Optimal shielding design for minimum materials cost or mass

Woolley, Robert D.

doi:10.13182/nt14-133

Title: Optimal shielding design for minimum materials cost or mass

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Abstract

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. Furthermore, the associated Hamiltonian function and application of Pontryagin's theorem lead to conditions for a shield to be optimal.

Authors:

Woolley, Robert D. ^[1]

Princeton Univ., Princeton, NJ (United States). Princeton Plasma Physics Lab. (PPPL)

Publication Date:: Wed Dec 02 00:00:00 EST 2015

Research Org.:: Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1256374

Report Number(s):: PPPL-5200 REV
Journal ID: ISSN 0029-5450

Resource Type:: Accepted Manuscript

Journal Name:: Nuclear Technology

Additional Journal Information:: Journal Volume: 192; Journal Issue: 3; Journal ID: ISSN 0029-5450

Publisher:: American Nuclear Society (ANS)

Country of Publication:: United States

Language:: English

Subject:: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; shielding; optimization; Pontryagin; partial-differential-equations; Pontryagin maximum principle

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                    Woolley, Robert D. Optimal shielding design for minimum materials cost or mass.  United States: N. p., 2015. 
Web.  doi:10.13182/nt14-133.

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                    Woolley, Robert D. Optimal shielding design for minimum materials cost or mass.  United States.  https://doi.org/10.13182/nt14-133

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                    Woolley, Robert D. Wed .  
"Optimal shielding design for minimum materials cost or mass".  United States.  https://doi.org/10.13182/nt14-133.  https://www.osti.gov/servlets/purl/1256374.

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@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 Euler-Lagrange equations. Furthermore, the associated Hamiltonian function and application of Pontryagin's theorem lead to conditions for a shield to be optimal.},

  doi          = {10.13182/nt14-133},

  journal      = {Nuclear Technology},

  number       = 3,

  volume       = 192,

  place        = {United States},

  year         = {Wed Dec 02 00:00:00 EST 2015},

  month        = {Wed Dec 02 00:00:00 EST 2015}

}

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