Optimal shielding design for minimum materials cost or mass
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 EulerLagrange equations. Furthermore, the associated Hamiltonian function and application of Pontryagin's theorem lead to conditions for a shield to be optimal.
 Authors:

^{[1]}
 Princeton Univ., Princeton, NJ (United States). Princeton Plasma Physics Lab. (PPPL)
 Publication Date:
 Report Number(s):
 PPPL5200 REV
Journal ID: ISSN 00295450
 Type:
 Accepted Manuscript
 Journal Name:
 Nuclear Technology
 Additional Journal Information:
 Journal Volume: 192; Journal Issue: 3; Journal ID: ISSN 00295450
 Publisher:
 American Nuclear Society (ANS)
 Research Org:
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; shielding; optimization; Pontryagin; partialdifferentialequations; Pontryagin maximum principle
 OSTI Identifier:
 1256374
Woolley, Robert D. Optimal shielding design for minimum materials cost or mass. United States: N. p.,
Web. doi:10.13182/nt14133.
Woolley, Robert D. Optimal shielding design for minimum materials cost or mass. United States. doi:10.13182/nt14133.
Woolley, Robert D. 2015.
"Optimal shielding design for minimum materials cost or mass". United States.
doi:10.13182/nt14133. https://www.osti.gov/servlets/purl/1256374.
@article{osti_1256374,
title = {Optimal shielding design for minimum materials cost or mass},
author = {Woolley, Robert D.},
abstractNote = {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 EulerLagrange equations. Furthermore, the associated Hamiltonian function and application of Pontryagin's theorem lead to conditions for a shield to be optimal.},
doi = {10.13182/nt14133},
journal = {Nuclear Technology},
number = 3,
volume = 192,
place = {United States},
year = {2015},
month = {12}
}