# Modelling of the Production of Source Neutrons from Low-Voltage Accelerated Deuterons on Titanium-Tritium Targets

Authors: A. Milocco; A. Trkov
Journal: Science and Technology of Nuclear Installations
 (2008)

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## Abstract

Fast quasi-monoenergetic neutrons can be produced by accelerating
charged deuterons on tritium solid targets. Benchmark experiments
were performed in many laboratories with intense D-T neutron
sources. The aim is to validate the computational models and
nuclear data for fusion applications. The detailed information on
the neutron source term is highly important for the benchmark
analyses. At present, the MCNP family of codes cannot explicitly
model the D-T reaction for Deuterons in the KeV energy range. The
physics for the D-T neutron production was modelled at ENEA
(Italy) in the SOURCE and SRCDX subroutines to compile with the
MCNP source code. Some improvements to the original subroutines
were introduced. The differential cross-sections for the D-T
reaction from the ENDF/B-VII library were built into the code. The
relativistic approach was implemented for neutron kinematics. The
new D-T neutron source model was applied to the MCNP5 simulation
of the tungsten integral experiment performed at the OKTAVIAN
facility. The uncertainty associated with the realistic D-T
reactions was separated from the total uncertainty of the source
term. The outcome of the benchmark analysis was an improvement in
the quality of the computational model of the experiment.


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## Body

## 1. Introduction

The first device for the acceleration of charged
particles  has been constructed by Cockroft and Walton in 1932, the
same year when Chadwick discovered the neutron.
Since the 1950s tritium was available as a  target material to produce
~14 MeV neutrons  by theH3(d,n)4He reaction, which is still the first candidate for plasma fusion
technology. Thus, these  neutron
generators have been widely used to study the interaction of the neutrons with
the structural materials  of fusion reactors. Other applications of the
device include neutron activation analysis, low cross-section measurements,
and neutron therapy. The broad resonance of the D-T cross-section
at the deuteron energy of 109 KeV permits
high yields of fast neutrons to be obtained with low-voltage deuteron
accelerators [1]. Integral experiments for fusion technology have been
collected in the International Database for Integral Shielding Experiments (SINBAD),
which is coordinated by the OECD Nuclear Energy Agency
(http://www.nea.fr/)
and Radiation Safety Information Computational Center
(http://www-rsicc.ornl.gov/).A lot of effort is devoted to
computational techniques for neutron transport. A real source is not isotropic or monoenergetic. Primary neutrons are
generated by deuterons which have interacted in the target and lost part of
their original energy. The experimentalists usually provide the source
specifications, but these specifications need a detailed investigation to
determine parameter uncertainties, whose different contributions are difficult
to separate out in a real experiment. Special attention is needed to define the
anisotropy of the source and the neutron yield as a function of its flight
directions, as well as the spread in the emitted neutron energies.The MCNP family of codes cannot explicitly model
the deuteron transport and neutron emission from the D-T reaction for
incident deuterons with energies in the KeV range. At ENEA (Italy), a D-T source model
was developed, which includes the effect of the deuteron slowing down inside a titanium-tritium target and
the D-T reaction
kinematics. The model is implemented in MCNP subroutines (e.g., SOURCE, SRCDX),
which define the neutron source when compiled with the MCNP source code. The
subroutines are available in SINBAD database.The present work is a case study to
identify the essential information which is needed for the source definition in
computational analyses. Section2 illustrates the approach to the D-T reaction kinematics
from first principles. These results allow a refinement of the original ENEA
source subroutines (described in Section 3). The upgraded D-T source model is
internally validated by reproducing the theoretical angle dependence of the
neutron energy and yields and by cross-validating the
cell flux with the point detector flux. In Section 3 a brief description of the
deuteron transport model is also provided. The sample case (Section 4) concerns
the 14 MeV neutron facility OKTAVIAN, which was built
at Osaka University
and has been operating since
1981. In the framework of the SINBAD project the measured neutron leakage
spectra from a Tungsten sphere were analysed. In this work the source model
from the previous analysis is compared to the MCNP5 calculation with the
improved neutron source model. The outcome of
the benchmark analysis represents an improvement in the quality of the
computational model of the experiment.


