MINISTRY OF EDUCATION
AND TRAINING

MINISTRY OF SCIENCE
AND TECHNOLOGY

VIETNAM ATOMIC ENERGY INSTITUTE

TRAN MINH TIEN

RESEARCH ABOUT POSSIBILITY OF USING
THORIUM AS FUEL FOR THE ACCELERATOR
DRIVEN SUBCRITICAL REACTORS

Speciality: Atomic and nuclear physics
Code: 9.44.01.06

SUMMARY OF THE PHD THESIS

Ho Chi Minh City – 2022


This thesis was completed at: Vietnam Atomic Energy
Institute

SUPERVISORS:
1. Assoc. Prof. Dr. TRAN QUOC DUNG
2. Assoc. Prof. Dr. NGUYEN MONG GIAO

Referee 1: . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Referee 2: . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Referee 3: . . . . . . . . . . . . . . . . . . . . . . . . . . . .
This dissertation will be defended in front of the evaluating assembly at academy level, place of defending: . . . . . .
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Contents


List of abbreviations

i

List of figures

ii

Introduction

1

CHAPTER 1. OVERVIEW

2

1.1

The Accelerator Driven Subcritical Reactor
(ADSR) . . . . . . . . . . . . . . . . . . . . .

2

1.2

The current development of ADSRs . . . . .

2

1.3


Studies on (p,n) reactions, neutron distribution on solid targets for ADSR . . . . . . . .

3

Researching about using thorium as fuel in
conventional nuclear reactors . . . . . . . . .

4

Possibility to use thorium as fuel for ADSR .

5

1.4
1.5

CHAPTER 2. SIMULATING THE STRUCTURE OF ADSR USING LIQUID LEAD AND
THORI FUEL
6
2.1

Model of (p,n) interaction on the liquid lead
target . . . . . . . . . . . . . . . . . . . . . .

6

2.1.1

Model and calculations


. . . . . . . .

6

2.1.2

The distribution of the neutrons from
(p,n) reaction . . . . . . . . . . . . . .

7

2.1.3

The angular distributions of neutrons

8

2.1.4

The neutron yields according to angles

9


2.1.5
2.2

The double-differential of the neutrons
cross-section . . . . . . . . . . . . . .


9

Model of TRIGA Mark II subcritical reactor
using liquid lead and thorium fuel . . . . . .

10

2.2.1

Model of TRIGA Mark II reactor simulated by MCNPX . . . . . . . . . . .

10

2.2.2

The neutron yields Yn/p . . . . . . . .

11

2.2.3

The effective neutron multiplication factor kef f . . . . . . . . . . . . . . . . . 11

CHAPTER 3. CALCULATION THORIUM
FUEL FOR ADSR
13
3.1

Radioactive decay of thorium in the liquid lead 13

3.1.1

Model and calculations

. . . . . . . .

13

3.1.2

The energy spectrums of alpha, beta,
antineutrino particles and gamma rays

13

The energy of daughter nucleus . . . .

15

Comparison of neutron flux distributions in
ADSR using liquid lead, mixed thorium fuel
with ADSR using solid target, mixed fuel uranium . . . . . . . . . . . . . . . . . . . . . . .

15

3.1.3
3.2

3.2.1


The case of UZrH fuel and light water
coolant . . . . . . . . . . . . . . . . .

15

The case of UZrH fuel and liquid lead
coolant . . . . . . . . . . . . . . . . .

16

The case of ThUO fuel and molten
lead coolant . . . . . . . . . . . . . . .

17

The distributions of neutron fluxes in ADSR
using thorium fuel . . . . . . . . . . . . . . .

18

3.2.2
3.2.3
3.3


3.3.1

3.4

The distributions of neutron fluxes by

neutron energy . . . . . . . . . . . . .

18

3.3.2

The axial distributions of neutron flux

19

3.3.3

The radial distributions of neutron flux 19

Neutron flux distributions using mixed thorium and uranium fuel . . . . . . . . . . . . .
3.4.1

The radial distributions of neutron flux 20

3.4.2

The axial distributions of neutron flux

20

3.4.3

The energy ditributions of produced
neutron . . . . . . . . . . . . . . . . .


21

Comparison of neutron flux distribution with fuels U O2 , T h233 U O2 and
T h235 U O2 . . . . . . . . . . . . . . . .

21

The neutron multiplication factors in ADSR
using thorium fuel . . . . . . . . . . . . . . .

