Nuclear Engineering and Design xxx (xxxx) xxx

Contents lists available at ScienceDirect

Nuclear Engineering and Design
journal homepage: www.elsevier.com/locate/nucengdes

Effect of nuclear heat caused by the 6Li(n,α)T reaction on tritiumcontainment performance of tritium production module inHigh-Temperature Gas-Cooled reactor for fusion reactors
Yuki Koga a, *, Hideaki Matsuura a, Kazunari Katayama b, Teppei Otsuka c, Minoru Goto d,
Shimpei Hamamoto d, Etsuo Ishitsuka d, Shigeaki Nakagawa d, Kenji Tobita e, Satoshi Konishi f,
Ryoji Hiwatari g, Youji Someya g, Yoshiteru Sakamoto gaDepartment of Applied Quantum Physics and Nuclear Engineering, Kyushu University, 744 Motooka Nishi-ku Fukuoka-shi Fukuoka, 319-0395 Japan
Department of Advanced Energy Engineering Science, Kyushu University, 6-1 Kasugakouen Kasuga-shi Fukuoka, 816-0811 Japanc
Department of Electrical and Electrtonic Engineering, Kindai University, 3-4-1 Kowakae, HigashiOsaka city Osaka, 577-0818 Japand
Japan Atomic Energy Agency, 4002 Narita-cho Oarai-machi Higashi-Ibaraki-gun Ibaraki, 311-1393 Japane
Department of Quantum Sci. Energy Eng., Tohoku University, 6-6-01-2 Aoba, Sendai City, Miyagi 980-8579, Japanf
Institute for Advanced Energy, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japang
National Institutes for Quantum and Radiological Sci. Tech., Rokkasho, Aomori 039-3212, Japanb

A R T I C L E I N F O

A B S T R A C T

Keywords:
Fusion reactor
Tritium production
HTGR
Tritium production module
Nuclear reaction heat

Tritium is required for research and development activities for the deuterium–tritium (DT) fusion reactor andfueling the DEMOnstration Power Station (DEMO). However, tritium is a very rare nuclide and must be produced
artificially. Tritium production by loading Li compounds (Li rods) into burnable poison holes of a hightemperature gas-cooled reactor (HTGR) has been proposed (H. Matsuura, et al., Nucl. Eng. Des. 243 (2012)
95–101.). Al2O3 and Zr are used to prevent tritium leaks. Nuclear reaction heat caused by the nuclear reaction (e.
g., 6Li(n,α)T reaction) can cause a spatial temperature profile in the Li rods and may change its tritiumcontainment performance, because Al2O3 and Zr performance strongly depend on these temperatures. The effectof nuclear reaction heat by the 6Li(n,α)T reaction on the tritium containment performance of the Li rods wasevaluated by simulation. The temperatures of the Li rods for the high-temperature engineering test reactor(HTTR) and gas turbine high-temperature reactor 300 (GTHTR300) increased by 36 K and 46 K, and the leaked
tritium decreased by 32% and 37% via nuclear reaction heat, respectively.

1. Introduction
To conduct research and development for the deuterium–tritium(DT) fusion reactor, tritium is required. Tritium must be produced
artificially in nuclear facilities because it is a rare nuclide in nature, anddeuterium can be obtained from water. Approximately 200 g of tritium
are consumed per day in a fusion reactor with 1.5 GW of thermal output
power. A large quantity of initial tritium is also required to start up afusion reactor, which operates with producing tritium more thanconsuming tritium. It has been reported that the amount of initial
tritium required for the DEMOnstration Power Station (DEMO) isseveral 100 g - approximately 27 kg (Hiwatari, 2018; Asaoka et al.,1996). In addition, ≥100 g of tritium is required for an engineering test

