%0 Journal Article
%T Generalized and Stability Rational Functions for Dynamic Systems of Reactor Kinetics
%A Ahmed E. Aboanber
%J International Journal of Nuclear Energy
%D 2013
%R 10.1155/2013/903904
%X The base of reactor kinetics dynamic systems is a set of coupled stiff ordinary differential equations known as the point reactor kinetics equations. These equations which express the time dependence of the neutron density and the decay of the delayed neutron precursors within a reactor are first order nonlinear and essentially describe the change in neutron density within the reactor due to a change in reactivity. Outstanding the particular structure of the point kinetic matrix, a semianalytical inversion is performed and generalized for each elementary step resulting eventually in substantial time saving. Also, the factorization techniques based on using temporarily the complex plane with the analytical inversion is applied. The theory is of general validity and involves no approximations. In addition, the stability of rational function approximations is discussed and applied to the solution of the point kinetics equations of nuclear reactor with different types of reactivity. From the results of various benchmark tests with different types of reactivity insertions, the developed generalized Pad¨¦ approximation (GPA) method shows high accuracy, high efficiency, and stable character of the solution. 1. Introduction The multigroup neutron diffusion equations, which are derived from the general mathematical form of neutron transport equation, are represented generally by a system of time- and space-dependent coupled partial differential equations for which approximate solutions are sought from neutron transport equation. The point reactor kinetics equations are a useful simplification of the time-dependant neutronic neutron diffusion equations for most reactors operating near delayed critical. Included in that system are equations which describe the neutron level, reactivity, an arbitrary number of delayed neutron groups, and any other variables that enter into the reactivity equation in the case of reactivity feedback. One of the important properties in a nuclear reactor is the reactivity, due to the fact that it is directly related to the control of the reactor. The startup process of a nuclear reactor requires that reactivity is varied in the system by lifting the control rods discontinuously. In practice, the control rods are withdrawn at time intervals such that reactivity is introduced in the reactor core linearly, to allow criticality to be reached in a slow and safe manner. For safety analysis and transient behaviour of the reactor dynamics, the neutron density and the delayed neutron precursor concentration are important parameters to be studied.
%U http://www.hindawi.com/journals/ijne/2013/903904/