22

3.4.4

3.5

19

T h233 U O2

3.5.1

The kef f with

mixure fuel .

23

3.5.2


The kef f with T h235 U O2 mixure fuel

23

3.5.3

The kef f with T h238 U O2 mixure fuel .

24

CONCLUSIONS

25

LIST OF PUBLICATIONS

27

REFERENCES

28


List of abbreviations
Abbreviations
ADS
ADSR
ADTR
ENDF
FNS

GEANT
JENDL
JENDLHE–2007
KIPT
KUCA
LFR
LWR
MCNP
MSR
MYRRHA
NF
SCWR
SFR
TNF
VHTR

Meaning
Accelerator Driven System
Accelerator Driven Subcritical Reactor
Accelerator Driven Thorium Reactor
Evaluated Nuclear Data File
Fast Neutron Flux
Geometry And Tracking
Japanese Evaluated Nuclear Data
Library
Japanse Evaluated Nuclear Data Library/High Energy
Kharkov Institute of Physics and
Technology
Kyoto University Critical Assembly
Lead Fast Reactor

Light Water Reactor
Monte Carlo N-Particle
Molten Salt Reactor
Multi-purpose hYbrid Research Reactor for High-tech Applications
Neutron Flux
Super Critical Water Reactor
Sodium Fast Reactor
Thermal Neutron Flux
Very High Temperature Reactor

i


List of Figures
2.1

Model of (p,n) reaction on the liquid lead target

7

2.2

The position of the generated angles of the
neutrons . . . . . . . . . . . . . . . . . . . . .

8

2.3

The cross-section of ADSR reactor core based

on the structure of the TRIGA Mark II reactor 10

2.4

Structure of a fuel rod . . . . . . . . . . . . .

10

3.1

Model of radioactive decay of thorium in liquid lead . . . . . . . . . . . . . . . . . . . . .

14

ii


INTRODUCTION
Nuclear energy is facing problems such as high cost, safety,
uranium fuel sources, along with challenges from radioactive
waste transmutation. One of the current solutions is to develop Accelerator Driven Subcritical Reactors - ADSRs [1-3].
ADSR works on a basic principle: an accelerator generates
a high-energy proton beam, which interacts with a target,
producing a (p,n) reaction. The reactions take place in the
subcritical state. Many previous studies have performed calculations of neutron parameters for the solid target; the fuel
is mainly uranium, while thorium is also a potential fuel [4].
However, the using of a solid target after a period of time
must change the target, then the reactor operation must
be stopped. In this thesis, liquid lead is proposed both as
an interactive target to maintain the ADSR’s activity and

a coolant and transfer heat to the outside. This is a new
model that has not been studied much in the world. With
the using of liquid lead as both coolant and target, there
will be no need to change the target during nuclear reactor
operation. All liquid lead in the path of the incident proton beam will be the interaction target, so the number of
neutrons generated will increase compared to using a solid
target.
The thesis is carried out towards two main objectives: (1)
building a model of an accelerator driven subcritical reactor using liquid lead both as an interactive target and as a
coolant; (2) evaluating the possibility of using thorium fuel
for ADSR through the calculation of basic neutron parameters of the reactor. Here, the TRIGA Mark II reactor model
was chosen because there are many other studies that also
use this model for calculations for ADSR [5-8].

1


CHAPTER 1. OVERVIEW
1.1

The Accelerator Driven Subcritical Reactor (ADSR)

ADSR works on a basic principle: an accelerator generates a proton beam with energies from a few hundred MeV
to several GeV, which interacts on a heavy target, causing
a (p,n) interaction. Proposals to use high-energy proton
beams were made decades ago [9-12]. This process will produce many neutrons emitted in different directions; these
neutrons will cause many reactions such as (n,n), (n,2n),
(n, γ), ... ; participates in many processes such as neutron
absorption, elastic scattering, and inelastic scattering. The
processes inside the reactor are maintained in a subcritical

state. The neutrons generated from the interaction (p, n)
will act as additional neutrons, maintaining the subcritical
operating state of the reactor.
The basic issues related to ADSR have been studied since
2001 [13-15]. Currently, the problems are being focused on
such as thermal neutron spectrum, fast neutron; fuel type:
solid (metal, oxide, nitric, carbide, ...); or liquid (chloride,
fluoride); target types (lead, lead-bismuth, tungsten, molten
salt, ...). In Vietnam, there are also some studies on ADSR,
as Nguyen Mong Giao et al. [16-19] and Vu Thanh Mai et
al. [20-25].

