Lecture onLecture onApplications of the Monte Applications of the Monte

Carlo Adjoint ShieldingCarlo Adjoint ShieldingMethodologyMethodology

ByByRoger A. RydinRoger A. Rydin, University of Virginia, , University of Virginia,

Consultant U.S. ArmyConsultant U.S. ArmyCraig R. HeimbachCraig R. Heimbach, formerly with Army , formerly with Army

Pulse Radiation FacilityPulse Radiation Facility

PersonnelPersonnel

RydinRydin - University Expert, NGIC, VA - University Expert, NGIC, VA

Computational Studies of Military Vehicles Computational Studies of Military Vehicles and Structuresand Structures

HeimbachHeimbach – Experimentalist, APG, MD – Experimentalist, APG, MD

Neutron and Gamma Ray SpectroscopyNeutron and Gamma Ray Spectroscopy

1.1. APRF,APRF, Crane-Mounted Bare Fast Reactor Crane-Mounted Bare Fast Reactor

2.2. WWD,WWD, Munster, Germany, Movable Munster, Germany, Movable Fallout SimulatorFallout Simulator

3.3. ETBS,ETBS, Bourges, France, Fallout Simulator Bourges, France, Fallout Simulator

Order of TalkOrder of Talk

1.1. GeneralitiesGeneralities About Shielding About Shielding MethodologyMethodology

2.2. Available Computer Available Computer CodesCodes

3.3. Statement of Statement of ProblemProblem

4.4. SolutionSolution – Hybrid Method Called – Hybrid Method Called MASHMASH

5.5. ExamplesExamples Galore Galore

Comments on Mixed FieldComments on Mixed FieldNeutron-Gamma Ray ShieldingNeutron-Gamma Ray Shielding

Shielding is an ArtShielding is an Art

Requires Skilled ModelingRequires Skilled Modeling Shielding Requires Transport TheoryShielding Requires Transport Theory

Highly Anisotropic Cross SectionsHighly Anisotropic Cross Sections Discrete Ordinates Sn MethodsDiscrete Ordinates Sn Methods

Large Distances In Regular GeometryLarge Distances In Regular Geometry Monte Carlo MethodsMonte Carlo Methods

Short Distances In Detailed GeometryShort Distances In Detailed Geometry

General Mixed FieldGeneral Mixed FieldNeutron-Gamma Ray ShieldingNeutron-Gamma Ray Shielding

Shield Neutrons With Shield Neutrons With LightLight Materials Materials

Water, Plastic, BoronWater, Plastic, Boron Shield Gamma Rays With Shield Gamma Rays With HeavyHeavy

MaterialsMaterials

Lead, IronLead, Iron Beware ofBeware of

Holes and GapsHoles and Gaps ! !

Shielding CodesShielding Codes

ORNLORNL (Shielding) (Shielding) ANISN, DORT, TORT,ANISN, DORT, TORT, Discrete Ordinates Discrete Ordinates MORSE,MORSE, Multi-group Monte Carlo Multi-group Monte Carlo LANLLANL (Weapons Design) (Weapons Design) TRIDENT, etc,TRIDENT, etc, Discrete Ordinates Discrete Ordinates MCNP,MCNP, Continuous Energy Monte Carlo Continuous Energy Monte Carlo Cross Section Libraries, QuadraturesCross Section Libraries, Quadratures Incompatible! (2 l +1) / 2 FactorIncompatible! (2 l +1) / 2 Factor

Monte Carlo CodesMonte Carlo Codes MORSEMORSE

Volumetric Primitives - SPH, RPP, ARB, Volumetric Primitives - SPH, RPP, ARB,

ARS, TRC, BOX, ELL, etcARS, TRC, BOX, ELL, etc

Boulean Combinatorial GeometryBoulean Combinatorial Geometry MCNPMCNP

Define Surfaces, Make VolumesDefine Surfaces, Make Volumes

Easy Replication, RestartEasy Replication, Restart

Can’t Do Can’t Do AdjointAdjoint Problem Problem

Basic QuestionBasic Question

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

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

Monte CarloMonte Carlo Can’t Handle the Can’t Handle the DistanceDistance or a or a Small SizeSmall Size Dose Receiver Dose Receiver

Air-Over Ground ProblemAir-Over Ground Problem 2D Problem Covers 2+ Kilometers2D Problem Covers 2+ Kilometers

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

42 Neutron, 17 Gamma Ray Groups42 Neutron, 17 Gamma Ray Groups

Cover Inelastic ScatteringCover Inelastic Scattering P6 Cross SectionsP6 Cross Sections

Compton Scattering AnisotropyCompton Scattering Anisotropy S16 Forward – Biased Quadrature SetS16 Forward – Biased Quadrature Set

Adjoint ProblemAdjoint Problem

Every Every Integro – Differential EquationIntegro – Differential Equation Has Has

a a Dual, Adjoint or ImportanceDual, Adjoint or Importance Counterpart Counterpart Equations Are ConnectedEquations Are Connected Through an Through an

Integral Variational Principle FunctionalIntegral Variational Principle Functional They Have the They Have the Same Boundary ConditionsSame Boundary Conditions The The OperatorsOperators Are Obtainable By Are Obtainable By

