Nuclear Technology / Volume 192 / Number 3 / December 2015 / Pages 191-207
Technical Paper / Radiation Transport and Protection / dx.doi.org/10.13182/NT14-133
The mathematical underpinnings of cost optimal radiation shielding designs based on an extension of optimal control theory are presented, a heuristic algorithm to iteratively solve the resulting optimal design equations is suggested, and computational results for a simple test case are discussed.
A typical radiation shielding design problem can have infinitely many solutions, all satisfying the problem's specified set of radiation attenuation requirements. Each such design has its own total materials cost. For a design to be optimal, no admissible change in its deployment of shielding materials can result in a lower cost. This applies in particular to very small changes, which can be restated using the calculus of variations as the Euler-Lagrange equations. The associated Hamiltonian function and application of Pontryagin's theorem lead to conditions for a shield to be optimal.