## 2. Theoretical Framework of the D-T Reaction

TheH3(d,n)4He reaction is properly modelled
as a two-body reaction. Some nomenclature: in Figure 1 the subscript “a”
denotes the incident particle (deuteron), “b” the target particle (tritium), “1”
the emitted neutron and “2” the alpha particle. P and θ are the momenta in the laboratory
frame and the angles between the outgoing particle and the deuteron direction.
The energy of the outgoing neutron (E1) is calculated according to
the relativistic equation (1). Ea is the relativistic energy of the
deuterons, which are given a  nominal kinetic energy of 280 KeV: (1)E1={(Ea+mb)2−Pa2cos2θ1}−1×[(Ea+mb){mbEa+12(ma2+mb2+m12−m22)}+Pacosθ1[{mbEa+12(ma2+mb2−m12−m22)}2−m12m22−m12Pa2sin2θ1]1/2].    The effect of the relativistic kinematics formulation is studied in comparison
with the classical kinematics equations. The relativistic equations
are implemented in a MATLAB function (RELKIN.M) for graphical purposes (Figure 2). The original source for the particle masses is the NIST reference on
constants, units, and uncertainties web site
(http://physics.nist.gov/), except
for triton. This is computed subtracting the electron contribution to the
tritium mass taken from the atomic mass tables of
G. Audi and A. Wapstra
(http://www-nds.iaea.org/amdc/web/masseval.html).
It is worthwhile to point out that in the ENDF-6 formats manual [2]
this datum is incorrect. The calculation of the Q-value for the D-T reaction is
17.589 MeV. The relativistic calculation agrees with the one provided by the
DROSG2000 code (http://www-nds.iaea.org/ndspub/libraries/drosg2000/), which also uses the
relativistic approach. The classical results are obtained from the kinematics
formulas available in the ENDF-6 formats manual.
The difference in energy when solving the two-body
reaction problem with the
classical equations is about 30 KeV.Figure 1
Scheme of two body reaction model.Figure 2
Comparison of relativistic and classical approach
of energy-angle dependences
of D-T neutron
yielding.The angular distributions of the
outgoing neutrons in the centre-of-mass system are
represented by Legendre polynomials. The Legendre coefficients up to the tenth
order are available in the ENDF files (MAT = 2, MF = 50, MT = 6) at the nominal
deuteron energy of 280 KeV. For the conversion into the angular distribution in
the laboratory frame it is necessary to calculate the momentum of the deuteron(Pa), whose evaluation is trivial, and of the neutron (P1)
and apply the Jacobian (dΩcm/dΩlab) as follows: (2)P1={(Ea+mb)2−Pa2cos2θ1}−1×[Pacosθ1{mbEa+12(ma2+mb2+m12−m22)}+(Ea+mb)[{mbEa+12(ma2+mb2−m12−m22)}2−m12m22−m12Pa2sin2θ1]1/2],dΩCMdΩLAB=KP12(Ea+mb)P1−PaE1cosθ1,K is a constant independent of the angle, so it is
adjusted to normalise the distribution at zero
degree. This
normalisation is a common practice because the angular dependence of both the
neutron energy and the neutron yield on the angle is comparatively small in the
forward direction [3]. The effect of both the anisotropy in the CM
system and the transformation into the LAB frame can be assessed in
Figure 3.
For the CM anisotropic reaction the data of DROSG2000 code are replaced by the
Legendre expansion from the ENDF/B-VII library. The same coefficients are used
in the RELKIN function. The calculations with the new equations coincide with
the DROSG 2000 results for the angular distribution in the LAB system. It is
noticeable that the anisotropy of the reaction with 280 KeV deuterons implies a
difference of ~3% at backward angles in the laboratory angular distribution. As
a matter of fact, at energies typical for deuteron accelerators the assumption of
isotropic CM distribution is to be considered a rough
approximation.Figure 3
Comparison of isotropic and anisotropic D-T neutron yields
in CM and LAB frames.


