Lecture on applications of the monte carlo adjoint shielding methodology
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Lecture on Applications of the Monte Carlo Adjoint Shielding Methodology. By Roger A. Rydin , University of Virginia, Consultant U.S. Army Craig R. Heimbach , formerly with Army Pulse Radiation Facility. Personnel. Rydin - University Expert, NGIC, VA

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Lecture on Applications of the Monte Carlo Adjoint Shielding Methodology

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Lecture onApplications of the Monte Carlo Adjoint ShieldingMethodology


Roger A. Rydin, University of Virginia, Consultant U.S. Army

Craig R. Heimbach, formerly with Army Pulse Radiation Facility


  • Rydin - University Expert, NGIC, VA

    Computational Studies of Military Vehicles and Structures

  • Heimbach – Experimentalist, APG, MD

    Neutron and Gamma Ray Spectroscopy

  • APRF, Crane-Mounted Bare Fast Reactor

  • WWD, Munster, Germany, Movable Fallout Simulator

  • ETBS, Bourges, France, Fallout Simulator

Order of Talk

  • Generalities About Shielding Methodology

  • Available Computer Codes

  • Statement of Problem

  • Solution – Hybrid Method Called MASH

  • Examples Galore

Comments on Mixed FieldNeutron-Gamma Ray Shielding

  • Shielding is an Art

    Requires Skilled Modeling

  • Shielding Requires Transport Theory

    Highly Anisotropic Cross Sections

  • Discrete Ordinates Sn Methods

    Large Distances In Regular Geometry

  • Monte Carlo Methods

    Short Distances In Detailed Geometry

General Mixed FieldNeutron-Gamma Ray Shielding

  • Shield Neutrons With Light Materials

    Water, Plastic, Boron

  • Shield Gamma Rays With Heavy Materials

    Lead, Iron

  • Beware of

    Holes and Gaps !

Shielding Codes

  • ORNL (Shielding)

    ANISN, DORT, TORT, Discrete Ordinates

    MORSE, Multi-group Monte Carlo

  • LANL (Weapons Design)

    TRIDENT, etc, Discrete Ordinates

    MCNP, Continuous Energy Monte Carlo

  • Cross Section Libraries, Quadratures

    Incompatible! (2 l +1) / 2 Factor

Monte Carlo Codes


    Volumetric Primitives - SPH, RPP, ARB,

    ARS, TRC, BOX, ELL, etc

    Boulean Combinatorial Geometry

  • MCNP

    Define Surfaces, Make Volumes

    Easy Replication, Restart

    Can’t Do Adjoint Problem

Basic Question

  • How Do You Accurately Calculate the Dose Inside a Geometrically Complicated Shield a Large Distance from a Mixed Source of Neutrons and Gamma Rays ?

  • Discrete Ordinates Can’t Handle The Shield Geometry (Stair Steps ?)

  • Monte Carlo Can’t Handle the Distance or a Small Size Dose Receiver

Air-Over Ground Problem

  • 2D Problem Covers 2+ Kilometers

    Large, Geometrically Increasing, Mesh Spaces in Air, Small Mesh in Ground

  • 42 Neutron, 17 Gamma Ray Groups

    Cover Inelastic Scattering

  • P6 Cross Sections

    Compton Scattering Anisotropy

  • S16 Forward – Biased Quadrature Set

Adjoint Problem

  • Every Integro – Differential Equation Has

    a Dual, Adjoint or Importance Counterpart

  • Equations Are Connected Through an

    Integral Variational Principle Functional

  • They Have the Same Boundary Conditions

  • The Operators Are Obtainable By

    Transpositions, Role Reversals, and

    Energy Direction Reversal

Solution - MASH Methodology

  • Transport from Source = Discrete Sn Calculation with DORT (2D) or TORT (3D)

    NoDistance and Geometry Limitations to Vicinity of Shield

  • Dose in Complicated Shield = Stochastic Calculation with MORSE in Adjoint Mode

    Shield Geometry Complexity, Orientation, and All Particles Start from Detector Volume

  • Couple Over a Surface Around Shield

MASH Methodology

  • Implied – The Presence of the Shield Doesn’t Perturb the Discrete Ordinates Solution

  • If Untrue, Add a Dummy Shield

  • Rotation of the Shield Before Coupling Doesn’t Affect the Answer – Not True for Big Shields