Transpositions, Role Reversals, andTranspositions, Role Reversals, and

Energy Direction ReversalEnergy Direction Reversal

Solution - MASH Solution - MASH MethodologyMethodology

Transport from SourceTransport from Source = Discrete S = Discrete Snn

Calculation with DORT (2D) or TORT (3D)Calculation with DORT (2D) or TORT (3D)

NoNo Distance and Geometry Limitations to Vicinity Distance and Geometry Limitations to Vicinity of Shieldof Shield

Dose in Dose in Complicated ShieldComplicated Shield = Stochastic = Stochastic Calculation with MORSE in Adjoint ModeCalculation with MORSE in Adjoint Mode

Shield Geometry Complexity, Orientation, and Shield Geometry Complexity, Orientation, and AllAll Particles Particles StartStart from Detector Volume from Detector Volume

Couple Over a SurfaceCouple Over a Surface Around Shield Around Shield

MASH MethodologyMASH Methodology

ImpliedImplied – The Presence of the Shield – The Presence of the Shield Doesn’t Doesn’t PerturbPerturb the Discrete the Discrete Ordinates SolutionOrdinates Solution

If UntrueIf Untrue, Add a , Add a Dummy Dummy ShieldShield RotationRotation of the Shield Before of the Shield Before

Coupling Doesn’t Affect the Answer – Coupling Doesn’t Affect the Answer – Not True for Big ShieldsNot True for Big Shields

TheoryTheory

FLUXFLUX From Source From Source DistributionDistribution

IMPORTANCEIMPORTANCE From From Detector ResponseDetector Response

L-Terms CancelL-Terms Cancel

SL RL **

dVdPRSdVdP *

Dose CalculationDose Calculation

Need Flux at Need Flux at Detector or Detector or Importance at Importance at SourceSource

Or Flux and Or Flux and Importance at a Importance at a Coupling SurfaceCoupling Surface

DosedPRVSdPV DetectorSource *

CouplingS

dAdPnDose )(*

DefinitionsDefinitions Neutron Reduction Factor NRFNeutron Reduction Factor NRF NeutronNeutron Dose Outside (Gray) / Dose Inside Dose Outside (Gray) / Dose Inside

ShieldShield

Gamma Reduction Factor GRFGamma Reduction Factor GRF Gamma Dose Outside (Gray) / Dose Inside ShieldGamma Dose Outside (Gray) / Dose Inside Shield

Fallout Protection Factor FPFFallout Protection Factor FPF Fallout Gamma Dose Outside (Gray) / Dose Inside Fallout Gamma Dose Outside (Gray) / Dose Inside

ShieldShield

Further DefinitionsFurther Definitions

Neutron Protection Factor NPFNeutron Protection Factor NPFNeutronNeutron Dose Outside (Gray) / N and Dose Outside (Gray) / N and γγ Dose Dose

Inside Shield Caused by Neutron SourceInside Shield Caused by Neutron Source

Gamma Protection Factor GPFGamma Protection Factor GPFGamma Dose Outside (Gray) / Gamma Dose Outside (Gray) / γγ Dose Inside Dose Inside

Shield Caused by Shield Caused by γγ Source Source

ApplicationsApplications

BoxesBoxes Near a Prompt Source Near a Prompt Source Vehicles Near a Prompt SourceVehicles Near a Prompt Source BNCTBNCT Medical Therapy Room Design Medical Therapy Room Design TankTank on a Fallout Field on a Fallout Field Small Small Concrete BuildingConcrete Building FoxholeFoxhole Buildings in an Buildings in an UrbanUrban Environment Environment

Verification of Methodology for Verification of Methodology for Simple GeometriesSimple Geometries

1 Meter Box1 Meter Box, Rotated, With Holes and , Rotated, With Holes and GapsGaps

2 Meter Box 2 Meter Box ORNL CalculationORNL Calculation

RTKRTK Angled Box From Angled Box From WWDWWD

DetectorsDetectors

ROSPECROSPEC – 4 Spherical – 4 Spherical Proportional Proportional CountersCounters, Unfolding, Unfolding

DOSPECDOSPEC – Dose – Calibrated – Dose – Calibrated NaINaI Calibrated Calibrated GMGM Tubes Tubes TETE Ion Chambers Ion Chambers

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

Small Lined Iron BoxSmall Lined Iron Box

Small Lined Iron BoxSmall Lined Iron Box

Unlined, Polyethylene Liner, Unlined, Polyethylene Liner, Boron Polyethylene LinerBoron Polyethylene Liner 200 Meters200 Meters From APRF From APRF Calibrated Calibrated GM TubesGM Tubes, , Tissue Tissue

Equivalent DosimetersEquivalent Dosimeters

Learned The Value of Learned The Value of Source Energy Source Energy BiasingBiasing

Start More Particles That Give Start More Particles That Give High DoseHigh Dose

Medical Therapy RoomMedical Therapy Room

Medical Therapy RoomMedical Therapy Room Dummy Head Dummy Head in DORT Problem Givesin DORT Problem Gives Scattering Source to WallsScattering Source to Walls ConclusionsConclusions1.1. Doesn’t Make Much Difference If Doesn’t Make Much Difference If

Patient Is Prone In Beam, Seated Out Patient Is Prone In Beam, Seated Out Of Beam, Or Shadow ShieldedOf Beam, Or Shadow Shielded

2.2. Dose To Rest Of Body Comes Dose To Rest Of Body Comes Through the Neck !Through the Neck !

T72 Russian Tank ModelT72 Russian Tank Model>10000 Primitive Bodies:

ARS Arbitrary Surfaces;

ARB Arbitrary Polyhedrons; etc.