before DEMO reactors are built. The tritium supplied to the International
Thermonuclear Experimental Reactor (ITER) is produced from Canadian
Deuterium Uranium reactors (CANDU) in Canada (Gierszewski, 1989).
However, it has not been clarified how the tritium for the first DEMO
reactors, particularly those in Japan, will be supplied. Thus, we haveproposed a tritium production method using a high-temperature gascooled reactor (HTGR) (Matsuura et al., 2012) by loading tritium pro­duction modules containing a Li compound as a burnable poison (BP).
The HTGR is primarily composed of graphite (moderator) and He(coolant), which are chemically stable and do not react with the Licompound. Furthermore, the required amount of Li compound can beloaded without 6Li concentration because the HTGR core size is larger
than other types of fission reactors, such as the pressurized water reactor* Corresponding author.
E-mail address: koga_yuki@nucl.kyushu-u.ac.jp (Y. Koga).
https://doi.org/10.1016/j.nucengdes.2021.111584
Received 20 June 2021; Received in revised form 15 November 2021; Accepted 20 November 2021
0029-5493/© 2021 Elsevier B.V. All rights reserved.

Please cite this article as: Yuki Koga, Nuclear Engineering and Design, https://doi.org/10.1016/j.nucengdes.2021.111584

Y. Koga et al.

Nuclear Engineering and Design xxx (xxxx) xxx(PWR) and boiling water reactor (BWR). Normal BP is cylindrical solid
B4C, so with that same form, the module can be loaded without signif­
icantly changing the original core design from the standard one. We
assume that in the module the Li compound and Zr (tritium absorber)are sealed in cylindrical Al2O3 (Matsuura et al., 2019). This module is an
Li rod, which produces tritium, while Zr absorbs tritium during theoperation. The tritium must be contained so that leaking into the coolant
is maintained as low as possible. The tritium leakage rate was evaluatedto be below 1% at 800 K by performing numerical simulations of the Li
rods without Zr (Nakaya et al., 2015). It was supposed that the gas
turbine high-temperature reactor 300 (GTHTR300) (Nakata, 2002)
produced 400–600 g of tritium in six months on the simulation (Nakaya
et al., 2015). However, most of produced tritium might leak with theincreased Al2O3 hydrogen permeability (Katayama et al., 2015), if thenormal outlet temperature is supposed to be 1,070 K–1,170 K to main­
tain thermal efficiency. Accordingly, we considered using Zr as a tritium
absorber and its shape for the Li rods. Fig. 1 shows the current design of
the Li rods with Zr considered for efficient tritium absorption (Matsuura
et al., 2019). It has been reported that tritium absorption performance ofZr worsens during oxidation and a Ni coating can be applied to prevent
this (Matsuura et al., 2019). Moreover, Zr pebbles can be used for large
absorption areas. It was expected that Li rods with Zr can reduce tritium
leakage and contain enough tritium if the deterioration of Ni-coated Zr is
minimized during oxidation (Matsuura et al., 2019). We have been
advancing an irradiation test plan for the high-temperature engineering
test reactor (HTTR) (Saito, 1994) to confirm the Li rod and Ni-coated Zr
performance as well as demonstrate the HTGR’s tritium production(Koga et al., 2018). The HTTR is an experimental HTGR with 30 MW ofthermal output owned by the Japan Atomic Energy Agency (JAEA). The
structure of Li irradiation units has been investigated for feasible irra­
diation tests. So far, we have conducted hydrogen absorption experi­ments to measure the hydrogen absorption performance of Zr using Zr
powder (Izumino et al., 2018), Zr cylinders (Matsuura et al., 2019;
Matsuura, 2021), and one-side sealed Zr pipes (Katayama et al., 2018)
However, the tritium absorption performance of Zr in Li rods inserted
into the HTGR has not been measured yet. We have developed ananalysis model for tritium production and containment in the
GTHTR300 and HTTR (Matsuura, 2021).
Energy is generated per the following reaction when tritium is pro­duced

