Oddelek za fiziko
Seminar Ib -1. letnik, II. Stopnja
Production of gamma rays in fusion reactors
Author: Dijana Makivić
Mentor: doc. dr. Luka Snoj
Co-mentor: doc. dr. Igor Lengar
Ljubljana, March 2017
Abstract:
In the seminar the prompt and delayed gamma ray production in structural materials and in the
plasma of a tokamak is presented. The most important fusion reactions in the Joint European Torus
(JET) fusion reactor are described. The high energy neutrons (2,5 MeV and 14,1 MeV) interact with
matter and as a result of certain reactions, prompt and delayed gamma rays are emitted from
material. Gamma ray diagnostics in the JET fusion reactor is described. The calculations of neutron
activation and creation of gamma rays is usually performed with computer simulations. Results of
Monte Carlo simulations for the neutron and prompt gamma ray fluence in structural materials of
the JET fusion reactor are presented.
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Contents
1.
INTRODUCTION ............................................................................................................................... 2
2.
NEUTRON ACTIVATION.................................................................................................................... 2
3.
PRODUCTION OF GAMMA RAYS IN A FUSION REACTOR ................................................................ 4
3.1.
Prompt gamma rays in the plasma.......................................................................................... 5
3.2.
Neutron induced gamma rays ................................................................................................. 6
3.3.
Delayed gamma rays ............................................................................................................... 6
4.
GAMMA RAY MEASUREMENTS AND SIMULATIONS ....................................................................... 7
5.
CONCLUSION ................................................................................................................................... 9
6.
LITERATURE ................................................................................................................................... 10
1. INTRODUCTION
The main goal of fusion research is to develop a safe and practically inexhaustible source of energy
from fusion reactors. Fusion energy features many advantages compared to other energy sources,
such as relatively low environmental impact, relatively high level of safety and abundance of fuel (Li
and D).
Different types of fusion reactors have been built in the past, but the most promising is the torus
shaped reactor, called a tokamak in which hot plasma is separated from the walls of the containment
vessel with strong magnetic fields. The largest tokamak in the world currently is the Joint European
Torus (JET) [1]. The future ITER (˝The Way˝ in latin) machine now under construction will be twice as
large as a JET [2]. In fusion reactors there will be little emission of greenhouse gases or harmful
chemical substances such as carbon monoxide, carbon dioxide and sulphur oxides into the
atmosphere. Fusion reactors use isotopes of hydrogen - deuterium and tritium as fuel. The D-D
fusion reaction involves pure deuterium that has a natural abundance of 0.0156 at. % and is
relatively easily extracted. The D-T fusion reaction is the main candidate for fusion power plants and
involves equal parts of deuterium and tritium. The main product of the D-D and D-T reactions is the
helium gas. Neutrons with an energy of 2,5 MeV from D-D plasma and 14,1 MeV from D-T plasma are
produced and they interact with the structural materials. These neutrons interact with nuclei and
cause activation of structural materials which become radioactive, but most of the produced
radionuclides have half-lives of less than 100 years. Activation of materials changes the materials
chemical and physical properties. Alpha, beta and gamma radioactive decay causes delay heat in
tokamak components which requires cooling of components after the shutdown of the reactor.
Delayed gamma rays are responsible for dose rates after the shut down of and therefore evaluation
of delayed gamma rays is needed to provide safe access and maintenance of fusion reactors [3].
2. NEUTRON ACTIVATION
Neutrons are created in the plasma as a product of fusion reactions. The following nuclear reactions
are most promising for using fusion as energy source.
2
The D-D reactions, with two distinct channels known to occur with almost equal probabilities, when
two deuterium nuclei are fused
,
(1)
(2)
Due to the reaction kinematics in reaction (1) the energy of tritium is 1 MeV and the energy of the
proton is 3 MeV. In the second reaction (2) the energy of
is 0,8 MeV and the energy of the
neutron 2,5 MeV.
The D-T reaction, in which the deuterium and tritium are fused is:
.
(3)
The products of reaction (3) are an alpha particle with 3,5 MeV of energy and a neutron with 14,1
MeV of energy.
The high energy neutrons that are created by fusion are transported through the materials of the
fusion reactor. As neutrons are electrically neutral, they pass through the atomic electron cloud and
interact only with nuclei. The probability for a reaction between a nucleus in the target and a
neutron is given by the microscopic cross section, denoted by σ. The neutron cross section σ has
units of area in barns, where 1 barn is equal to 10-24 cm2, and is dependent on the energy of the
incident neutron, types of reaction and the target nuclide [4]. In fusion reactors, neutrons created in
D-D or a D-T plasma have different energy spectra.
