1. science
2. mathematics
3. geometry

Use of Monte Carlo Codes
Presentation to
NTEC; Radiation Shielding Module
Presented by
Albrecht Kyrieleis, AMEC
Overview
§  Summary of a Monte Carlo Code
§  MCBEND
§  Elements of a Monte-Carlo Calculation
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Geometry
Source
Scoring
Variance Reduction
§  Visualisation, Verification and Submission of a Monte
Carlo Calculation
§  Visual Workshop
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MCBEND
§ MCBEND : A generalised 3D Monte Carlo code for Neutron, Gamma
and Electron transport in sub-critical systems
§  It is licensed by ANSWERS Software Service, AMEC
•  http://www.answerssoftwareservice.com/
§  It is the acknowledged standard UK Monte Carlo computer code for
radiation shielding and dose assessments.
§  The main attributes of MCBEND are :
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Powerful Geometry Modelling Package
Automatic Acceleration options
Hyperfine energy nuclear data / collision processing
Easy-to-use Input Data Syntax - parameterisation, looping and formulae
Visual Workshop - Geometry Model Visualisation and Verification tool
Visual Workshop - User interface for submitting and controlling calculations
Expert help-desk support via telephone, email, fax
Quality Assurance including strict version control
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Elements of a Monte Carlo
Calculation
A Monte Carlo Calculation requires :
§  A specification of the geometry of the system.
§  The description of the materials.
§  The location and characteristics of the neutron, photon or electron
source.
§  The scores or tallies required.
§  Any variance reduction techniques to improve efficiency.
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Geometry Modelling in MCBEND
§  The MCBEND geometry modelling and tracking package
comprises:
§  A simple body component (Fractal Geometry or FG) using
conventional ‘ray tracing’
§  The additional power of hole geometries employing Woodcock
tracking
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Fractal Geometry
§  Fractal Geometry is a system of solid geometry modelling.
§  The problem geometry is subdivided into ZONES of uniform
material.
§  These zones are defined as the intersections and differences of
simple mathematical BODIES such as cuboids, cylinders and
spheres.
§  Any body can be rotated from its alignment with the part axes
§  A zone definition may include references to other zones that are to
be excluded from the volume it defines.
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Selection of Simple Body Types
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Zone formation in MCBEND
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Zones are formed by combinations of any number of bodies
Each body has a sequence number, n
+n refers to the volume inside a body
-n refers to the volume outside a body
Some simple, two-body combinations are sketched below
1
2
+1 -2
Difference
1
2
+1 +2
Intersection
1
Union
2
+1 OR+2
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Zone Contents
§  The contents of a zone can be :
§  A real material (a homogeneous mixture of nuclides)
§  A special material (void, black absorber, reflector)
§  In addition in MCBEND zone contents can be :
§  A subsidiary part
§  A hole material (further fine geometry detail)
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Fractal Geometry PARTS
§  The bodies are assembled into structures called PARTS. Parts are
self contained to simplify the construction and to take advantage of
any replication which may be present.
§  Parts have an outer boundary defined by the surface of one of the
simple bodies - the part container.
§  Parts may be included within other parts to any depth of nesting and
a given part may be included more than once within the geometry.
§  The ability to break down complex models into parts, each
separately described in its own local co-ordinate system, simplifies
the preparation and checking of the input data.
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Subsidiary Parts
§  Each subsidiary part is defined separately as a normal part
but then it is placed inside a zone of another part.
Control Assembly
Safety Assembly
Core Segment
Fuel Assembly
Reactor Segment
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Part Types
Container body
1
7
2
Container body
4
4
3
3
5
6
4
+4 +3
2
6
Cluster part
3
3
2
1
4
Container body
Nest part
1
Overlap part
Container body
+2 -1
+1 +2
2
1
+1 -2
Array part
General FG part
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Hole Geometries in MCBEND
§  Hole Geometries are used in conjunction with simple body
geometries by placing a hole geometry inside a zone (taking the
place of a physical material or a subsidiary part).
§  Hole Geometries can be used to model common replicating
arrangements and simple intersecting configurations in a shortcut form.
HELIX
SPIRAL
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CAD Interfaces
§  Two CAD interfaces are being developed for use with MCBEND.
§  One approach is to convert a CAD file into an Ansys ASCIIformat tetrahedral mesh, and import this into ANSWERS codes
as a Hole Geometry.
§  Available in MCBEND 11 for evaluation: direct import of CAD
geometry
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Material Specification
A given material is defined by VOLUME or WEIGHT
or ATOM fractions of the following constituents:
§  Elements referenced by their chemical symbol e.g. Fe
§  A standard mixture from a library e.g. STAINLESS STEEL
§  A user-defined mixture of elements e.g. a mixture of sodium, chlorine, hydrogen and oxygen
defining a particular saltwater.