changes to thermal energy via collisions between particles and otheratoms. Tritium and α particles remain in the Li rods so that the tem­
perature in the rods increases, and the temperature distribution appears
via the temperature difference compared to its surroundings. The
amount of produced tritium in the GTHTR300 is more than that in the
HTTR due to the differences in reactor sizes, loaded amount of 6Li, andthermal outputs for these reactors. If about 193 g (6,550 g) of 6Li is
loaded into the HTTR (GTHTR300) and 30 g (800 g) of tritium is pro­
duced in a year, the nuclear reaction heat of Li rods is estimated to be
300 W (1,800 W) considering only the 6Li(n,α)T reaction. The results ofthis experiment imply that the tritium containment performance of the
Al2O3 layer deteriorated as the temperature increased (Katayama et al.,2015). Meanwhile, the hydrogen absorption performance using Zr cyl­
inders at 1,170 K and 1,120 K shows that the hydrogen absorption speed
at 1,170 K is faster than that at 1,120 K (Matsuura et al., 2019), implyingthat the tritium absorption performance of Zr is better at higher tem­
peratures. These evaluations were conducted under the assumptions
that Li rods do not have a temperature distribution and that the tem­
perature was the assumed temperature or coolant temperature (Mat­suura et al., 2012, 2019; Koga et al., 2018; Matsuura et al., 2012;
Nagasumi, 2017).
In research on fusion reactor blankets, a coolant system has been
designed by fluid dynamics analysis based on the coolant conditions for
PWR. Previous studies in the blanket system have shown the importanceof nuclear reaction heat on fusion and nuclear reactors. In the evalua­tion, it was assumed that the JA DEMO and temperature of the inlet
coolant water were 568 K, and the maximum temperatures of the Li/Be
mixed pebble region and the structural material were evaluated as
1,119 K and 817 K, respectively, and satisfied the permissible range(Someya, 2019). The maximum fuel temperature in the HTTR is limited
to 1,768 K for safety, and the temperature was calculated to be at a
maximum of 1,765 K in normal operation via simulation (Maruyama,1994). Moreover, we have evaluated reactor temperature and temper­
ature coefficient reactivity by simulation to confirm the nuclear andthermal feasibility of the HTGR loaded with Li rods (Goto, 2018). The
maximum fuel temperature was 1,746 K, i.e., lower than the limit, so the
LiAlO2 would not melt (Goto, 2018). Now, it is necessary to confirm thetemperature distribution in the Li rods via the nuclear reaction heat andevaluate the thermal effects on the rods’ tritium containment perfor­
mance. The amount of leaked tritium may change as the temperature
increases due to the reaction heat since a substantial amount of Zr isloaded into the Li rods.
In this study, we evaluate the effects of nuclear reaction heat by the6
Li(n,α)T reaction on the tritium containment performance of the Li rods
for the HTTR and GTHTR300 and compare the changes in the amount of
leaked tritium with previous evaluations in which the nuclear reaction
heat was not considered.

6Li + n→T + α + 4.8MeV
This energy appears as kinetic energy in generated particles and

2. Calculation model
2.1. Li rod structure and HTGR designs
The schematic diagram of the HTTR and GTHTR300 cores are shownin Figs. 2 and 3. The HTTR core consists of 30 fuel columns and sevencontrol rod guide columns surrounded with permanent/replaceablereflector columns and nine control guide columns. There are five corelayers and four reflector layers. The core is 2.9 m in height and 2.3 m inequivalent diameter. The block is 580-mm high and 360-mm wide
across the flats. The fuel blocks contain either 31 or 33 fuel rods andthree BP holes. The GTHTR300 is an HTGR design created by the JAEA
that has 600 MW of thermal output. Its core is ring-shaped, consisting of
90 fuel columns, 30 control rod guide columns, and 46 replaceablereflector columns. It is surrounded with permanent reflector columns
both inside and outside. There are eight core layers and two reflector
layers. The core is 8 m in height and about 5.6 m in diameter. The blockis 1,000-mm high and 405-mm wide across the flats. The fuel blocks

Fig. 1. Schematic diagram of Li rods.
2

Y. Koga et al.

Nuclear Engineering and Design xxx (xxxx) xxx

Fig. 2. Schematic diagram of the HTTR core. The HTTR consists of fivecore layers.