## 3. The Deuteron Beam Slowing Down

The deuteron particles hitting solid Titanium-Tritium targets
get slowed down by interactions with the electrons and nuclei in the medium. The
electronic stopping power, that is, the inelastic scattering with electrons, can
be considered independent on nuclear interactions. On interaction with Ti or T
nuclei, the deuteron deflects and loses part of its kinetic energy by elastic collisions.
Eventually, the deuteron interacts with the tritium nucleus to produce one
neutron. For low-energy deuterons, the only reaction branches to consider are
elastic scattering and nuclear fusion. The energy and angular distributions of
incident deuterons inside the target cause the primary energy spread of the
neutron energy at a fixed detection angle.For
the simulation of a D-T neutron source
the first choice was to search into the MCNP family of codes. The deuteron ion
transport in MCNPX is performed by physics models designed for incident
deuterons of 200 MeV and higher. They are able to provide a good response in
the 10–100 MeV range,
however, the results are poor down to the MeV range. Till now, there are no D and
T nuclear data libraries. Therefore, the D transport within the solid target
can be achieved with MCNPX, but results are to be interpreted with caution and
should be benchmarked against experiments or otherwise known answers. The D
energy cut-off for the D-T fusion reaction in MCNPX is 2 MeV, so neutrons
cannot be generated at the low energies of our interest. Starting from MCNP4
the possibility was introduced to develop and compile ad hoc source
subroutines. The SINBAD database makes available the subroutines to compile with
MCNP5 source codes for the simulation of the neutron emission in the Frascati neutron
generator. The routines were provided by Angelone et al. from ENEA, who developed a detailed
model of the FNG neutron source [4]. For the D slowing down inside
the solid  FNG target the basic-language source
code from TRIM software was translated into  FORTRAN language. The Monte Carlo program, the Transport of Ions in Matter (TRIM),
is the most comprehensive program included in SRIM
(http://www.srim.org/). SRIM is a well-established
collection of software packages which calculate many features of the transport
of ions in matter, such as  ion stopping powers and
ranges in targets, ion implantation, sputtering, ion transmission, ion beam
therapy. The main author
is James F. Ziegler.
TRIM does not model nuclear
reactions. M. Pillon implemented the D-T neutron
production in the TRIM-based model for
the D transport inside the Ti-T target. The essential
characteristics of the ENEA D-T source model
are the following:(1)
Monte Carlo method,(2)
free flight paths between collisions,
which “condense” negligible amounts of energy transfer and deflection
angles,(3)
impulse approximation for the free flight paths in the
low-energy range,(4)
universal interatomic potential,(5)
Rutherford scattering at higher ion energies,(6)
electron stopping power data from the TRIM code tables,(7)
D-T double
differential cross-sections retrieved from the DROSG2000 code calculations
at different deuteron energies,(8)
neutron generation by the modified von Neumann rejection
method,(9)
classical kinematics. The
MCNP5 source subroutines are SOURCE.F90 (coding the D slowing down in solid Ti-T target and
modelling the fusion reactions), SRCDX.F90 (specific for transporting neutrons
generated in SOURCE to point detectors), and six other subroutines for numeric
calculus. The D-T source routines
require the use of the RDUM card in the MCNP input file to specify deuteron
beam energy, target thickness, T/Ti atomic fraction, beam width, and target
axis coordinates.At ENEA the last version of the D-T source model
was prepared for MCNP5 on the Unix systems. The possibility to perform routine
calculations on Windows systems is achieved by producing a patch file to apply
to the original MCNP5 source code for Windows systems.Some flaws have been found
in the last version of the source routines. The range of the deuterons was
underestimated with reference to the TRIM calculations. The problem has been found