1.2

The current development of ADSRs

Since its proposal, many international conferences on ADSR
have been organized. The most typical is the conference
on technology and structure of accelerator control systems
(Technology and Components of Accelerator Driven Systems) held every three years, starting from 2010 [26-28]. In
European countries, there has been a joint effort to experimentally design an ADSR, called XT-ADS. Then, based
on this design, the Belgian Center for Nuclear Research
2


(SCK.CEN) preliminary designed a project called MYRRHA
(Multi-purpose hYbrid Research Reactor for High-tech Applications), in which a reactor with the ability to operate
in both critical and subcritical states [29]. In India, the development of ADSR has been in progress since 2001 [30].
The first operational phase of the program began in 2002.
At that time, India developed a 10 MeV linear accelerator,

which produced a proton current with an intensity of 10 mA;
used lead-bismuth as an interactive target, and started experimental research for ADSR. In Japan, research activities
on ADSR are located at the Proton Accelerator Research
Complex (PARC), which is a collaboration between KEK
(High Energy Accelerator Research Organization) and the
IAEA. In China there are also many projects to develop
ADSR; one of them is C-ADS [31]. The C-ADS project was
initiated by the Chinese Academy of Sciences (CAS), with
the participation of four institutes: the Institute of High
Energy Physics (IHEP); Institute of Plasma Physics (IPP),
University of Science and Technology of China (USTC). In
Ukraine, starting in 2012, the National Science Center Kharkov Institute of Physics and Technology (NSC KIPT)
cooperates with the Argonne National Laboratory of the
USA (ANL) to build a linear accelerator and a subcritical
reactor system [32].

1.3

Studies on (p,n) reactions, neutron distribution
on solid targets for ADSR

There have been many studies on (p, n) reaction, distributions of the neutron and neutron flux in the world; below
are some typical research works.
In 1999, the group of authors X. Ledoux, F. Borne, A.
Boudard, et al. calculated the energy spectrum of neutrons
produced at different angles when the proton beam carried
energies of 0.8 MeV, 1.2 MeV, and 1.6 MeV interacts on

3



the lead target [33]. Also, in 1999, the authors S. Meigo et
al. calculated the neutron flux distributions generated from
thick lead targets, with incident proton flux energies of 0.5
GeV and 1.5 GeV using the MCNP4A program [34]. In 2000,
the authors A. Letourneau, J. Galin, F. Goldenbaum performed calculations of neutrons generated on thick, heavy
targets such as W, Hg, Pb; the proton beam with energies
0.4 GeV, 0.8 GeV, 1.2 GeV, 1.8 GeV, and 2.5 GeV; with a
target size of 15 cm [35]. In 2001, the author G.S. Bauer
had analyzed the physical and technical characteristics of
neutron fission sources [36]. In this, the author presents the
results of calculating the angular distribution of neutrons
generated when a proton beam with energy 2 GeV interacts on a 20 cm thick lead target. In 2003, the authors H.
Nifenecker, O. Meplan, and S. David presented the results
of calculating the neutron multiplier per incident proton on
various targets, with the proton beam having different energies [37]. The author’s calculation results show that as the
energy of the proton beam increases, the number of neutrons emitted per incident proton increases. In 2008, author A. Krasa presented a study on the neutron spectrum
emitted in the fission reaction on a lead target with proton beam energy from 0.7 MeV to 2.0 GeV [38]. In 2018,
David Sangcheol Lee, in his doctoral thesis, presented many
calculation results related to neutron distributions inside an
ADSR [39].

1.4

Researching about using thorium as fuel in conventional nuclear reactors

Thorium is not a nuclear fission fuel; however, it can be
converted to U-233 by the neutron capture reaction of Th232. Although thorium can fission with fast neutrons of suitable energy; however, converting Th-232 to U-233 and using
it as a fission fuel will give greater efficiency. Several various


4


reactors have operated based on thorium fuel or combination with others. In early studies, thorium was combined
with uranium as a fission material. The pioneers of the idea
of combining uranium and thorium were Alvin Weinberg,
Ralph Moir, and Edward Teller, with the molten salt reactor (MSRE) experiment that ran successfully at Oak Ridge
National Laboratory (ORNL) in the US in 1969 [40]. The
Radkowsky reactor in Russia is also one of these reactors
[41]. The potential of thorium in fission energy production
has been recognized in many studies [42].

