A Nonlinear Study of Reactors with a Linear Feedback

Solutions of the point kinetic equations with delayed neutrons for reactor systems with arbitrary linear feedback are investigated. It is found that the solutions that are Laplace transformable are bounded for all initial perturbations regardless of whether or not the system is linearly stable, provided the Laplace transform of the feedback kernel has no zeros on the positive real axis. This criterion is applied to some reactor models previously investigated by others. It is shown that there are also nontransformable solutions that possess a finite escape time and that such solutions can exist only if the reactor has a prompt positive reactivity coefficient. The asymptotic behavior of these solutions near the escape time is also obtained. These general conclusions are verified by considering some specific feedback models for which exact solutions are available. Numerical solutions for reactor systems with more realistic feedback models, such as one used to describe EBR-I, are obtained by a digital computer.