ON PERTURBATION THEORY AND REACTOR KINETICS: FROM WIGNER'S PILE PERIOD TO ACCELERATOR DRIVEN SYSTEMS

This Eugene P. Wigner Keynote Lecture at the PHYSOR 2002 International Meeting in Seoul, Korea, addresses the fundamental basis for formulating the equations that model the time and spacedependent behavior of an Accelerator Driven Sub-Critical Core System (ADS), and highlights the limited applicability to ADS of the traditional Wigner-type perturbation theory formulation of neutron kinetics. In particular, a paradigm ADS neutron-kinetics model is presented, and its exact solution is compared with the incomplete results produced by the traditional approaches originally developed for critical reactors. It is shown that the exact ADS-model is basically non-perturbative; consequently, the exact model cannot be obtained by using the traditional perturbation theory-based approaches as developed originally for critical reactors. In particular, the point-kinetics equations obtained in previous works by using traditional perturbation theory methods are shown to be inadequate for describing the space- and time-behavior of the neutron distribution in the target and the dynamic phenomena at the interface between the ADS target and the ADS sub-critical core regions. In retrospect, this conclusion is not surprising, since the problem for a critical reactor is that of maintaining and controlling a self-sustained reaction (much like treating small perturbations around equilibrium in a self-sustaining harmonic oscillator), whereas the problem for an ADS should be that of optimal control (however complicated) of an externally driven system (much like an externally driven oscillator). Not only physically, but also mathematically, the two problems are fundamentally distinct: mathematically, the critical reactor is described by a homogeneous eigenvalue problem for the non-zero (self-sustaining) flux solution, whereas the ADS is described by an inhomogeneous problem where the corresponding homogeneous problem should by design admit only the identically zero flux solution. This is the basic reason why, for example, it is quite difficult to find a practically useful “fictitious ADS steady-state”, which is required by the traditional perturbation-theory-based methods to work. In this Wigner Keynote Lecture, a new conceptual framework is proposed for treating an ADS, by adopting an optimal control theory point of view rather than the traditional perturbation theory point of view. This new conceptual framework encompasses not only the time- and space behavior of the coupled neutron kinetics but also the ADS thermal-hydraulic balance equations, and is based on optimization and optimal control of ADS operational objectives, which would include minimization of local flux disturbances, load and source following, etc. In particular, this new conceptual framework makes no use of a “fictitious ADS steady-state”, as required by the traditional approaches, and, also in contradistinction to the traditional approaches, delivers the correct and complete (i.e., including sources) adjoint equations, without leaving any room for ambiguities. Thus, this new conceptual framework provides a natural basis for developing new computational methods,