Most common interactions and symbols of reactions between neutrons and nonfissile materials are
listed below.





Elastic scattering (n, n),
Inelastic scattering (n, n‫)׳‬,
Radiative capture (n, γ),
Charged particle production (n, α), (n, p),
Neutron-producing reactions (n, 2n), (n, 3n).
Elastic scattering is a process, in which the neutron hits the nucleus and changes direction. The
nucleus is left in its ground state, but the neutron changes its outgoing direction, and also loses some
kinetic energy because of the energy transfer to the recoil of the scattering nucleus. Inelastic
scattering is similar to elastic scattering but the nucleus is left in an excited state. Inelastic scattering
of neutron in the material can happen only when the neutron energy is above the energy of the first
excited state of the scattering nucleus. When transition from the excited to the ground state occurs,
usually a photon is emitted. The radiative capture is a process, where the neutron is captured by the
nucleus. Whenever a nucleus absorbs a neutron, a compound nucleus is formed. Excitation energy of
a new compound nucleus is equal to the kinetic and binding energy of the neutron. With this process
new unstable radioactive nuclei are possibly created in the material, which will decay to a stable
nuclei by radioactive decay. In this process delayed gamma rays are produced. Creation of new nuclei
also affects the material properties. Radiative capture and charged particle reactions are partly
absorption reactions, where the neutrons are absorbed and other particles, like gamma rays, alpha
particles or protons, are emitted. In fusion reactors neutrons with a high energy are present and
therefore neutron producing reactions can occur, which means that, from one neutron that interacts
with the nucleus, two or more neutrons can originate from the struck nucleus [5][6].
Neutron flux spectra
:
is defined as a product of neutron speed
.
3
and the neutron density
(4)
The reaction rate, which is defined as the number of neutron reactions with target atoms per unit
volume per second, is given by the equation (5):
∫
.
(5)
Where
is the neutron flux spectra, is the atom density of the target and
is the cross
section. The product of the atom density and the cross-section is called the macroscopic crosssection
and the equation for the reaction rate (5) can be written by the equation (6)
[5].
∫
.
(6)
The fusion reactor has a complicated geometry and material composition. Neutron flux spatial
changes across the reactor are significant. Computational simulations are basically the only tool for
calculating neutron flux and neutron interactions with the atoms of the structural materials in such
complex systems like the fusion reactor.
3. PRODUCTION OF GAMMA RAYS IN A FUSION REACTOR
Gamma rays are produced in nuclear reaction and arise from the nucleus of an atom. A typical
nuclear reaction with two reaction products can be written as
.
(7)
Where is the initial particle, is the target, and and are the reaction products (it is possible to
have more than two reaction products). Usually and are heavier particles than and , which
are usually nucleons or light nuclei. When is a gamma ray, the reaction is called radiative capture. A
compact way of indicating the same reaction is
. The conservation of total energy and total
momentum in the nuclear reaction gives the equation (8)
(8)
where
presents the kinetic energy of the th particle and
the rest masses. The reaction Q
value is defined as the difference between the initial and final mass energy.
∑
(∑
From the conservation of total energy (8),
kinetic energy of the particles
(9)
can be written as the difference between final and initial
∑
∑
(10)
and from the conservation of the proton and neutron number,
between final and initial binding energy of the interacting nuclei.
∑
)
∑
(∑
can be written as difference
∑
)
(11)
Where is the binding energy of nuclei that have to be provided to dissociate the nucleus into its
component neutrons and protons.
(
)
(12)
Here
is proton mass,
is neutron mass and is the mass of the nucleus with atomic number
and mass number . The
value may be positive, negative or zero. If
the reaction is
exothermic and binding energy is released as kinetic energy of the final products. When
the
reaction is endothermic, and initial kinetic energy is converted into binding energy [7].
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3.1.
Prompt gamma rays in the plasma
Gamma rays in the plasma are produced when fast ions with energies in the MeV energy range react
either with plasma fuel ions or with plasma impurities from the first wall (the plasma-facing tiles) and
divertor (coils for shaping the plasma and target plates, which are located at the bottom of the
vacuum vessel) such as beryllium, boron, carbon and oxygen. Fast ions are created in the JET plasma
as fusion products such as fast tritons, protons, 3He and 4He ions from fusion reaction (1),(2),(3) and
also by acceleration with ICRF (Ion Cyclotron Range of Frequency) and NBI (Neutral Beam Injection)
heating. From the measured gamma ray spectra, different fast ion species in the plasma can be
identified. Also the temperature distribution and relative concentrations of fast ions can be
measured. Emitted gamma ray spectra from the plasma depends on the type of reaction, the energy
and density of the interacting particles and on the structure of the energy levels of the final nucleus.