Fig. 5. Schematic diagram of Li rods for the GTHTR300. The characteristics of
the Zr and LiAlO2 layer are same to Fig. 4.

using the continuous-energy Monte Carlo transport code MVP-BURN(Nagaya, 2017; Okumura et al., 2000) with the Japanese EvaluatedNuclear Data Library-4.0 (JENDL-4.0) (Shibata, 2011). We assumed the
HTTR and GTHTR300 core system with Li rods loaded into all BP holes
for a 360-day operation period. The average moderator temperature of
the Li rods for the HTTR was set at 1,140 K, and that for the GTHTR300
was set at 1,190 K. It was assumed that all control rods were pulled up onthese simulations. Considering the actual reactor operation, the keff on
day 360 was supposed to be over 1.02. The time steps for the burn-up
simulation were set as 0, 1, 5, 30, 60, 120, 180, and 360 days. The
thermal outputs for the HTTR and GTHTR were set at 30 and 600 MW,
respectively, throughout the operation. Moreover, six million neutron
particles were generated in these simulations so that the statistical error
was guaranteed to be less than 0.1% for the keff and reaction rates on
nuclides in fuel and Li rods.

Fig. 3. Schematic diagram of the GTHTR300 core. The GTHTR300 consists ofeight core layers.

contain 57 fuel rods and three BP holes. The moderator temperature of
the HTTR is in the range of 900 K–1,280 K.
Figs. 4 and 5 show the Li rod designs proposed for both reactors
currently. The Li rods for the HTTR are 450 mm in height and 14 mm indiameter. They consist of a hollow portion, Li compound (LiAlO2) with
85% theoretical density (Kawamura et al., 1992), Zr layer/pebbles, andAl2O3 layer. The concentration of 6Li in the LiAlO2 was set at its naturalabundance. The Li rods for the GTHTR300 were 1,000 mm in height and
44 mm in diameter, and their structure was the same as that of the HTTR
Li rods. In this simulation, Zr pebbles were inserted with 60% hollow
portion volume into each Li rod.

2.3. Nuclear reaction heat generation model

2.2. Nuclear calculation

The nuclear reaction heat of only the 6Li(n,α)T reaction wasconsidered here. The nuclear reaction heat was converted from thetritium produced in an Li rod as follows:

To evaluate the amount of tritium produced in the Li rods andeffective multiplication factor (keff), we conducted a nuclear calculationq‘‘‘ =nQ
VLi NA(1)

where q‘‘‘, n, VLi, NA, and Q are the nuclear reaction heat per volume(W/m3), tritium production rate by an Li rod (mol/s), volume of the
LiAlO2 layer (m3), Avogadro‘s constant, and Q value of the 6Li(n,α)T
reaction energy (J), respectively. A stationary heat diffusion equation
was used in the cylindrical coordinate with q‘‘‘, and the temperature
distribution of an Li rod was evaluated for the radius direction:
(
)
1 ∂
∂T
kr
+ q‘‘‘ = 0
(2)
r ∂r
∂r
where r, k, and T are the distance of the radius direction (m), thermal
conductivity (W/m K) of each layer at 1,073 K, and temperature (K),respectively. It was assumed that the Li rods and He gas in the fuel block
were sealed by graphite dowel pins as the design data shows. Therefore,
the existence of He gas between the Li rods and fuel block was consid­
ered. The applied thermal conductivity values of each layer are shown in
Table 1 (Schulz and Wedemeyer, 1986; Fink and Leibowitz, 1995;
Auerkari, 1996; Faubert and Springer, 1973; Powell, 1965). The thermal
conductivity of Zr was smaller than that of Ni so that we adopted pure-Zr

