Phase Space Analysis of Reactor Kinetics

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Abstract
A method for studying systems of differential equations employing an interactive computer system with a display screen is presented and applied to three nonlinear problems in reactor kinetics. Interactively it is possible to construct phase space solutions of second- and third-order systems of equations. It is also possible to project from the three-dimensional space and to consider the solutions of the equations as explicit functions of the independent variable. The method is demonstrated on three different nonlinear problems of interest to nuclear reactor kinetics. A second-order problem with temperature-dependent reactivity is considered. Two third-order problems with reactivity a function of two effective temperatures and 135Xe concentration, respectively, are also considered. The method of analysis makes it possible to efficiently study the effect of various parameter values on the solutions of the equations. Limit cycle behavior is investigated and the effect of the parameters of the model o...

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