Constrain effect on reactivity while optimization of xenon transient processes

A problem is analyzed of finding out the reason why, in case there are reactivity limits, the optimum curve turns out to be the trajectory to follow the limit, rather than trajectories with maximum or zero reactor power. The problem is considered in two modifications. In the first case the 135Xe build-up is not limited, in the second case the reactor has a certain reactivity margin resulting in limiting the build-up of 135Xe. To make the problem more concrete, some numerical solutions are considered for illustration. Different trajectories in phase space are analysed in these solutions. The results of the comparison show that follow the limit the trajectory is more advantageous than that along the two-step trajectory. The solutions of synthesis and perturbation theory problems are given that do not make it possible to establish whether the trajectory is optimum for trajectories lying on the limit Xsup((2))=Xm, where Xsup((2)) is the 135Xe build-up averaged across the reactor, and Xm is the reactivity margin (given value). One can make sure whether the trajectory is optimum only implementing the Pontryagin maximum for concrete conditions of the problem. However, the successive perturbation theory developed in this paper for Xe transient processes may be used for developing numerical optimization methods