Fig. 4. Schematic diagram of Li rods for the HTTR. The Zr layer is Ni-coated.
The LiAlO2 layer has 85% of theoretical density.
3

Y. Koga et al.

Nuclear Engineering and Design xxx (xxxx) xxx

Table 1
Thermal conductivity of Li rod layers.
Thermal conductivity(W/m K)√̅̅̅CAl0 = SAl P

LiAlO2

Zr

Al2O3

He

Ni

3.96

22.8

6.34

0.375

73.7

(7)

where CAl0 , SAl , and P are the tritium concentration in the innersurface of the Al2O3 layer (mol/m3), the solubility coefficient of the
Al2O3 layer (mol/m3/Pa1/2) and partial pressure in the hollow portion(Pa), respectively. Sieverts’ law can be adopted for Al2O3 layer because
the gas diffused by atomic form in the high density Al2O3 tube in theexperiment (Katayama et al., 2015). The inner boundary temperature of
the Al2O3 layer was used for the SAl and DAl values for conservative
calculation. The DAl and SAl values for Al2O3 used in Eqs. (6) and (7)were cited from Katayama, K. et al. (Katayama et al., 2015), and it was
assumed that their temperature functions were also held for any tem­
perature. To calculate the amount of permeated tritium in the inner(outer) surface of the Al2O3 layer, Fick’s law was used:⃒∂CAl ⃒⃒
Jin,out = − Ain,out DAl(8)∂rAl ⃒in,out

thermal conductivity for the Ni-coated Zr.
2.4. Tritium absorption model for Zr
We applied the hydrogen diffusivity and solubility coefficient for Zr
measured by the outer Zr pipe in a previous study1 (Katayama et al.,2018). Diffusion calculations by the diffusion equation and Sieverts’ law
were conducted to evaluate the amount of tritium absorbed into the Zr.
The Zr pebbles and Zr layer were assumed to have converted to a Zr
cylinder with the same surface area. The diffusion equation in a cylinder
coordinate system was as follows:()∂CZr (t, rZt ) DZr ∂∂CZr (t, rZt )
rZr
(3)
=
∂t
rZr ∂rZt∂rZr

where Jin (Jout ) and Ain (Aout ) are the tritium flux from the inner sur­face of the Al2O3 layer (the inner Al2O3 layer) to the inner Al2O3 layer(the outer surface of the Al2O3 layer) (mol/s) and the inner (outer)surface area of the Al2O3 layer (m2), respectively. The tritium in theouter surface of the Al2O3 layer was assumed to leak into the He coolant
immediately. Finally, Eqs. (5)–(8) were united with the tritium balance
equation shown below to evaluate the tritium absorption and leakage:where CZr , t, DZr , and rZt are the tritium concentration in Zr (mol/m3), time (s), the diffusion coefficient of the Zr (m2/s), and distance ofthe radius direction (m), respectively. This equation was used to
calculate the tritium concentration distribution in the Zr. Sieverts’ law
was used as the boundary condition of the Zr surface.
√̅̅̅
CZr0 = SZr P
(4)

dP
GRT
JZr RT
Jin RT=++
dt
Vhp+Li(15) Vhp+Li(15) Vhp+Li(15)(9)

where G, R, and Vhp+Li(15) are the tritium molecule generation speed(mol/s), gas constant (J/K mol), and volume of the hollow portion andvoid of the LiAlO2 layer in an Li rod (m3), respectively. We ignored theanti-permeation property of Zr that prevented the tritium from perme­ating into the Al2O3 layer for the conservative evaluation. Finally, Fig. 6
shows the tritium leakage model using Eq. (9). The tritium produced in
the LiAlO2 quickly entered the hollow portion, and a portion of it wasabsorbed by the Zr. The tritium diffused into the Al2O3 layers and thenleaked into the He region (tritium concentration: C = 0).

