Kinetics of two phase fuel reflected reactors

In the present work a self-consistent mathematical model for the local dynamics of a quite particular class of fission reactors has been developed and solved. These devices consist of an innermost multiplying region, in which a significant fraction of the fissile fuel is diluted into a liquid phase, while the complementary fuel fraction operates as a standing solid matrix. This unconventional active region is surrounded by a standard peripheral re¯ector. For cooling purposes, thefluid fraction of the fuel needs to be circulated through external heat exchan- gers. The pump driven circulation causes the delayed neutron precursors, dissolved inside the ¯uid phase, to be spatially homogenized in the core volume well before decaying, while a continuous removal of precursor nuclei from the core takes place as a consequence of the outside circulation. Furthermore, the fraction of the extracted precursors still surviving after the solenoidal trip through the heat exchangers is continuously reinserted into the core. A new type of dynamical model is required to account for these unusual technological features. The mathematical structure of the evolution model presented in this paper consists of a system of integro±di€erential-di€erence equations, whose solution is derived in closed-form, by means of fully analytical techniques. Many dynamics and safety features of reactors of this type can be clarified a priori, upon inspection of the mathematical properties of the solution of the model. The rigorous time±eigenvalue generating equation can be explicitly established in the present theoretical context, together with the evaluation of any kind of transients. A short survey on the possible fields of application of these reactors is also presented.