In gamma ray diagnostic, the two most important types of reactions are reactions with a threshold or
a resonance in the cross section. A list of all essential nuclear reactions that have been identified in
the gamma ray spectra measured at JET is given in table 1 [8].
Table 1: nuclear reactions in JET plasma, which are producing gamma rays. [8]
These reactions are classified by types of fast ions interacting with different target ions in the plasma.
The nuclear reaction energies, the Q values, which characterize the mass balance of the reactions are
presented. The table also contains assessments of the minimum energy of fast particles required to
produce gamma ray yields at levels that can be measured in JET.
The detected gamma ray spectrum consist of gamma lines and the background. Gamma rays created
in the plasma by nuclear reactions produce line spectra, while background originates from structural
materials that have been activated by fusion product neutrons and from X-rays. It is important to
evaluate the gamma rays which come from the neutron activation of the materials, in order that
correct data processing of the measured gamma ray spectra from the plasma can be made [9].
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3.2.
Neutron induced gamma rays
With respect to the time from the original reaction to their creation, gamma rays are divided into
prompt and delayed gamma rays. Gamma rays that are created immediately after the neutron
interaction with the matter are so called prompt gamma rays and gamma rays that are created with
a delay after the neutron irradiance are called delayed gamma rays.
Figure 1: Illustration of a possible path for gamma ray creation by neutron reactions with nucleus
[10].
After inelastic scattering of the neutron or neutron capture in the material, the target nuclide is left
in the excited state. A nuclide in an excited energy state is referred to as a nuclear isomer, and the
transition from a higher to a lower energy state is referred to as isomeric transition. Gamma rays are
emitted in discrete energies corresponding to the difference in energy states of the nuclear isomers.
(13)
Here
is the energy of the electromagnetic radiation and
and
represent the energy levels of
the nuclear isomers. The excided nucleus reaches its ground state, typically in 10-12-10-9 s, by emitting
gamma rays in a cascade. Most nuclides emit several hundreds (sometimes several thousands)
prompt gamma rays with different energies. Only light elements (below 19F) have simple prompt
gamma spectra [6][11].
The intensity of created prompt gamma ray depends on the neutron flux, neutron energy, type of
material on which neutrons are scattered or captured and cross sections for inelastic scattering and
neutron capture [12]. Most of the prompt gamma rays are created in materials, which are close to
the plasma. Gamma rays are then transported through the material, where they can be attenuated
by the photoelectric effect, pair production and Compton scattering or they can escape the material.
3.3.
Delayed gamma rays
If after the neutron capture the ground state of the nucleus, reached by emitting prompt gamma
rays, is not stable, radioactive decay radiation may be emitted with a given half-life. Gamma rays
emitted in a radioactive decay are called delayed gamma rays. With very intense or long neutron
irradiance, a large number of material nuclides will transmute. Unstable nuclides can transit to a
stable nuclides via α, β, γ or internal conversion. Unstable nuclides are produced with a neutron
capture reaction rate and decay with a decay constant . The rate of the production of an unstable
nuclide
, which is produced from just one element is given in equation (14).
(14)
Here
and
is the number of target atoms,
is the cross section for
reaction for
element
is the neutron flux. Equation (14) is nonhomogeneous first order differential equation, in
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which first part of right side presents reaction rate which is constant, if approximation that neutron
flux is constant during irradiation of the sample is made. Solution for equation (14) with boundary
conditions
at time
is given by the equation:
(15)
Here
presents the reaction rate of production of nuclide and stands for the time
after the start of irradiation. Equation (15) can be also written as activity of nuclide . Activity of
radioactive nuclide is defined as a rate of decay
. Equation for induced activity of
nuclide is [12]:
(16)
In fusion reactor structural materials composites of several elements are found. The rate of
production of a certain nuclide in the composite material is given by the Batemann equation (17),
where the first part on the right side of the equation presents the decay of nuclide and the second
part presents the creation of the nuclide .
