World Journal of Engineering and Technology, 2015, 3, 328-333
Published Online October 2015 in SciRes. http://www.scirp.org/journal/wjet
http://dx.doi.org/10.4236/wjet.2015.33C049
How to cite this paper: Pazirandeh, A. and Shirmohammadi, L. (2015) Simulation of an Accelerator Driven Subcritical Core
with Mixed Uranium-Thorium Fuel. World Journal of Engineering and Technology, 3, 328-333.
http://dx.doi.org/10.4236/wjet.2015.33C049
Simulation of an Accelerator Driven
Subcritical Core with Mixed
Uranium-Thorium Fuel
Ali Pazirandeh, Laia Shirmohammadi
Department of Nuclear Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
Received 17 May 2015; accepted 23 October 2015; published 30 Oct ober 2015
Abstract
During recent years, a new generation of nuclear reactors, known as “Accelerator Driven Subcrit-
ical Reactors”, has been developed. One of the new application aspects for such reactors (besides
transmutation of High Level Waste and burning Minor Actinides) is usage of thorium as nuclear
fuel. In this work a subcritical core in experimental scale is simulated by MCNPX code. The core
contains two types of fuel assemblies: (85% ThO2 + 15% UO 2) and MOX (U-Pu). In the first step,
only the thorium-contained fuel assemblies are loaded into the core. Criticality calculations using
MCNPX show that the keff is so low that the fuel assemblies cannot run the subcritical core. This
implies that MOX (U-Pu) assemblies must be loaded as well. Neutronic parameters of the tho riu m-
fueled Accelerator Driven Subcritical core are then calculated as well as some other parameters
related to accelerator coupled with the core. The main objective of this simulation is to study the
behavior of Accelerator Driven Subcritical core with thorium assemblies.
Keywords
Accelerator Driven Subcritical Reactor, Thorium, MC NP X, Neutronic Calculation
1. Introduction
Accelerator Driven Syste ms (ADS) attract world wide attention owing to their superior aspects and their ability
to burn Minor Actinides (MA) and fission products in conjunction to their ability to transmute HLW and to
produce energy. Furthermore, ADS benefit from vitally important advantage of employing thorium (as a new
generation of nuclear fuel) with drastically wider safety margin compared with that of uranium. Thorium is an
actinide, metallic element whose abundance in earth’s crust i s 6 p pm (i.e . , three times more than that of uranium)
and is found naturally on the earth only as 232Th (t1/2 = 1.4 × 1010 y) [1]. Tho rium has several advantages as a
nuclea r fuel:
It produces less of the nuclear by-products normally used to make nuclear weapons and less of the long-lived
radioactive products of conventional nuclear power Its uses in suitable nuclear reactors can reduce the hazard of
nuclea r acci dents unlike na tural uranium, Its energy content can be used al most in its entirety, and thorium ore