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Elements of a Monte Carlo
Calculation
A Monte Carlo Calculation requires :
§  A specification of the geometry of the system.
§  The description of the materials.
§  The location and characteristics of the neutron, photon or
electron source.
§  The scores or tallies required.
§  Any variance reduction techniques to improve efficiency.
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Source Specification
The Source Variables are :
§  The position of the source defined by its x, y and z co-ordinates.
§  The geometrical extent of the source.
§  The energy of the source particle.
§  The initial direction of the source particle.
§  The weight of the source particle (source strength).
§  The nature of the source - neutron, photon or electron.
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Source Bodies
§  In MCBEND any number of source bodies may be defined
§  Source bodies include the following solid shapes that match those
available in the geometry modelling
§  BOX, SPHERE, XROD, YROD, ZROD,
§  CONE, TORUS, REL etc.
§  The following bodies are specific to source modelling
§  XDISC, YDISC, ZDISC,
§  XP, YP, ZP (rectangular planes),
§  POINT and LINE
§  The parameters of a source body may be assigned by referencing
a body or a zone in the FG model
§  Source bodies may be subdivided to allow a variation of source
intensity to be defined.
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Energy Variation
§  A range of options are available for defining the energy
variation.
P(G)
P(L)
group
Histogram
Energy
Lines
P(E)
P(θ)
Energy
Continuous spectrum:
U235 Fission and/or
U238 Fission
Am/Be
1/E
θ
Angular spectrum
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Source Weight
The initial weight of the source particle contains a normalisation factor
which relates the results obtained in the Monte-Carlo calculation to the
physical system modelled.
§  This is usually the total source (particles/sec) in the model.
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Elements of a Monte Carlo
Calculation
A Monte Carlo Calculation requires :
§  A specification of the geometry of the system.
§  The description of the materials.
§  The location and characteristics of the neutron, photon or electron
source.
§  The scores or tallies required.
§  Any variance reduction techniques to improve efficiency.
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Scoring
The Scoring Variables are :
§  The scoring quantity (i.e. what we want to score)
§  Flux
§  Response
§  Contributions to Response
§  Sensitivity of Flux or Response
§  Energy Deposition
§  Pulse Height Distribution
§  Angular Flux and Current
§  The scoring energy group scheme
§  MCBEND has standard energy group schemes
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Scoring
The Scoring Variables are :
§  The scoring region (i.e. where we want to score it)
§  one or more FG regions
•  May need to be specifically defined in the Geometry unit
§  splitting mesh (MCBEND)
§  surfaces
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Response Estimates
§  It is possible to fold into the flux evaluation a response crosssection to give an evaluation of response.
§  Library responses are available in MCBEND.
§  An example of a library response is: Gamma Dose Rate
§  Contributions to Response
§  Useful in determining which energies are contributing to
the response
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Elements of a Monte Carlo
Calculation
A Monte Carlo Calculation requires :
§  A specification of the geometry of the system.
§  The description of the materials.
§  The location and characteristics of the neutron, photon or electron
source.
§  The scores or tallies required.
§  Any variance reduction techniques to improve efficiency.
25
Variance Reduction
§  The simplest Monte Carlo model for particle transport problems is
the analogue model that uses the natural probabilities that various
events occur.
§  A realistic shielding problem may involve attenuation by a factor
of 106 or more.
§  Typically, to provide acceptable results at least 100 particles must
reach the scoring region.
§  Thus, a direct analogue Monte Carlo calculation would involve
simulating 108 or more particles.
§  Techniques for getting round this problem are known as:
Variance Reduction Methods
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Variance Reduction Methods
The Main Variance Reduction Methods Used in
MCBEND are :
§  Splitting and Rouletting
§  tracking only particles expected to contribute to the score
§  Source Weighting
§  biasing the sampling of the source to regions expected to
contribute to the score
Both of these methods embody the idea of particle weights
§  Each particle carries a weight, W, which is a measure of the
number of physical particles it represents.
§  For any Monte Carlo event it is possible to alter the normal
probability of an event as long as the particle weight is adjusted to
compensate.
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Splitting and Rouletting - Importance Map
§  This leads to the concept of IMPORTANCE, a measure of the
expected contribution to the score as a function of space,
energy and direction.
§  Splitting and Rouletting require an Importance Map that covers the
whole problem space
There are two components of an Importance Map:
§  Importance Mesh
§  Importance Values
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Importance Mesh
§  In MCBEND the problem space is subdivided by a set of fictitious
surfaces, splitting surfaces, which divide the problem into a set of
volume cells. The entire system is referred to as the Splitting Mesh.