  • FLUX From Source Distribution

  • IMPORTANCE From Detector Response

  • L-Terms Cancel

Need Flux at Detector or Importance at Source

Or Flux and Importance at a Coupling Surface

Dose Calculation


  • Neutron Reduction Factor NRF

    NeutronDose Outside (Gray) / Dose Inside Shield

  • Gamma Reduction Factor GRF

    Gamma Dose Outside (Gray) / Dose Inside Shield

  • Fallout Protection Factor FPF

    Fallout Gamma Dose Outside (Gray) / Dose Inside Shield

Further Definitions

  • Neutron Protection Factor NPF

    NeutronDose Outside (Gray) / N and γ Dose Inside Shield Caused by Neutron Source

  • Gamma Protection Factor GPF

    Gamma Dose Outside (Gray) / γ Dose Inside Shield Caused by γ Source


  • Boxes Near a Prompt Source

  • Vehicles Near a Prompt Source

  • BNCT Medical Therapy Room Design

  • Tank on a Fallout Field

  • Small Concrete Building

  • Foxhole

  • Buildings in an Urban Environment

Verification of Methodology for Simple Geometries

  • 1 Meter Box, Rotated, With Holes and Gaps

  • 2 Meter Box ORNL Calculation

  • RTK Angled Box From WWD


  • ROSPEC – 4 Spherical Proportional Counters, Unfolding

  • DOSPEC – Dose – Calibrated NaI

  • Calibrated GM Tubes

  • TE Ion Chambers

    International Intercalibration Effort – US, UK, Germany, France, Canada

Small Lined Iron Box

Small Lined Iron Box

  • Unlined, Polyethylene Liner,

    Boron Polyethylene Liner

  • 200 Meters From APRF

  • Calibrated GM Tubes, Tissue Equivalent Dosimeters

    Learned The Value of Source Energy Biasing

    Start More Particles That Give High Dose

Medical Therapy Room

Medical Therapy Room

  • Dummy Head in DORT Problem Gives

    Scattering Source to Walls

  • Conclusions

  • Doesn’t Make Much Difference If Patient Is Prone In Beam, Seated Out Of Beam, Or Shadow Shielded

  • Dose To Rest Of Body Comes Through the Neck !

T72 Russian Tank Model

>10000 Primitive Bodies:

ARS Arbitrary Surfaces;

ARB Arbitrary Polyhedrons; etc.

>6000 Material Regions by Combinatorial Geometry

T72 Russian Tank Model

  • The Model Came From BRL CAD – CAM

  • Required Graphical Debugging – ORGBUG

  • Required Tolerance Debugging

    Lost Particles !

  • Required a MORSE Modification !

Fallout Field at Bourges, FranceUsing La-140

  • 80 by 80 Meter Dirt Field

  • At Corner, Rotated ~ 160 by 160 Meters

  • 30 by 30 Meter Concrete Pad

  • At Corner, Rotated ~ 60 by 60 Meters

Experiment vs. Calculation

  • Fallout simulated with Fission Products

  • Fallout Simulated with La-140

  • Comparison to ORNL Calculations

FPF Comparisons


  • Strong Variation, Seat to Head

  • Concrete FPF >Dirt , in General

  • Conc. vs. Dirt Difference, Probably Real

  • Calculation ~in Middle

  • Agreement Generally Within Error Bars

  • Fallout Protection is Significant

FPF Comparison, ORNL

General Conclusions for T 72

  • Fallout Protection Factor ~ 40

  • Driver Less Well Protected ~ 15

  • Some Differences for Source Type

  • Some Differences for Model Maker

  • Typical Accuracy, ~ 15 – 20 %

Concrete Building Photo

Concrete Building Model

Concrete Building, Neutrons

Concrete Building, Gammas

Concrete Building Conclusions

  • Reasonably Good Neutron Protection ~ 3

  • Fair Prompt Gamma Protection ~ 3.5

  • Good Fallout Protection ~ 9

    Stay Away From Doors and Windows

Foxhole Model

Foxhole Protection Factors

Foxhole Conclusions

  • Reasonably Good Neutron Protection ~ 3

  • Fair Prompt Gamma Protection ~ 2

  • Good Fallout Protection ~ 12

    Keep Head Down and Stay Inside

Tall Buildings

Buildings in an Urban Environment

Large Buildings

  • We Can Make a Geometry Model

  • But - New Problem, Not Yet Solved !

  • NoExperimental Data !

  • TORT Had Computational Limits for 10 Story Building!

  • MASH Coupling Over Large Surface ?

Large Buildings, cont.

  • Alternate Method, QAD Point Kernel Gamma Code

  • QAD Uses MASH Model

  • Chinese Building Study near Reactor

  • QAD Point Kernel Buildup Factors ?

  • Effect of Extended Shadowed Source ?


  • MASH Works Very Well for Small Shields

  • C/E Typically 10 – 20 %

  • Large Buildings Represent an Unsolved Problem

  • More Research Needed

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