is described by random differential equations (also called Langevin equation) for the neutron flux, where the coefficients of the corresponding diffusion or transport equation are random processes. Power reactor noise can be used to determine the statistical properties of the underlying technological processes, and hence monitor of the "health status" of the reactor in a non-intrusive way, as well as to detect and identify incipient failures at an early stage, such that corrective action can be taken in time.

In the talk the mathematical theory of both types of fluctuations will be given, with special emphasis on the master equation approach and its application to determining the mass of a fissile sample in nuclear safeguards and reactivity monitoring in subcritical systems. Applications of power reactor theory for reactor noise diagnostics will be given on how to detect and locate control and fuel rod vibrations as well as core barrel motion in PWRs and boiling in BWRs including measuring the steam content and two phase flow velocity etc. with the help of neutron detectors. Examples of applications in Swedish and Hungarian power plants will be given.