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 reflector. For cooling purposes, the fluid fraction of the fuel needs to be circulated through external heat exchangers. The pump driven circulation causes the delayed neutron precursors, dissolved inside the fluid 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-differential-difference 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