1.5

Possibility to use thorium as fuel for ADSR

Proposals to use thorium as fuel for ADSR have been
made by many researchers. Many countries are also having development projects related to this problem. In 1994,
C. Rubbia et al. proposed using thorium as fuel for ADSR
[1]. In this proposal, the ADSR system works mainly on
fast neutrons, using natural thorium fuel; all actinide elements are recycled independently. In this proposal, lead
was used as an interaction target to generate neutrons, the
heat capacity is estimated at 600 MW. C. Rubbia also suggested using Thorium as fuel for ADSR, using molten salt
as a coolant. Another proposal related to using thorium for
ADSR is ADTR (Accelerator Driven Thorium Reactor) by
the group of authors Victoria B. Ashey et al. [43]. Japan
developed ADSR to convert long-term radioactive waste to
limit its impact on the environment [44-45].

5



CHAPTER 2. SIMULATING THE STRUCTURE
OF ADSR USING LIQUID LEAD AND
THORI FUEL
2.1
2.1.1

Model of (p,n) interaction on the liquid lead target
Model and calculations

Previous studies concentrated on solid targets [46-49].
This thesis proposes to use liquid lead directly as both target
and coolant; that is, the proton beam will interact directly
with liquid lead [50]. Although liquid lead has a lower mass
density than solid lead, (10.66 g.cm−3 compares with 11.7
g.cm−3 ); however, this option will have great advantages
such as:
- There is no need for a separate target for the interaction
(p, n).
- The liquid lead is always convection and replaced during
the operating of the reactor. There will be no need to change
the target, and the reactor will not be shut down during the
operation.
- The proton beam interacts with the liquid lead target, the
length of the target increases, and therefore the number of
neutrons produced also increases.
From this idea, a model of (p,n) interaction with the liquid
lead has been built to calculate some paremeters for neutrons
such as distribution of energy, the angular distributions of

emitted neutrons, the neutron yield, and the neutron production double-differential cross-section. The basic interaction model is presented in figure 2.1.
Assume a proton beam with 25 mA intensity, 4 cm radius
interacts on the liquid lead, creating a (p,n) reaction.
The data used for the calculations in this section are extracted from the JENDL data (Japanese Evaluated Nuclear
Data Library), JENDL-HE-2007 of Japan [51-53].
From these data, a Matlab program was written to calculate
6


Figure 2.1: Model of (p,n) reaction on the liquid lead target

the parameters of neutrons emitted from the (p,n) reaction
on the liquid lead target. The results are given and commented below.

2.1.2

The distribution of the neutrons from (p,n)
reaction

The results have shown that for each energy level of the
incident proton beam, the levels of neutron energy change
from 0 to about 120 MeV, concentrated at energies from 1
MeV to 3 MeV. These results also show that the number
of neutrons with energies from 1 MeV to 3 MeV is about
73.4% when the intensity proton beam has energy of 250
MeV. These rates are 74.4%; 68.5%; 69.1%; and 60.5% for
protons with energies of 350 MeV, 500 MeV, 1 GeV and 2
GeV, respectively. Comparing the neutron spectrum for different energy levels of the incident proton, as the proton
energy increases, the neutron energy is increased. The num-


7


ber of neutrons in the energy range from 5 MeV to 15 MeV
increases more strongly than in other regions. These results
have a small difference compared with the calculation on
solid lead target [46].

2.1.3

The angular distributions of neutrons

The ratios of neutrons at 19 positions, corresponding to
19 different angles from 00 to 1800 compared to the total
number of neutrons, were calculated. The positions of angles ares determined as shown in the figure 2.2. These results
show that the neutrons are concentrated at angles from 00
to 200 . The proportion of neutrons generated in this region
is about 21.3% corresponding to the energy of 250 MeV of
the incident proton beam. These ratios ares 22%, 23.4%, respectively; 24.8%; 25% and 25.7% for incident proton energy
levels of 350 MeV, respectively; 500 MeV; 1 GeV; 2 GeV and
3 GeV. These results are consistent with the calculations on
solid lead targets [54].