where CZr0 , SZr , and P are the tritium concentration in the Zr surface(mol/m3), solubility coefficient of the Zr (mol/m3/Pa1/2), and tritium
partial pressure (Pa), respectively. It has been confirmed that tritium
absorption phenomena by Zr are consistent with Sieverts’ law in the pastexperiments (Matsuura et al., 2019, 2021; Izumino et al., 2018;
Katayama et al., 2018). Then, CZr was integrated in the Zr volume anddifferentiated in time to evaluate the amount of tritium absorbed in theZr, as follows:∫∂
JZr = −C (t, r)d3 r(5)∂t Vzr Zr

3. Results and discussion

where JZr and VZr are the tritium flux from the surface of Zr (mol/s)and the volume of the assumed Zr cylinder (m3), respectively, while DZrand SZr were cited from Katayama et al. (2018). The value of SZr was
obtained from DZr and the hydrogen permeability. It was assumed thatthe coefficient functions were held for any temperature. The tempera­ture of the center of any Li rod was adapted to the functions. Further­more, DZr was reduced by 1/2,000 to consider the reported influence of
the Ni coating (Otsuka, et al., 2020).

3.1. Tritium produced in the HTGRs and calorific value of the Li rods
Fig. 7 shows the cumulative amount of tritium produced and the keffover 360 days of operation for the HTTR and GTHTR300. The amount oftritium produced and the keff values after 360 days of operation for the
HTTR (GTHTR300) were 30.4 g/y (807.3 g/y) and 1.028 (1.020). The

2.5. Tritium leakage model for Al2O3 layer
To evaluate the tritium leakage, we used this tritium diffusion
equation in the cylindrical coordinate:()∂CAl (t, rAl ) DAl ∂∂CAl (t, rAl )
rAl
(6)
=
∂t
rAl ∂rAl∂rAl
where CAl , t, DAl , and rAl are tritium concentration in the Al2O3 layer(mol/m3), time (s), diffusion coefficient of the Al2O3 layer (m2/s), anddistance of the radius direction (m), respectively. The temperature at the
inner boundary was used for the DAl value as a conservative evaluation.
Sieverts’ law was used as the boundary condition just as in the Zr tritium
absorption model:
Fig. 6. Schematic diagram of the tritium leak model in the Li rod. The blue
curve shows the tritium concentration. (For interpretation of the references tocolour in this figure legend, the reader is referred to the web version ofthis article.)

1

The diffusivity coefficient was cited from the study. The permeability co­efficient is the product of diffusivity and solubility coefficient so that the sol­ubility coefficient converted from it and the permeability coefficient.
4

