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Optimal Shielding Design for Minimum Materials Cost or Mass

Robert D. Woolley

Nuclear Technology / Volume 192 / Number 3 / December 2015 / Pages 191-207

Technical Paper / Radiation Transport and Protection /

First Online Publication:November 6, 2015
Updated:December 2, 2015

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.

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