∑
(17)
is the amount of the nuclide and
the amount of the nuclide at time t,
is the decay
constant of the nuclide , is the cross section for radiative capture reactions with the nuclide ,
is the decay constant for nuclide producing the nuclide ,
is the cross section for the reaction
with the nuclide producing nuclide and is the neutron flux [13]. While the material is irradiated,
activity from different nuclides can build up, but after the end of the irradiation the activity will decay
with the rate of decay dependent on the half-lives of the unstable nuclides. Although many nuclides
are present in the material, at a certain time the activity of one nuclide usually prevails. With an
increasing number of elements in the material, different neutron energies and some decay-activation
schemes that are very difficult to solve analytically, make the use of reliable computational technique
necessary.
4. GAMMA RAY MEASUREMENTS AND SIMULATIONS
Gamma ray diagnostic systems in large tokamaks like JET or future ITER present an important tool for
measuring reaction rates in the plasma, determining fast ion properties and perform tomographic
radial profile of the gamma ray flux. For neutron producing reactions such as in DD or DT plasmas,
gamma ray diagnostic for determining reaction rates is complementary to the neutron flux
measurement, but in the case of HD, HT and D3He plasmas, where in these particular reactions no
neutrons are produced, gamma ray diagnostic is the only tool for measuring reaction rates in the
plasma. Measurement systems for gamma ray diagnostic developed and applied at JET are important
for development of appropriate gamma ray diagnostic system at ITER and other future fusion
reactors.
Three different gamma ray spectrometers for measurement of energy spectra can be used on the JET
fusion reactor. Two lines of sight through the plasma centre are installed, one horizontal and one
vertical.


A High purity Germanium (HpGe) crystal provides high energy resolution for gamma ray
energies up to 5 MeV, but is sensitive to neutron damage and therefore is not an appropriate
detector in a high neutron flux field.
Bismuth Germanate (BGO) scintillation detector, viewing at the plasma centre horizontally
and Sodium Iodide (NaI) vertically, were used for a number of years because of their high
efficiency and energy resolution.
7

Lanthanum Bromide (LaBr3) is a new scintillating material, which is insensitive to neutrons
and has high energy resolution and fast response.
For the spatial distribution of the gamma ray emission, the neutron profile monitor is used. The
monitor consists of two cameras, 9 lines of sight vertically and 10 horizontally. Detectors in the
camera are organic liquid scintillators (NE213). For measurement of high energy gamma rays the 19
Thallium activated Cesium Iodide (CsI(Tl)) photo-diodes are placed in the front of neutron detectors.
Scheme of the JET vacuum vessel cross-section and the profile monitor measurement system are
shown in figure (2) [14].
Figure 2: Neutron and gamma profile monitor at JET. Divertor, first wall, vacuum vessel, horizontal
and vertical ports, in a vertical cross section of the tokamak, are shown. The dimensions on the figure
are given in millimeters [1].
Measured gamma ray energy spectra and spatial distribution contains background, which are
neutron induced prompt and delayed gamma rays, originating from reactions with structure
materials. For the analysis of the measured spectra, the gamma ray background must be well
evaluated. Prompt gamma rays are present only during the plasma discharge and thus can not be
measured separately from plasma gamma rays. The only tool for calculation and prediction of energy
spectra and spatial distribution of neutron induced gamma rays in such a complex systems like the
fusion reactors JET or ITER are computer simulations. One of the most widely used computer
simulation methods is the Monte Carlo method. An essential of Monte Carlo simulation is modelling
of the physical process by probability density functions, which have its origins in theoretical model or
experimental data. Monte Carlo method simulates the transport and interactions of particles
(neutron, proton, electron, photon, etc.) through a defined geometry and materials in the model.
Source particles, including the energy, direction and position, are defined and the path of individual
particles from the source, through all events, until it is terminated (absorption, escape, etc.), follows.
The solution for the defined problem is the average over the number of sampled outcomes. With
increasing number of simulated particles the statistical error of the solution decreases, therefore the
Monte Carlo method can be loosely described as statistical simulation method that utilizes
sequences of random numbers to perform the simulation. The computational time increases linearly
with the number of the simulated particles, and also with the volume and the number of materials in
the model [15]. It is reasonable to simplify the geometry in the case of a tokamak, which is nearly
rotational symmetric, since it is possible to simulate just one sector of the fusion reactor. Figure (3)
8
presents the a cross-section of the geometrical model of Octant 1 of the JET torus for the Monte
Carlo N-Particle Transport Code (MCNP) [16]. This model was originally developed on JET and
upgraded by co-workers of the Reactor physics department (F8) of the Jozef Stefan Institute; details
can be found in Ref. [17].
Figure 3: Vertical cross-section of the geometrical model of Octant 1 of the JET reactor, where
colours represent the different materials.
