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
Computational Studies of Military Vehicles
and Structures

Heimbach – Experimentalist, APG, MD
Neutron and Gamma Ray Spectroscopy
1. APRF, Crane-Mounted Bare Fast Reactor
2. WWD, Munster, Germany, Movable
Fallout Simulator
3. ETBS, Bourges, France, Fallout Simulator

Order of Talk
1.
2.
3.
4.
5.
Generalities About Shielding
Methodology
Available Computer Codes
Statement of Problem
Solution – Hybrid Method Called MASH
Examples Galore
Comments on Mixed Field
Neutron-Gamma Ray Shielding
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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 Field
Neutron-Gamma Ray Shielding
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Shield Neutrons With Light Materials
Water, Plastic, Boron
Shield Gamma Rays With Heavy Materials
Lead, Iron
Beware of
Holes and Gaps !
Shielding Codes
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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

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MORSE
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
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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
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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
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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)
No Distance 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
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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
Theory
L  S
L  R
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* *
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FLUX From Source
Distribution
IMPORTANCE From
Detector Response

SdVdP

R

dVdP


*
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L-Terms Cancel
Dose Calculation
VSource   SdP  VDetector  RdP  Dose
*

Need Flux at Detector
or Importance at
Source
Dose 

Or Flux and
Importance at a
Coupling Surface


*


(


n
)
dAdP

CouplingS
Definitions
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Neutron Reduction Factor NRF
Neutron Dose Outside (Gray) / Dose Inside Shield
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Gamma Reduction Factor GRF
Gamma Dose Outside (Gray) / Dose Inside Shield
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Fallout Protection Factor FPF
Fallout Gamma Dose Outside (Gray) / Dose Inside
Shield
Further Definitions
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Neutron Protection Factor NPF
Neutron Dose 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
Applications
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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
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1 Meter Box, Rotated, With Holes and
Gaps
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2 Meter Box ORNL Calculation
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RTK Angled Box From WWD
Detectors
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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
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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
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1.
2.
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
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The Model Came From BRL CAD – CAM
Required Graphical Debugging – ORGBUG
Required Tolerance Debugging
Lost Particles !
Required a MORSE Modification !
Fallout Field at Bourges, France
Using La-140
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80 by 80 Meter Dirt Field
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At Corner, Rotated ~ 160 by 160 Meters
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30 by 30 Meter Concrete Pad
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At Corner, Rotated ~ 60 by 60 Meters
Experiment vs. Calculation
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Fallout simulated with Fission Products
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Fallout Simulated with La-140
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Comparison to ORNL Calculations
FPF Comparisons
Observations
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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
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Driver Less Well Protected ~ 15
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Some Differences for Source Type
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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
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Fair Prompt Gamma Protection ~ 3.5
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Good Fallout Protection ~ 9
Stay Away From Doors and Windows
Foxhole Model
Foxhole Protection Factors
Foxhole Conclusions

Reasonably Good Neutron Protection ~ 3
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Fair Prompt Gamma Protection ~ 2
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Good Fallout Protection ~ 12
Keep Head Down and Stay Inside
Tall Buildings
Buildings in an Urban Environment
Large Buildings
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We Can Make a Geometry Model
But - New Problem, Not Yet Solved !
No Experimental Data !
TORT Had Computational Limits for 10 Story
Building!
MASH Coupling Over Large Surface ?
Large Buildings, cont.
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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 ?
Conclusions

MASH Works Very Well for Small Shields

C/E Typically 10 – 20 %
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Large Buildings Represent an Unsolved
Problem
More Research Needed