Comparison function techniques in multigroup space dependent reactor stability

In this paper a mathematical model for a bare homogeneous cylindrical reactor core is formulated which accounts for an arbitrary number of prompt and six delayed neutron groups. The feedback is expressed as linear temperature coefficients of the core parameters. The resulting system of weakly coupled non-linear mixed (partial and ordinary) set of differential equations are examined from a stability point of view. With the aid of a generalization of Naguma-Westphal theorem a method of constructing comparison functions are presented. The comparison function can either be used to check the stability of the system under perturbations or to determine bounds for the ensuing transients. Perturbations may be changes (not necessarily small) in the initial distributions or in the system parameters. Knowledge of the equilibrium solutions enables one to test the system for asymptotic stability and also determine a region of stability in the solution space. Furthermore, a bound for the rate of convergence to equilibrium becomes obtainable, since the comparison functions bound the true solution from above and below. One can specify the bounds on the changes in the initial distributions in order to get the bounds on the resulting transients or conversely one can limit the transient and obtain the allowable perturbations. Similarly, changes in the system parameters can be limited by bounds on the ensuing transients and/or the new equilibrium solutions. (author)