in the stopping power of the Ti-T mixture. Since
the units of the data imported into the routines from TRIM tables changed from
the original MCNP4B version, some parameters needed to be modified accordingly.
It is now possible to ascertain that the mean average range of the deuteron
ions is about 1.5μm, about the same value given by the TRIM code.A new condition is
implemented into the source routines to terminate the Monte
Carlo history when the cumulative deuteron free flight path
exceeds the target thickness.The calculation of the
neutron spectra on a very fine energy binning with the original source routines
showed an unphysical spike at the deuteron maximum energy, corresponding to
uncollided deuterons. After discussion with M. Pillon
the special treatment of the first collision was dropped and the spike
disappeared.The major new contribution
to the D-T source routines
involves items 7 and 9 of the list above. The use of
double differential cross-sections in the ENEA code had two drawbacks. First,
it was not easy to check if the data were wrong or approximate because the data
section was huge. Second, the cross-section data relied on DROSG2000 Legendre
coefficients, which could change according to new experimental evidence or
refinement of theoretical nuclear models. The source routines are modified to
reconstruct the double-differential cross-sections from tabulated reaction
cross-sections and the Legendre coefficiens, defined by DATA statements in the
code with values as given in the ENDF/B-VII library. The results of a test
calculation comparing the original source routines and the modified routines
with the data from ENDF/B-VII are shown in Figure4. The deuteron
energy is 280 KeV. The other parameters are set to their standard values: the
beam width is 0.7 cm, T/Ti atomic ratio is 1.5, and target
thickness is 0.001 cm. The energy binning is 10 KeV. The source and the detectors are placed in
the void. In the MCNP5 input file point detectors are located at different
angles from 0 to 180 degrees. The slight differences
between the cross-sections in last ENEA version of the source routines (labelled
“enea”) and the modified routines with ENDF/B-VII cross-sections (labelled “leg.”)
result in a small difference in the absolute yield (~5%). Except for this
detail, the distributions at each angle agree very well.Figure 4
Neutron spectra calculated with the original and ENDF/B-VII
cross-sections.For the present work the source
routines are further improved to introduce the neutron relativistic kinematics
as given by equations defined in the previous section. The use of relativistic
kinematics results in a shift in energy, as seen from
Figure5.Figure 5
Effect of relativistic kinematics.The modifications above
imply a revision of the SRCDX subroutine for point detectors. A
cross-validation of the source model coding is performed by comparing the MCNP5
cell flux estimator (“cf”) and the point detector (“pd”) flux. Figure6 shows
that both tallies are consistent, except from some fluctuations in the cell
flux estimator. The energy range starts at the theoretical neutron energy. The
energy spread is greater in the forward direction. The shape of the neutron
spectra can be explained by considering that the maximum of the H3(d,n)4He
integral cross-section is at 109 KeV.Figure 6
Comparison of D-T energy leakage
spectra calculated with MCNP using both cell flux estimators and point
detectors.To calculate the mean values
of the neutron energy and the yields at different angles a MATLAB function
(ACEPD.M) is developed which reads from ACEFLX output. Thanks to the newly
introduced target thickness condition described above, the target thickness is progressively
reduced to simulate a very thin target (0.1μ). The neutron mean energies and
yields at different angles converge to the theoretical values (indicated by
crosses), as shown in Figures 7 and 8. This also confirms that the random
variables are properly sampled from the angular distributions.Figure 7
Ti target
thickness effect on D-T energy-angle dependence.Figure 8
Ti target
thickness effect on D-T neutron yields-angle
distribution.