§  The splitting mesh is independent of the material geometry.
§  The splitting Mesh can be defined in XYZ or RθZ co-ordinates
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Choice of Splitting Mesh Intervals
§  Splitting boundaries should generally be placed so that there is a
factor of about two attenuation across each mesh interval.
§  The attenuation will vary between energy group, and a
compromise must be reached. The energy range which has the
most influence over the choice of mesh interval in any region
should be the range which contributes most to the final result.
§  There may be regions of the problem which are not significant
paths from source to detectors, in these regions the choice of
mesh intervals is of little importance.
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Importance Values
In MCBEND the Importance Values can be :
§  Automatically Generated within MCBEND
§  using MAGIC adjoint diffusion calculation
§  Read in.
§  e.g. calculated values from an adjoint MCBEND
§  Exponential
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The Adjoint Function
The Adjoint Flux is a measure of the importance of a
particle in space and energy, in contributing to
the score.
§  MAGIC adjoint diffusion calculation
§  automatically run within the MCBEND calculation
§  ‘target’ regions are specified by the user
§  ‘target’ response is specified by the user
§  Adjoint MCBEND calculation.
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§ 
§ 
§ 
run separately
source is put in detector region
response function is source spectrum
solves ‘backwards’ - starts at lowest energy group and up-scatters
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MAGIC - Target Specification
TARGET
Splitting mesh
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Source Weighting
§  Particles from some parts of the source are more likely to reach
detectors than those from other parts.
§ 
e.g. Upper regions of the fuel elements contribute more to the dose on
the lid
§  Particles emitted at some energies are more likely to contribute to
detector responses than others.
§  e.g. Low energy particles are unlikely to penetrate a thick shield
§  Sampling particles equally from all parts of the source and at all
energies will be inefficient.
§  We want to sample particles from important parts and energy ranges
more frequently, without biasing the result.
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Source Weighting
In MCBEND a source can be weighted by :
§  Space
§  Energy
§  Angle
For Space and Energy weighting, there are two options:
§  Automatic
§ 
§ 
§ 
The importance map is used to control the sampling of source points
It ensures that sources are preferentially sampled in important regions
Robust and recommended
§  Manual
§ 
User chooses the weights
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Source Angular Weighting
§  Particles emitted in certain directions are more likely to contribute to
the detector response than others.
§  Only manual angular weighting is available so care must be taken
when using angular weighting.
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Elements of a Monte Carlo
Calculation
A Monte Carlo Calculation requires :
§  A specification of the geometry of the system.
§  The description of the materials.
§  The location and characteristics of the neutron, photon or electron
source.
§  The scores or tallies required.
§  Any variance reduction techniques to improve efficiency.
37
Visualisation, Verification and
Submission
Once a Monte Carlo Input has been generated,
the user must :
§  Visualise the model
§  Check the model
§  Select Nuclear Data Libraries
§  Run the Calculation
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Visual Workshop
§  Supports ANSWERS codes – MCBEND10A.
§  Load model and prepare/modify input.
§  Display a wire frame of the model geometry (FG bodies), source
bodies/mesh and importance mesh.
§  Display a ray traced 3D image of zones/regions/materials, Holes,
Unified source and multiple definitions.
§  Display a ray trace 2D image of zones/regions/materials, Holes,
source bodies/mesh, importance mesh and multiple definitions.
§  Create datsets files, select nuclear data libraries, run a case, view
output.
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Visual Workshop: Real time
interactive 3D ray trace
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Visual Workshop: 2D ray trace with
rulers and overlays
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Visual Workshop: Example Input
Deck
&
&
EXAMPLE B1 - FUEL TRANSPORT FLASK, NEUTRON CASE
Variation using structured parts and holes.
BEGIN CONTROL DATA
SAMPLE LIMIT 100000
Seeds 12345 54321
END
& Using SQUARE and PLATE Holes for fuel assemblies
BEGIN MATERIAL GEOMETRY
PART 1 NEST ! Flooded container
BOX BH1 1.0 0.5 75.0 24.0 24.0 400.0
BOX M3 0.5 0.5 75.0 25.0 25.0 400.0
BOX M4 0.0 0.0 75.0 26.0 26.0 400.0
...
Etc.
...
END
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Visual Workshop: LaunchPad
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Conclusions
§  Summary of a Monte-Carlo Code
§  MCBEND
§  Elements of a Monte-Carlo Calculation
§ 
§ 
§ 
§ 
Geometry
Source
Scoring
Variance Reduction
§  Visualisation, Verification and Submission of a Monte
Carlo Calculation
§  Visual Workshop
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