A. Pazirandeh, L. Shirmohammadi
329
minerals are abundantly available in man y countries including, Austra lia , India, …
Accelerator Driven Thorium Reactor (ADTR) has some special properties that make it different from classic
reactors. All AD systems consist of three main components: a Subcritical Core (SC), a spallation targets (ST)
and an accelerator coupled with SC. Physics of AD reactors, in both structure and operation method, is quite
different from other reactors. No control rod is used in these systems; instead, a proton beam from the accelera-
tor coupled with SC controls and handles the core. This implies that the safety of the ADS basically depends on
the fu nction of the accelerator [2]-[4].
2. Accelerator Driven Subcritical Core Simulation by MCNPX Code [5]
The subcritical system adopts a hexagonal fuel array in order to compact the core and to achieve hard neutron
energy spectrum by minimizing neutron moderation. The core is simulated using Monte Carlo code MCNPX
2.4.0. The core includes a cylindrical accelerator driven subcritical system loaded with (85% T hO2 + 15% UO2)
and MOX (U-Pu) fuel assemblies. The MOX (U-Pu) n uc lide s c an b e d i sc ha rge d fr om hig hl y b ur nt -up spent fuel
assemblies of a PWR. The core consists of 66 hexagonal (85% T hO 2 + 15% UO2) fuel assemblies, 54 MOX
(U-Pu) fuel assemblies, 90 reflector assemblies and 54 shield assemblies (see Figure 1). Each assembly com-
prises 37 rods. The radius of accelerator tube is 2.5 cm and 32.6 cm below the top of subcritical core. There is
no control rod in the core. The subcritical core is generally driven by external neutrons emerged from the spalla-
tion target that is bombarded by charged particles accelerated and collimated in a high-power accelerator. Here,
the system is driven b y 1 GeV proton beam aimed to LBE (Lead-Bismuth Eutectic) target. The structure walls
and beam window are made of stainless-steel (HT-9). Owing to its outstanding nuclear properties, liquid lead-
bismuth (44.5% Pb + 55.5% Bi) is employed as both coolant and spallation target. Low melting point, high
boiling point and very low vapor pressure of LBE make it proper to operate within a wide range of temperature
that implies a n extraor dinary natur al conve ction a nd coo ling melti ng point, high bo iling p oint and ve ry lo w va-
por pressure of LBE make it proper to operate within a wide range of temperature that implies an extraordinary
natural convection and cooling capability leading to an enhanced passive safety. Because of its low neutron
capture cross section, LBE is transparent to neutrons, allowing much relaxed core design. The configuration of
the core is illustra te d in Figure 1.
The shield is made of B4C. Fig ure 2 shows a cro s s -sectio nal vie w of a single assembly. The structural assem-
bly walls are made of stainle ss-steel (HT -9). No separate target is included in the core. As depicted in Figure 1,
the buffer region is between LBE target and the core. The buffer zone flattens the power distribution. Figure 3
demonstrates the array of assemblies in the core simulated by MCNPX2.4.0.
3. The Neutronic Performance Calculation and Results for Simulated ADS Core
The calculation of neutron multiplication factor for ADS was performed by MCNPX code using KCODE option.
In an ADS, keff must be between 0.95 and 0.98 indicating that ADS is a subcritical system. ADS reactors, as a
matter of fact, ar e s ubcritica l in all co ndit ions a nd power leve ls. T he syste m was firs t si mula ted with onl y (Th -U)
fuel asse mblies loaded and the multiplication factor was calculated. This being the case, keff was muc h less tha n
0.9 5, implyin g that the c ore would not run. T hen the MOX (U-Pu) fuel assemblies were loaded into the core as
shown in Figure 1 and the multiplication factor increased to 0.966 where the chain reaction could sustain. The
Figure 1. Cutaway of simulated ADS core.

A. Pazirandeh, L. Shirmohammadi
330
Figure 2. Cutaway of an assembly.
Figure 3. Cutaway of assembly arra y in the core si mulated by MCNPX : (a) one assembly (b) par t of the core
assemblies, buffer r egion and target.
spallation neutrons were produced from interaction between 1 GeV proton beam and LBE target. A critical sys-
tem (in which neutron production and consumption are balanced) is well defined in the phase space (E, r, Ω) by
Boltzmann eq uation:
P
A=Φ Φ
(1)
In the subcritical syste m the condition to ha ve a statio nary state is to have an exter nal sour ce S(E,
r
,
Ω
) so
Equation (1) changes to:
in in
APSΦ=Φ+
(2)
in
Φ
is the so lutio n of the in homoge neous Eq uation ( 2). Rel evant i ntegral p aramete rs chara cterizing t he sub-
critical core is done exactly as in critical systems, characterized by, is formally possible to describe a subcritical
s ys tem with the introduction of a parameter
eff
k
as gi ven in Equa t ion (3).
1
eff
AP
k
Φ= Φ
(3)
To improve the defini tion of sub-criticality a different definition of the sub-criticality has been proposed, by
means of a k-source “
S
k
” the external sourc e multiplication factor one ob ta ins:
in
Sin
P
kPS
Φ
=Φ+
(5)

A. Pazirandeh, L. Shirmohammadi
331
S
k
depends on the incident proton energy, target material and dimension of the target. Therefore, in ADS
safety and dynamic development accelerator technology with high energy beams in parallel with subcritical core
study appears necessary. In ADS core,
( )
1
S
kM M = −
and
M
is the number of neutrons produced per pro-
ton, so for simulated core, in the top Z = 32 cm of core M = 27.53 is approached. The relative importance of the
sourc e neut rons to the fis sion neutro ns gene rated in the SC is intr oduce d by a parameter
∗
Φ
as neutron source
importance is related to
eff
k
as:
11
eff
k
ϕ
ν
∗
Γ= −
(6)
where
ν
is the average of prompt neutrons per fission and
Γ
is the average number of source neutrons per
fission.
Another equation for this parameter is:
11
11
eff S
kk
ϕ
∗


