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Monte Carlo Simulation of Nuclear

Reactions Dr Albrecht Kyrieleis MCnet, August 2014

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Content

After particle physics

AMEC

Nuclear fission: Shielding and criticality

Nuclear Fusion and ITER

Conclusion

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PhD (2003) in Hamburg / DESY

Small-x Physics: Diffractive DIS, BFKL

Topic: Calculation of the γ* impact factor at NLO with the aim to make

prediction using NLO BFKL.

PhD: Calculation of the real corrections and combination with virtual

corrections.

Collaboration with S. Gieseke

Many discussions with A. Sabio-Vera and J. Anderson

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Postdoc at Manchester (2003-2006)

pQCD - Gaps between jets – resummation – BFKL

Mainly analytical calculations.

Collaboration with Jeff Forshaw and Mike Seymour

Discovery of a new tower of super-leading logarithms in gaps-

between-jets cross sections (J. Forshaw, A Kyrieleis, M Seymour,

2006)

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Into industry ..

NNC: Company specialised on providing technical consultancy in the

area of nuclear technology and physics.

Using specialised software: simulation of different aspects a of a

nuclear power plant, e.g.:

Interplay of heat production from nuclear fission, cooling by

gas/water, fission rate variation in presence of water/steel/graphite

Statistical analysis of failure of engineering parts due to

heat/irradiation/mechanical stress

Consequences analysis for faults occurring in a nuclear plant

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University of Manchester / Diamond light source (Oxforshire)

Project: develop a prototype x-ray tomography station for material

science at a Synchrotron and

Develop new algorithms for image reconstruction and analysis and for

artefact suppression.

Analysis of nuclear materials

... and back

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Since 2009: at AMEC

Developing Monte Carlo based software to model radiation transport

(neutron, photon)

Using simulation software for radiation analysis

Leading projects involving development/testing/application of

simulation software.

Developing (deterministic) simulation software for crack initiation and

evolution in materials.

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AMEC at a glance

FTSE 100 company

Operating in over 40 countries worldwide

Serving oil & gas, mining, clean energy and environment & infrastructure markets across the world

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Over 29,000 employees in:

Europe 10,000 Americas 16,000 Growth Regions

3,000

Revenue some £4.2 billion

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Sectors

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Oil & Gas

Unconventional Oil & Gas

Nuclear

Renewables/ Bioprocess

Transmission & Distribution

Power

Water

Transportation/ Infrastructure

Government Services

Industrial/ Commercial

Mining

Oil & Gas Mining Clean Energy Environment & Infrastructure

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Our offices around the world

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Our 29,000 employees operate in 40 countries

AMEC office locations

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Key nuclear markets

Decommissioning

Waste Management

Environmental

Radiological

Lifetime Extension

Operational

Performance

Reactor Servicing

NUCLEAR

CLEAN UP

REACTOR

SUPPORT

NEW

BUILD

Strong renaissance in

Europe, potentially

>30 new reactors in

next two decades

10 GW new capacity

planned for UK at

£20bn by 2020.

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Nuclear – UK locations

Westlakes

Warrington

Knutsford

Gloucester

Winfrith

Thatcham

Harwell

Regional Office

Site Presence Hinkley

Dungeness

Torness

Hunterston

Heysham

Aldermaston

Faslane

Dounreay

Sizewell

Wylfa

Trawsfynydd

Oldbury

Barnwood

Chapelcross

Hartlepool

Culham

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Physics & Performance technical

disciplines

Nuclear Physics

Reactor Core Physics

Criticality

Shielding analysis

Radiological

Health Physics

Radiological Protection,

Dosimetry

Transport

Radiological safety

Environmental

Environmental control, pollution

prevention and control,

sustainability, contaminated land

Environmental safety

Plant Performance

Performance optimisation

Dynamic analysis of system

behaviour

Simulation-based analysis of

operational and control problems

Thermal hydraulics

CFD

Heat transfer & Fluid Flow

Transient analysis

Nuclear reactor behaviour during

faults

Gas Cooled Reactors

Water Cooled Reactors

(PWR/LWR)

Fast Reactors

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Nuclear Fission

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Nuclear fission

MeV192.9 fragments fission4.2235 nnU

decay

α, β, γ radiation

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Resulting physics problems:

Fuel elements are produced by enriching with U235. Protection

against neutron radiation in production process of fuel.