## 4. The OKTAVIAN Tungsten Experiment

The OKTAVIAN
facility has been devoted to perform studies on fusion neutron-related subjects
by university researchers and has also  served for international collaborations.
The facility was a contributor to the SINBAD Project. SINBAD
declared objective is the validation and benchmarking of computer codes and
nuclear data used for radiation transport and shielding problems and the
preservation of a unique set of experiments for
the present and future needs.The
integral experiment under  consideration consisted of measurements
of the neutron leakage spectra from a 40 cm diameter tungsten (W) sphere pile.
W is a candidate material for the first wall of fusion reactors. In the
computational models, the evaluated nuclear data for W are from the IAEA files
compiled in April 2007 [5]. The source neutrons were produced by bombarding a
solid Ti-T target at the
centre of the W pile with a 250 KeV deuteron beam. The geometry of the MCNP5
input file is based on the available information about the experimental setup.
The precollimator and the main collimator bodies are modelled whereas the simulations in the
original analyses neglected them. The information on the target assembly is
retrieved from the report [6] and allows only an approximate model of the
accelerator structures. The results presented here tend to focus on the issues
arising in the analyses of MCNP5 simulations of integral experiments and
directly concerning the D-T neutron source.
Three approaches to the source specifications in the MCNP5 input file are
assessed.(a)
In this first
approach, the monoenergetic angle-dependent yields of source neutrons are given
by empirical expressions which hold for thick targets. The method is
illustrated by Csikai et al. [7] and is commonly used for modelling neutron sources.
For comparison with measured spectra, the calculated spectra usually need to be
resolution-broadened.(b)
In the second
approach, the use is made of the measured spectrum in the forward direction of the
bare source, provided by the experimentalist. The source is defined by scaling the
outgoing-energy and the magnitude of the measured spectrum such that the
positions of the  peak and the yield match the measured average values. In this
way, resolution broadening and certain  geometrical features (such as
room-return, collimator, etc.) are implicitly taken into account. This procedure
has been used by A. Trkov for the OKTAVIAN nickel sphere benchmark experiment [8].(c)
The upgraded D-T source model
described in Section2 is applied. The deuteron energy is
250 KeV, while the
other parameters are left at their standard values. An equivalent source
definition (in the form of the SDEF and DS cards) is prepared for users that do
not wish to recompile MCNP5 with the source routines by calculating the neutron
energy distributions and yields in point detectors in void at different angles.
These two forms of input give the same results and are not treated separately. The source spectra at forward angle for cases (b) and (c)
are compared in Figure 9. For clarity, the plotted spectra are normalised at the
peak. The scattering effects of source neutrons with
the structures of the experimental setup are intrinsic to the measured response
function, as can be inferred from the tail below the main peak (labelled “OKTAVIAN
spectrum”). The energy spread due to the deuteron interactions inside the
target as calculated by the source routine is small (labelled “SRCDX spectrum”).
The calculated spectrum partly justifies the approximation in case (a), in
which the energy distribution is a delta function. At other angles the source
neutron distributions are similar, except for a shift in energy and the total
yield.Figure 9
Comparison of
OKTAVIAN source spectrum in forward direction versus the one generated by the
SRCDX subroutine.Due to the finite
resolution of the detectors, their finite size, resolution of the electronics, and
so forth, some smearing in the measured spectrum is inevitable. To compare the
calculated and measured spectra, the calculated ones usually have to be
resolution-broadened. Assuming the
applicability of the central limit theorem, the calculated spectra for cases (a)
and (c) are broadened with a Gaussian resolution function. Note that resolution-broadening is not
needed in case (b), because it is approximately accounted for in the source
definition. The neutron leakage spectra obtained with the sources above described
are compared in Figure10. The best agreement with experimental spectrum is
obtained with the recommended OKTAVIAN source. The calculated spectra at the
peak agree well with the measurement. The observed discrepancy in cases (a) and
(c) between 5 and 12 MeV is an indication of inadequate modelling of the
detailed geometry of the experimental setup: the use of the measured response
function for source definition in case (b) effectively corrects for some
modelling deficiencies. Although the source in case (c) is physically better,
the overall result compares worse with the measurements because it is not
possible to improve the physical models of the experimental setup due to lack of information. The
differences below 0.5 MeV could be due to the W nuclear data or the modelling
assumptions about the surrounding structures.Figure 10
Neutron leakage spectra obtained with different source models
implemented, benchmarked with the experimental measurements of OKTAVIAN W
sphere test.


## 5. Conclusions

The interest in the materials for nuclear fusion
reactors promoted extensive research in facilities producing D-T source neutrons
on small scale, as the low-voltage deuteron accelerators with Ti/T targets.In the present work, the basic principles of the D-T fusion reaction
are clarified. The calculations of the neutron energy and angular distribution are
performed in the framework of relativistic kinematics. The source routines
allow realistic modelling of the Ti-T target assembly, which is the starting
point for the analysis of the integral experiments. The uncertainties contained
in the source spectrum propagate to the neutron leakage spectrum. The analysis
of the OKTAVIAN experiment showed the energy regions and the magnitude of the
corresponding discrepancies which arise from the source definition and not from
the nuclear data of the primary measured structural material.In this early stage of the analysis, progress is made
in establishing codes and procedures for the modelling of the D-T source
neutrons. The importance of detailed and accurate specifications of the
experimental setup is
emphasized if integral experiments are to be used to discriminate between
different sets of nuclear data.



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*Source: 340282-2008-12-25.xml*