A Short Inroad to Optimized Compactification of Composite Neutronic Shields

Abstract

Compact neutronic shields for mobile nuclear reactors or accelerator-based neutron beams are known to be optimized multilayered composites. This paper is a simplified short inroad to the complex problem of optimizing the design of such shields when they attenuate a neutron beam to extremise certain quality criteria, in plane geometry, subject to equality and inequality constraints. In the equality constraints, the interfacial polychromatic neutron fluxes are solutions to course-mesh finite difference holonomic state equations. The set of these interfacial fluxes act as state variables, while the set of layer thicknesses, or their poisoning (by added neutron absorbers) concentrations are decision variables. The entire procedure is then demonstrated to be reducible to standard Kuhn-Tucker semilinear programing that may also lead robustly to an optimal sequence for these layers.