Figure 2.2: The position of the generated angles of the neutrons

8


2.1.4


The neutron yields according to angles

The neutron yields in 19 angles from 00 to 1800 were calculated. The calculation results have shown that the higher
the incident proton energy levels, the higher the neutron
yield. The calculation results show that the higher the incident proton energy levels, the higher the neutron yield.
When compared with other studies on solid lead targets,
such as that of David Sangcheol Lee [30], These results are
quite consistent at positions corresponding to angles of 900
or more, however, at larger angles, there are big differences.
Calculation results have shown the difference in the angular
distribution of neutrons from the reaction (p, n) on the lead
target with two cases of solid and liquid [55-56].

2.1.5

The double-differential of the neutrons crosssection

Calculating the double-differential of the neutrons crosssection will evaluate the energy distribution of the neutrons
produced; how neutrons produced at the corresponding energy level. The results have shown that neutrons were concentrated at an energy of about 2 MeV. Comparison with
the results from calculations on solid lead by the group of
authors X. Ledoux, F. Borne, A. Boudard et al. [57] calculated at 1200 MeV proton energy, there are similarities at
energies of 5 MeV and higher. However, there is a difference
in the neutron energy region of less than 5 MeV; These show
the difference between liquid and solid targets [57].

9


2.2
2.2.1


Model of TRIGA Mark II subcritical reactor using liquid lead and thorium fuel
Model of TRIGA Mark II reactor simulated
by MCNPX

The basic details of the TRIGA Mark II reactor were
simulated and shown in figure 2.3.
The basic structure of the core consists of 108 fuel rods ar-

Figure 2.3: The cross-section of ADSR reactor core based on the
structure of the TRIGA Mark II reactor

ranged in 6 rings around, all placed in a liquid lead medium.
The details of one fuel rod was shown in the figure 2.4.

Figure 2.4: Structure of a fuel rod

From this structure, the input data file was built, the MCNPX program read the data, and output the calculation re10


sults. The neutron yields (Yn/p ) were calculated as a proton
beam with 2 mA current, carrying different energies interacted on the liquid lead in the core. The energy levels of the
proton beam were chosen according to the parabolic spatial
distribution. The effective neutron multiplication factors
(kef f ) were calculated from kcode in MCNPX.

2.2.2

The neutron yields Yn/p


The neutron yields Yn/p is the number of average neutrons produced per incident proton. In these calculations,
the proton beam with energies ranging from 115 MeV to
2000 MeV interacts on the liquid lead target. The results of
calculating the neutron yield are compared with those from
the work of Hasanzadeh, C. Rubbia et al. [51-54]. The results show that the neutron yield increases with increasing
the energy of the incident proton beam. At an energy of 115
MeV, the neutron yield on liquid lead and on tungsten differs by 4.2 %; for an energy level of 300 MeV, this difference
is 14.2 %; these values are 8.2% and 2.9% for 600 MeV and
1000 MeV energy levels, respectively. This difference is not
significant, indicating that it is completely feasible to use
liquid lead as an interaction target to generate neutrons for
ADSR.

2.2.3

The effective neutron multiplication factor
kef f

The effective neutron multiplication factors kef f were calculated for different fuel mixtures of uranium and thorium,
in different proportions placed in a liquid lead. For the
TRIGA reactor, the fuel used in the previous calculations
was UZrH (uranium zirconium hydride) placed in light water. The calculations in this thesis also use UZrH, along with
the proposed use of a thorium - uranium oxide (Th-UO) fuel
11


mixture. The results have been shown that for UZrH mixed
fuel, the higher the ratio of Uranium in the mixture, the
higher the k. Let the k reach to values higher than 0.9 then
the proportion of uranium in the mixture must be greater

than 24%. For Th-UO mixture fuel, the results show a correlation between Th-232 and U-233 in fuel composition. The
component ratio U-233 increases, the k coefficient increases.
The parameter k reaches a value greater than 0.9 when U233 accounts for about 29% of the mixture.
With the simulation and calculation results using the TRIGA
Mark II reactor model, the conditions for the fuel composition have been shown for the values of the neutron yield
and the effective neutron multiplication factors to reach the
necessary values for the ADSR.

12


CHAPTER 3
CALCULATION THORIUM FUEL FOR ADSR
3.1

Radioactive decay of thorium in the liquid lead

To evaluate the possibility of using thorium in ADSR
using liquid lead both as a target and coolant, one of the
issues is studying about the radioactive decay spectrum of
thorium in the liquid lead. Knowing the energy characteristics, running distance, ratio, ... of radioactive rays, and the
daughter nucleus, we can study their influence on the operation of ADSR. The GEANT4 program was used for these
studies [58].