It is possible to calculate the neutron and gamma ray fluence in structural materials of fusion
reactors with the MCNP code. Figure (4) shows the calculation of the distribution of the neutron
fluence (left) and prompt gamma ray fluence (right) in the JET reactor for a D-D plasma calculated
with 108 simulated neutrons.
Figure 4: Distribution of the neutron and gamma ray fluence calculated with the MCNP code for a DD plasma at the JET reactor. The geometry of the torus can be easily anticipated from the figures.
5. CONCLUSION
Neutrons are created in DD or DT plasmas with energies of 2,5 MeV and 14,1 MeV. While neutrons
propagate through material in a fusion reactor they interact with nuclides possibly producing new
nuclides and particles. Gamma rays, which are created in the material and neutrons from the plasma
have long free paths due to their high energies, thus shielding in a fusion reactor must be carefully
constructed. Neutron and gamma radiation has impact on the materials physical and chemical
9
properties. When a material is exposed to intense and long lasting radiation, the material properties
change. After shutdown of the plasma, neutron and prompt gamma rays are no longer present, but
delayed gamma rays are still created from the activated materials. Delayed gamma rays are
responsible for dose rates after shutdown and values of the dose rates must not exceed the upper
permissible limit in parts of the fusion reactor, which require maintenance. Measurements of gamma
ray energy spectra and spatial distribution during the discharge are performed in tokamaks with
different detectors, which have a high energy resolution, fast response and are insensitive to
neutrons. Gamma ray diagnostics is an important tool for determining fast ion properties and
reaction rates. For analysis of gamma ray spectra from the plasma, the background gamma rays from
materials must be predicted and evaluated. Insight into gamma ray production inside the materials in
fusion reactors is possible by the use of computer simulations. The Monte Carlo method can be used
for numerical simulation of the particle transport in the structural materials of the tokamak. Good
evaluation of neutron induced gamma rays is not only important for exiting fusion reactors but also
for the choice of structural materials and design of radiation protection in the future fusion reactors
like ITER.
6. LITERATURE
[1] J. Mlynar, Focus On: JET The European Centre of Fusion Research (Culham, Oxfordshire, 2007).
[2] D. E. Post et. al., ITER Physics (IAEA, Vienna, 1991).
[3] J. Freidberg, Plasma Physics and Fusion Energy (Cambridge university press, Cambridge, 2007).
[4] J. J.Duderstandt and L. J. Hamilton, Nuclear Reactor Analysis (John Wiley & Sons, Michigan, 1976).
[5] J. R. Lamarsh and A. J. Baratta, Introduction to Nuclear Engineering (Prentice-Hall, New Jersey,
2001).
[6] G. L. Molnar, Handbook of Prompt Gamma Activation Analysis (Kuwer Academic Publishers,
Dordrecht, 2004).
[7] K. S. Krane, Introductory Nuclear Physics (John Wiley & Sons, New York, 1988).
[8] V. G. Kiptily et. al., Gamma ray diagnostics of high temperature magnetically confined fusion
plasmas, Plasma Phys. Control. Fusion 48, R59-R82 (2006).
[9] V. G. Kiptily et. al., γ-ray diagnostics of energetic ions in JET, Nucl. Fusion 42, 999-1007 (2002).
[10] http://archaeometry.missouri.edu/naa_overview.html (4. 12. 2015).
[11] M. F. L‫׳‬Annunziata, Handbook of Radioactivity Analysis (Academic Press, San Diego, 2003).
[12] G. F. Knoll, Radiation Detection and Measurement (John Wiley & Sons, New York, 2000).
[13] A. Davis, Radiation shielding of fusion systems (University of Birmingham, 2010).
[14] M. Nocente, et. al., Energy Resolution of LaBr3(Ce) Gamma-Ray spectrometer for Fusion Plasma
Studies on JET, Proc. 22 IAEA Fusion Energy Conference, Geneva, Switzerland (2012).
[15] T. Goorley, et. al., Features of MCNP6, Joint International Conference on Supercomputing in
Nuclear Applications and Monte Carlo (Paris, October 27-31, 2013).
[16] X-5 MONTE CARLO TEAM, MCNP – A General Monte Carlo N-Particle Transport Code, Version 5,
Volume I: Overview and Theory, LA-UR-03-1987 (Los Alamos National Laboratory, Los Alamos, 2003).
[17] R. Villari et. al., Shutdown dose rate benchmark experiment at JET to validate the threedimensional Advanced-D1S method, Fusion Engineering and Design 87, 1095–1100 (2012).
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