Y. Koga et al.

Nuclear Engineering and Design xxx (xxxx) xxx

the distribution was constant at 1,140 K (moderator temperature). Whenconsidering the reaction heat, the temperature increased. The maximum
temperature was 1,176 K (a 36 K increase) in the hollow portion and Zr
pebble regions, and the temperature dropped in the outer region. The
temperature distribution was always constant in the hollow and Zr
pebble regions at steady state regardless of effective thermal conduc­tivity by any material forms. This is derived from Eq. (2). If the effective
thermal conductivity reduces in LiAlO2, Zr, and Al2O3 layer by irradia­tion, temperature will increase there. The temperature dropped the mostin the He region because the He thermal conductivity was low andworked as a heat gap. The amount of tritium produced by the Li rods for
the HTTR and the leaked tritium with/without the reaction heat after
360 days of operation are shown in Fig. 9. If the reaction heat was notconsidered, the amount of leaked tritium was 5.03 × 10− 1 g, and theleakage rate was 1.66%. When considering the reaction heat, theamount of leaked tritium was 3.43 × 10− 1 g, and the leakage rate was
1.13%. Thus, there was a 31.8% decrease in the leaked tritium via thereaction heat.
The temperature distribution in the Li rods for the GTHTR300 was
evaluated in the same way as for the HTTR. Fig. 10 shows the temper­
ature distribution. If the reaction heat was not considered, the distri­bution was constant at 1,190 K. The maximum temperature was 1,236 K(a 46 K increase) in the hollow portion and Zr pebble regions. The higher
reaction heat simply increased the maximum temperature. Large ma­
terials have high heat retention, and thick layers generally retain heat.
Therefore, it was considered that the larger size of the Li rods and thicker
Al2O3 layer caused the higher temperature increase. Fig. 11 shows the
cumulative tritium produced and leaked from the Li rods for the
GTHTR300 with/without reaction heat after a one-year operation
period. The amount of leaked tritium was 2.67 × 10− 1 g, and the leakrate was 3.31 × 10− 2 % when the reaction heat was not considered. The
tritium leakage of the Li rods for the GTHTR300 decreased even morethan that for the HTTR by loading more Zr, although the GTHTR300
produced more tritium. Considering the reaction heat, the amount of
leaked tritium was 1.68 × 10− 1 g, and the leak rate was 2.08 × 10− 2 %.
There was a 37.1% decrease in the leaked tritium via the reaction heat,higher than that for the HTTR. This was because the temperature in­crease caused by the nuclear reaction heat for the GTHTR300 was
higher, and the Zr performance was better. These results show that theamount of leaked tritium was decreased by the reaction heat for the
GTHTR300 as well.
To confirm roughly the time that the temperature distributions reachsteady state, we evaluated the time that the Li rods reach maximum
temperature when heat does not transfer outside the Li rods. Table 2

Fig. 7. The cumulative amount of tritium produced, and the keff value
throughout the 360 days of operation for the HTTR and GTHTR300.

keff for the GTHTR300 decreased more rapidly than that of the HTTR
during the operation. The produced tritium was used to evaluate thecalorific values of the Li rods for both reactors. The tritium production
speed per one Li rod for the HTTR (GTHTR300) was 2.17 × 10− 9 g/s(1.20 × 10− 8 g/s). The Q value of the 6Li(n,α)T nuclear reaction energy
is 4.8 MeV, so the nuclear reaction heat for one Li rod for the HTTR
(GTHTR300) was 333 W (1,845 W). The volume of the LiAl2O layer inthe cylinder-shaped VLi for the HTTR (GTHTR300) was 2.79 × 10− 5 m3
(1.97 × 10− 4 m3), and the 6Li atoms were assumed to be uniform in the
LiAl2O layer. Using Eq. (1), the nuclear reaction heat per volume (W/m3) for the HTTR (GTHTR300) was evaluated as 1.20 × 107 W/m3
(9.36 × 106 W/m3).
3.2. Evaluation of the nuclear reaction heat and its effect
Before the evaluation of the effect by nuclear reaction heat, we
compared the accuracy of the tritium leakage calculation to the accurate
evaluation (Matsuura, 2021) and found that the accuracy was
acceptable.
We evaluated the radial profile of the temperature in the Li rods for
the HTTR (Fig. 8) using the values of the nuclear reaction heat shown in
Section 3.1 and Eq. (2). If the nuclear reaction heat was not considered,Fig. 8. Temperature distribution of the Li rods for the HTTR. The nuclear re­action heat was 333 W. The maximum temperature was 1,176 K in the hollow
and Zr pebble region.

Fig. 9. The amount of tritium produced and leaked by the Li rods for the HTTR
with and without the nuclear reaction heat throughout the 360 days of oper­
ation. There was a 31.8% decrease in the leaked tritium via the reaction heat.
5

Y. Koga et al.

Nuclear Engineering and Design xxx (xxxx) xxx

Fig. 12. Tritium leakage rate of the Li rods and tritium partial pressure for the
HTTR after 360 days of operation at 770– 1,176 K with only Al2O3 layer as
tritium containment function or Zr. The percentage of Zr was the Zr loading rateof the Zr layer and pebbles. When it was 100%, the amount of loaded Zr in the
Li rods is the same as those evaluated in Section 3.2.