>6000 Material Regions by Combinatorial Geometry

T72 Russian Tank ModelT72 Russian Tank Model

The The ModelModel Came From BRL CAD – Came From BRL CAD – CAMCAM

Required Required Graphical DebuggingGraphical Debugging – – ORGBUGORGBUG

Required Required Tolerance DebuggingTolerance Debugging

Lost ParticlesLost Particles ! ! Required a Required a MORSE ModificationMORSE Modification ! !

Fallout Field at Bourges, Fallout Field at Bourges, FranceFrance

Using La-140Using La-140 80 by 8080 by 80 Meter Meter DirtDirt Field Field

At At CornerCorner, Rotated ~ , Rotated ~ 160 by 160160 by 160 Meters Meters

30 by 3030 by 30 Meter Meter ConcreteConcrete Pad Pad

At At CornerCorner, Rotated ~ , Rotated ~ 60 by 6060 by 60 Meters Meters

Experiment vs. CalculationExperiment vs. Calculation

Fallout simulated with Fallout simulated with Fission Fission ProductsProducts

Fallout Simulated with Fallout Simulated with La-140La-140

Comparison to Comparison to ORNLORNL Calculations Calculations

FPF ComparisonsFPF Comparisons

ObservationsObservations

Strong Variation, Strong Variation, Seat to HeadSeat to Head ConcreteConcrete FPF FPF >> DirtDirt , in General , in General Conc. vs. Dirt Conc. vs. Dirt DifferenceDifference, , Probably RealProbably Real Calculation Calculation ~~ in Middlein Middle Agreement Generally Within Agreement Generally Within Error BarsError Bars Fallout Protection is Fallout Protection is SignificantSignificant

FPF Comparison, ORNLFPF Comparison, ORNL

General Conclusions for T General Conclusions for T 7272

Fallout Protection Factor Fallout Protection Factor ~ 40~ 40

DriverDriver Less Well Protected Less Well Protected ~ 15~ 15

Some Differences for Some Differences for Source TypeSource Type

Some Differences for Some Differences for Model MakerModel Maker

Typical Accuracy, ~ Typical Accuracy, ~ 15 – 20 %15 – 20 %

Concrete Building PhotoConcrete Building Photo

Concrete Building ModelConcrete Building Model

Concrete Building, NeutronsConcrete Building, Neutrons

Concrete Building, GammasConcrete Building, Gammas

Concrete Building Concrete Building ConclusionsConclusions

Reasonably Good Reasonably Good NeutronNeutron Protection Protection ~ ~ 33

Fair Prompt Fair Prompt GammaGamma Protection Protection ~ 3.5~ 3.5

Good Good FalloutFallout Protection Protection ~ 9~ 9

Stay Away From Doors and WindowsStay Away From Doors and Windows

Foxhole ModelFoxhole Model

Foxhole Protection FactorsFoxhole Protection Factors

Foxhole ConclusionsFoxhole Conclusions

Reasonably Good Reasonably Good NeutronNeutron Protection Protection ~ ~ 33

Fair Prompt Fair Prompt GammaGamma Protection Protection ~ 2~ 2

Good Good FalloutFallout Protection Protection ~ 12~ 12

Keep Head Down and Stay InsideKeep Head Down and Stay Inside

Tall BuildingsTall Buildings

Buildings in an Urban Buildings in an Urban EnvironmentEnvironment

Large BuildingsLarge Buildings

We Can We Can Make a Geometry ModelMake a Geometry Model But - But - New ProblemNew Problem, , Not Yet SolvedNot Yet Solved ! ! NoNo Experimental DataExperimental Data ! ! TORT Had Computational LimitsTORT Had Computational Limits for for 10 10

StoryStory Building! Building! MASH Coupling Over MASH Coupling Over Large SurfaceLarge Surface ? ?

Large Buildings, cont.Large Buildings, cont.

AlternateAlternate Method, Method, QADQAD Point Kernel Point Kernel Gamma CodeGamma Code

QADQAD Uses Uses MASH ModelMASH Model ChineseChinese Building Study near Reactor Building Study near Reactor QADQAD Point Kernel Point Kernel Buildup FactorsBuildup Factors ? ? Effect of Effect of Extended Shadowed Extended Shadowed

SourceSource ? ?

ConclusionsConclusions

MASH Works MASH Works Very WellVery Well for for Small Small ShieldsShields

C/EC/E Typically Typically 10 – 20 %10 – 20 %

Large Buildings Represent an Large Buildings Represent an Unsolved Unsolved ProblemProblem

More ResearchMore Research Needed Needed