During operation: ensure shielding against any radiation and

containment of radioactive substances (e.g. coolant) under a variety

of possible fault conditions.

‘spent’ fuel contains various fission products; highly radioactive; most

importantly radiating gammas (from nuclear decay). Ensure protection

against this radiation during extraction from reactor, transport,

processing, storage.

Material may be activated by Neutrons becoming a gamma source

In a nuclear chain reaction the number of Neutrons rapidly increases.

Only if balanced by neutron absorption (e.g. in the control rods) and

loss can a controlled nuclear reaction be maintained. When does the

n-production rate exceeds the absorption rate (criticality) ?

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The Shielding Problem

Neutrons/photons/electrons emitted from the source move through a

geometry undergoing:

• Capture

• Scatter

• Escape

Given a specified source: What is the particle flux in a specified

area?

Source Scatter Capture

Escape

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The Criticality Problem

Neutrons emitted from the source undergo a sequence of events:

• Fission

• Capture

• Scatter

• Escape

Fission events are sources of further neutrons. For given geometry

and materials: what is the ratio of produced and lost neutrons ?

Source Fission Scatter Capture

Escape

Source’

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Estimating K

A neutron generation starts with the emergence of a neutron

from a fission event and ends with it escaping from the system or

being captured or initiating a further fission event.

k = neutrons produced in one generation

neutrons lost in the same generation

Therefore in a simple Monte Carlo calculation we can calculate

the value of k for a large number of sample neutrons and then

compute an average value.

In civil nuclear applications we want k<=1 !

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Monte Carlo solution (shielding and

criticality problem)

Model the system and simulate the tracking of a sample of particles.

Sample position, energy and direction of a particle emitted from the source.

Sample distance to be travelled in the current material before a collision

occurs (using total cross section)

Sample nuclide with which a collision occurs (using specified material

composition)

Now (and here is most of the physics) :

– Sample type of reaction with the collided nucleus

– For scattering events: the energy and direction of the scattered particle(s)

– For fission events: the number of emergent neutrons, their energies and

directions.

Compute tally

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Main particle reactions

(x, y): x in, y out

Neutrons

Elastic, inelastic scattering, (n, n), (n,n’)

Fission

Radiative capture (n, γ)

Alpha decay

(n, p), (n, 2n)

Photons:

Compton scattering (tracking of electron)

Photo-electric effect (tracking of electron)

Pair production (e+e- may be tracked)

Cross section available in library shipped with software

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Monte Carlo software by AMEC

MCBEND : A generalised 3D Monte Carlo code for Neutron, Gamma

and Electron transport in sub-critical systems

– acknowledged standard UK Monte Carlo computer code for radiation

shielding and dose assessments.

MONK: A 3D Monte Carlo code for nuclear criticality safety and

reactor physics analysis.

Both codes are licensed by ANSWERS Software Service, AMEC

http://www.answerssoftwareservice.com/

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Elements of a Monte Carlo Calculation

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

+1 -2

2 1

+1 +2

1 2

+1 OR+2

1 2

Difference

Intersection

Union

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Selection of Simple Body Types

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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 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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Part Types

+4 +3 +1 +2

+2 -1

+1 -2

3 2

1

4 Container body

General FG part

Cluster part

1 2 3

5

4 6

Container body

Nest part

6

Container body

Overlap part

1

Container body

7 1

2 3

4

2

3

4

Array part

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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.

Reactor Segment

Core Segment

Fuel Assembly

Safety Assembly

Control Assembly

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Hole Geometries in MCBEND

Woodcock tracking: Introduce fictitious material to make free path

length the same in all materials: No need to solve equation to

check in which zone particle is.

Additional geometric complexity

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)

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Hole Material Types

SPIRAL TETMESH

CONE LATTICE

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Hole Material Types

PLATE

POLY

PIPES

QUADRIC

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Hole Material Types

RANDOM

RZMESH

RANDRODS

VOXELA

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CAD Interfaces

Two CAD interfaces are being developed for use with MCBEND.