=−−





(7)
The
ϕ
∗
parameter plays an important role in assessing the ADS performance parameters. For this simulated
core
ϕ
∗
is 0.967. Table 1 shows some data related to simulated core.
Figure 4 shows the varia tio n o f ne utro n yie ld p er inc ide nt p ro ton ver sus t he e ner gy o f the pr oto n in ta rget r e-
gion. The neutron yield is calculated by simulating an LBE cylindrical target outside the core and an incident
proton beam. Neutrons in the both types of fuel assemblies are fast, implying that the simulated core behaves
like a fast reactor core. The neutron spectra in shielding, MOX(U + T h), buffer and (U + Pu) regio ns are sho wn
in Figure 5.
Figure 4. Variation of neutron yield per incident proton beam in target.
Table 1. Data o f the simulated accelerator d riven su bcritical core.
eff
k
(multiplicati on f actor) 0.966
S
k
(external sour ce multiplicatio n f acto r ) 0.965
M (the number of neutron produce per proton beam) 27. 53
ρ
(reactivity) −0.0351
ϕ
∗
(adj oint flux) 0.9 673
G (energy gain) 60.8
Core ther mal power 4 4. 49 MW
Peaking factor (tota l core) 1.56
Cycle length 3 00 d
Av neutron energy 190 KeV
Av neutron flux 3.56e15 (n/cm3s)
Active cor e high t 1 00 cm

A. Pazirandeh, L. Shirmohammadi
332
Figure 5. Neutron flux in buffer region.
4. Conclusions
Why we should use thorium instead of uranium?
Because of simply reason, it involves nuclear reactions that are much more effective than those in conven-
tiona l nuc lear r eacto rs. T horium i s abo ut thr ee ti mes mor e ab undant on Ear th t han ura niu m; it is abo ut as ab un-
dant as lead. Another advantage of thorium is that it is less of a proliferation threat—there is a uranium bomb
and a plutonium bomb, but no thorium bomb can be produced. The use of thorium has received a lot of attention
from many scientists, such as Alvin Weinberg, Ed Teller and Carlo Rubbia. But the main drawback with tho-
rium is that you need t wo neutrons, rather than the one in ordinary uranium powered reactions, to produce we
need to use a proton accelerator It is a problem that demands 1 - 1.5 GeV accelerator. To produce fissile isotope
is shown in reaction below:
232 233233233
N ThTh*PaU ββ
−−
+→→+→ +
Researches on thorium fuel cycle are currently underway and thorium-fuelled reactors must be brought into
the service to let their technological aspects be practically investigated. ADS reactor is a new generation, high-
tech system that can burn thorium-based fuel to produce power. This work simulates an ADS core having two
different types of fuel assemblies and burning thorium fuel. ADS systems produce less nuclear wastes, elimi-
nating the complicated problem confronted in the nuclear waste management. The new generation of nuclear
fuel ( e.g. , Mi nor Ac tinides (MA) and MOX (Th-U) or MOX (Th-Pu) ) ne eds no urani um enr ich ment and no plo-
tuinum, therefore, is much more economic. The accelerator that drives the system plays a very essential role in
technological and safety aspects. Further studies on the proton beams produced by the accelerator and on the in-
teractions o f proto n with matt er may help to choose b etter materials as t he spallation target a nd to optimize the
neutron flux emerged from the external source. In Accelerator Driven Thorium Reactors (ADTR), on the other
hand, very rare radio-isotopes may be produced for medical application [6]. As pointed out the multiplication
factor ought to be greater than 0.95, since for an ADS with a neutron multiplication factor of 0.95, the reduction
amounts to about 12%. This means that the accelerator driven system produces about 14% more high-level
waste and rejects about 20% more heat to the atmosphere than a normal power plant with the same net electrical
output. The advantages and disadvantages of accelerator-driven systems as compared with corresponding critical
reactor systems applies not only to transmutation applications, but also to other applications such as the breeding
of fissile material, transmuta tion of lon g lived fission products, the d e velopment of the 233Th to 233U fuel cycle,
and the d eve lo pment of ul tr a -safe energy producers [7]. Extended neutron energy spectrum promotes fast fission
reactions in actinides. Transmutation aims at reducing the radiological impact of actinides and fission products
in the HLW by nuclear transformation of troublesome long-lived nuclides in strong radia tion fields. The appli-
cation of the ADS concept to a minor actinide burner core is an interesting possibility to compensate the safety
disadvantages arising from the small Doppler coefficient and the small keff value which cannot be otherwise
compensated.

A. Pazirandeh, L. Shirmohammadi
333
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