3.1.1

Model and calculations

Model: Th-233 was placed in the center of a cylindrical
tube, the radius and height were 20 cm and 60 cm. These dimensions were chosen to correspond to the TRIGA reactor;

which was filled with liquid lead. The detailed structures
were shown in Figure 3.1. Here, the GEANT4 program was
used for simulations and calculations.

3.1.2

The energy spectrums of alpha, beta, antineutrino particles and gamma rays

From this model, the average energy, the ratio % of the
emitted energy, particles, the energy spectrum of the alpha,
beta, gamma, and antineutrino rays were calculated. The
results have shown that the alpha particles have the largest
average energy, with more than 6.2 %, and also accounts
for the highest percentage of emitted energy compared to
other particles, with nearly 90 %; the number of beta particles accounts for the most proportion with more than 45 %.
Meanwhile, gamma radiation and neutrinos were produced
with low average energy, and the percentage % of particles is
13


Figure 3.1: Model of radioactive decay of thorium in liquid lead

also low. These results have shown that the effects of these
particles on the thorium fuel cycle are negligible. The alpha
particles produced are concentrated at energies of about 3.7
MeV, 5.0 MeV, 6.7 MeV, and 8.4 MeV and are most concentrated at the peak energy of 3.7 MeV. Although beta
particles are abundant, they have energies very low , and
the energy peaks are not very clearly. Some energy peaks as
0.025 MeV, 0.09 MeV and 0.2 MeV can be seen. The generated gamma rays were concentrated at some energy peaks
such as 0.2 MeV, 0.6 MeV, 0.9 MeV, and 1.4 MeV. The generated neutrinos are concentrated at the energies of 0.5 MeV,

1.5 MeV, and 2.5 MeV. From these results, it is possible to
further study the effects of the generated radioactive rays
on the neutron parameters during the (p, n) interaction, as
well as the uranium, thorium fuel cycles; in the operations of
ADSR, especially the influence of alpha particles and beta
rays.

14


3.1.3

The energy of daughter nucleus

Also from this model, the minimum, average, and maximum energies of the resulting daughter nuclei were calculated. The results have shown that the energys of Pa-233
were the most, but its have the lowest energy, only from 0
to 6.2 eV; whereas Pb-213 was produced the least, with energies ranging from 0.1 MeV to 0.57 MeV. From the energy
ratio of the generated particles, nearly 60% of the energy is
mainly of the lead and bismuth nuclei. With the lead, it is
mainly the isotope Pb-209, while Pb-213 is negligible. With
the energy spectrum of the daughter nuclei, it is possible
to determine the corresponding running distances of these
nuclei in the liquid lead, thereby assessing their influence
on the operation of ADSR, especially for lead and bismuth
isotopes.

3.2

Comparison of neutron flux distributions in ADSR
using liquid lead, mixed thorium fuel with ADSR

using solid target, mixed fuel uranium

This part presents calculations and comparisons the neutron flux distribution from the thesis’s model with other
models, such as Hasanzadeh, C. Rubbia et al. [5-8]; to have
a basis for evaluating the possibility of using thorium fuel for
ADSR with the configuration proposed in the thesis. The
computational model of these authors had been presented in
chapter 2. The radial and axial neutron flux distributions
were calculated. The composition ratios of UZrH and ThUO are given in chapter 2. For each case, light water coolant
and liquid lead are investigated. The neutron flux was calculated using the MCNP5 program, with tally F4mesh.

3.2.1

The case of UZrH fuel and light water coolant

In this case, the neutron fluxes were calculated as the
proton beam interacted with the liquid lead target. The
15


fuel mixture was UZrH, which was placed in a light water. This computational configuration is similar to that of
Hasanzadeh, C. Rubbia et al.; differ only in the interaction
target to compare neutron flux distributions using a solid
lead target with a solid tungsten target. For each value of
the neutron multiplication factor k = 0.91 and k = 0.97,
the neutron flux distributions along the height of the core
were calculated. The results have shown that the neutron
flux distributions in the two cases of solid lead and tungsten
target are similar, both peaking in the middle and decreasing in the two sides. With the same neutron multiplication
factor, the neutron flux distribution depends on the neutron

emission efficiency, and the neutron emission efficiency depends on the properties of the target in the interaction (p,n).
These calculation results have also shown that for k = 0.91,
the maximum neutron flux is about 2.8.1013 n.cm−2 s−1 for
the target. solid lead and ranges from 1, 3.1013 n.cm−2 s−1
to 1, 4.1013 n.cm−2 s−1 for tungsten target. For the case
k = 0.97, the maximum neutron flux is around 1, 6.1013
n.cm−2 s−1 , compared to the range from 7.5.1012 n.cm−2 s−1
to 7, 6.1012 n.cm−2 s−1 for tungsten target. It can be seen
that when using a solid lead target, the maximum neutron
flux was from 2.0 times larger than when using a tungsten
target.