Either convert a CAD file into tetrahedral mesh and import as a

Hole Geometry. Or directly convert into MCBEND geometry.

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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.

Material Specification

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Elements of a Monte Carlo Calculation

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 nature of the source - neutron, photon or electron.

The position of the source defined by its x, y and z coordinates.

The geometrical extent of the source (e.g. using bodies as above)

The energy of the source particle.

The initial direction of the source particle.

The weight of the source particle (source strength).

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Energy Variation

A range of options are available for defining the energy

variation.

group

Histogram

P(G)

Energy

P(L)

Lines

Energy

Continuous spectrum:

U235 Fission and/or

U238 Fission

Am/Be

1/E

P(E)

q

P(q)

Angular spectrum

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Elements of a Monte Carlo Calculation

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

Need to specify :

The scoring quantity (i.e. what we want to score), e.g. Flux

Response, e.g. Gamma dose rate

Sensitivity of Flux or Response

Pulse Height Distribution

The scoring energy group scheme MCBEND has standard energy group schemes

The scoring region (i.e. where we want to score it)

one or more FG regions or surfaces

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MCBEND: Example Input File

& 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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Elements of a Monte Carlo Calculation

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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Variance Reduction

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 techniques

Particle weights:

Each particle carries a weight, W, which is a measure of the number of physical particles it represents.

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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Variance Reduction: Splitting and Russian

Roulette

score

Splitting mesh

• Define splitting mesh covering model geometry

• Define importance values in each cell

• When particle crossing boundary with increasing importance

double particle number but half their weight

• When crossing boundary with decreasing importance: sample

particle death or survival. Double weight if survival.

• Importance values can be calculated automatically in

MCBEND

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Variance Reduction: Source Weighting

Particles from some parts of the source or emitted in certain directions

or with certain energies are more likely to contribute to the detector

response than others.

Sample particles more frequently which are more likely to reach the

scoring area. Compensate by adjusting the weights.

Angular source weighting:

Polar axis

Particle Track

Bin of highest importance

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Variance reduction: Forced Flight

Forced Flight Interface

Track of real particle

created at the interfaceTrack of Forced Flight Particle

Track of

original

part ic le

Detector

Collis ion

Collis ion

Collimator

• Particles are forced into a particular direction towards a geometric interface located near the detector.

• At each collision, a ‘forced flight particle’ is created and transported directly to the interface without further collision.

• The weight of the particle is adjusted accounting for the true probability of a particle scattering in that direction and travelling uncollided to the interface.

• The original particle is also tracked onwards and can produce further forced flight particles.

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Visual Workshop

Software offered by ANSWERS

Visualise model

Check model

Run calculation

View results

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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: results display

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Nuclear Fusion

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ITER / France

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Gamma radiation after shut-down

Materials activated

by n-irradiation act

as gamma source

150Mio °C hot

plasma in here

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CONGA (COupled Neutron Gamma Analysis)

Bespoke software suite currently under development at AMEC

Couples MC code MCNP and nuclear activation code FISPACT

MCNP

Neutron

fluxes

FISPACT

MCNP Photon

spectra

Photon

fluxes

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ANSWERS Software Service

High quality software and consultancy services for customers world-

wide in the areas of reactor physics, radiation shielding, dosimetry,

nuclear criticality, well logging and nuclear data.

Based in Dorset /UK

Close collaboration with various universities

Codes:

MCBEND, MONK

WIMS (General purpose reactor physics program for core physics

calculations, deterministic and Monte Carlo)

PANTHER (Advanced 3D nodal code for reactor core analysis)

FISPIN (calculates the changes in the numbers of atoms of the nuclides as

a result irradiation and cooling)

...

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Conclusions

Nuclear renaissance in Europe; New build in UK

Shielding and Criticality problem Monte Carlo solution MCBEND

/ MONK

Elements of a Monte-Carlo Calculation

Geometry

Source

Scoring

Variance Reduction

Visual workshop: Visualisation, Checking, Results

Fusion/ITER: CONGA for gamma radiation from activated materials

We are always on the watch out for enthusiastic highly skilled new

people.

Contact: Albrecht.Kyrieleis@amec.com