3.2.2

The case of UZrH fuel and liquid lead coolant

From the configuration described above, the neutron flux
distributions were calculated along with the height of the reactor core. In case 1, a UZrH fuel mixture was used, liquid
lead is both an interactive target and a coolant. In case
2, the fuel is also a mixture of UZrH but with a solid lead
target, and placed in a light water environment. In case 3,
calculations were conducted by Hassanzadeh et al., with the
fuel being a mixture of UZrH, tungsten target, and placed
16


in light water. The neutron flux distribution was calculated
corresponding to the multiplication factors k = 0.91; 0.97
and 0.99. These results were compared with other results,
also calculated for UZrH fuel mixture but on solid tungsten

target. The maximum and minimum neutron fluxes were
also calculated and compared with the results from other
studies. These results have shown that the neutron fluxes
along the height of the core was maximum in the center and
decreased to the core edge. These results have also shown
that with the same k value, the neutron flux of the fuel configuration UZrH in molten lead as the coolant and spallation
neutron target (Case 1) has the highest value. The lowest
value of the neutron flux belongs to the fuel profile UZrH in
light water and the neutron generated by the tungsten target (Case 3). For k equal 0.91 and 0.97, the neutron fluxes
in Case 1 is about 8-11 and 6-9 times greater than in Case
3, respectively. The maximum-to-minimum ratio of neutron
fluxes have also shown that neutron fluxes in Case 1 were
more uniform than in other cases. These results in Case 2
have also shown that solid lead could be used as spallation
neutron target for UZrH fuel in light water.

3.2.3

The case of ThUO fuel and molten lead coolant

In this case, the axial and radial distributions of neutron
fluxes were calculated. The fuel was a mixture of Th-UO,
placed in a liquid lead. The neutron multiplication factors
were k = 0.91 , 0.97 and 0.99. The results were compared
with the calculations of Hassanzadeh, C. Rubbia et al.
These results have shown that the axial distributions of the
neutron fluxes were symmetrical at the center of fuel pin,
and peaks at that position. These results differ from the
published results. The neutron fluxes in this study peak at
a position of about 3-5 cm along the radius from the center

of the reactor core, while they were in the 8-10 cm range
17


as shown in the references. The results have also shown
that, comparisons with the reference results, the value of
the maximum flux in this study is about 4.8 and 3.7 times
greater than that of k equal to 0.91 and 0.97, respectively.
The study results suggest that lead in solid or molten form
should be considered for use in designing ADSR systems
with the fuel UZrH or ThUO. The use of molten lead as both
spallation neutron target and as a coolant with ThUO fuel
results in a high neutron flux, and the design and operation
of the ADSR system will be simpler.

3.3
3.3.1

The distributions of neutron fluxes in ADSR using thorium fuel
The distributions of neutron fluxes by neutron energy

The neutron fluxes were calculated according to the emitted neutron energy, with a range from 0 to 10 MeV. The
neutron fluxes were calculated for the position of some angles such as 250 , 450 , 600 , 750 , 850 ; along with the height
from 5 cm to 65 cm, and along the radius from 2 cm to 24
cm. The results have shown that the lower the energy neutrons, the larger the neutron flux distribution, concentrated
in the range from 0 to 0,5 MeV; then decrease to an energy of
about 4 MeV and remains almost constant when the energy
is greater than 4 MeV. The energy flux distribution of the
neutron was almost unchanged for different angular positions. These results had also shown that there was a similar
shape corresponding to different positions along with the

height. The neutron flux peaks at the center of the core,
at about 7, 3.1014 n.cm−2 s−1 with neutron energies ranging
from 0.3 MeV to 0.5 MeV. The region of maximum fluxes
were located at the L position from 25 cm to 45 cm and
gradually decreases in both directions. The results of neutron flux distributions according to emitted neutron energy,
corresponding to locations along the radius from the center

18