Fig. 10. Temperature distribution of the Li rods for the GTHTR300. The nu­
clear reaction heat was 1,845 W. The maximum temperature was 1,236 K in thehollow and Zr pebble region.

tritium containment function or with Zr. The percentage of Zr was the Zr
loading rate of Zr layer and pebbles. When it is 100%, the amount ofloaded Zr in the Li rods is the same as those evaluated in Section 3.2.
Fig. 13 shows the tritium absorption rate of Zr per produced tritium astritium absorption performance at 770 K–1,176 K based on the evalua­tion of Fig. 12. The thickness of the Al2O3 layer was 2.0 mm when the Zr
layer was not considered. When only the Al2O3 layer was used for the Lirods, the tritium leakage rate increased due to the increase in moderator
temperature. This is because Al2O3 hydrogen permeability is directly
proportional to the temperature (Katayama et al., 2015). When Zr wasconsidered, the tritium adsorption rate increased with an increase intemperature since Zr hydrogen permeability is also proportional to thetemperature (Katayama et al., 2018). The tritium leakage rate increased
at peak temperatures from the minimum temperature due to the in­crease in temperature. This is because the tritium absorption perfor­
mance of Zr under the peak temperature was lower than the tritiumcontainment performance of the Al2O3 layer deteriorated by the tem­
perature increase. The tritium leakage rate and partial pressure
decreased over the peak temperature due to the increase in temperature.
This is because the tritium absorption of Zr performs better than tritiumFig. 11. The amount of tritium produced and leaked by the Li rods for the
GTHTR300 with and without the nuclear reaction heat throughout the 360 daysof operation. There was a 37.1% decrease in the leaked tritium via the reac­tion heat.
Table 2
Molar heat capacity of Li rod layers. Value for Al2O3 was converted from specificheat capacity.
Molar heat capacity(J/mol K)

LiAlO2

Zr

Al2O3

He

102.7

33.5

123.1

20.8

shows molar heat capacity values of each layer (Fink and Leibowitz,
1995; Auerkari, 1996; Chase, 1998; Kleykamp, 1999). The heat capacityof Li rods for the HTTR (GTHTR300) was calculated to be about 295(5652) J/K. If the temperature of the Li rods for the HTTR (GTHTR300)
increase by 36 (46) K, the required time was 32 (1 4 1) s. Therefore, theperiod during transient state was shorter than the operation time so thatthe influence of transient state could be ignored.
3.3. Analysis of the effect of nuclear reaction heat
We analyzed the results of Section 3.2. Fig. 12 shows the tritium
leakage rate and partial pressure of the Li rods for the HTTR after 360
days of operation at 770 K–1,176 K with only the Al2O3 layer as theFig. 13. Tritium absorption rate of Zr per produced tritium at 770–1,176 K
based on the evaluation of Fig. 12.
6

Y. Koga et al.

Nuclear Engineering and Design xxx (xxxx) xxx

containment of the Al2O3 layer. The peak temperature increased when
the Zr loading rate decreased from 100% because the tritium absorption
rate of Zr was proportional to the Zr loading rate.
Overall, the leaked tritium from the Li rods mainly decreased withthe temperature increase of Li rods caused by the nuclear reaction heat.
It is expected that the change in tritium leakage from the Li rods for the
HTTR caused by the nuclear reaction heat is almost consistent with
Fig. 12 since the influence of the temperature difference between the
Al2O3 layer and Zr shown in Fig. 8 is small. The case of the GTHTR300
has similar results. The leaked tritium from the Li rods for the HTTR
decreases at over 900 K by the nuclear reaction heat when the Zr loading
rate is 100%.

& editing. Shimpei Hamamoto: Validation, Writing – review & editing.
Etsuo Ishitsuka: Validation, Writing – review & editing. Shigeaki
Nakagawa: Validation, Writing – review & editing. Kenji Tobita:
Validation, Writing – review & editing. Satoshi Konishi: Validation,
Writing – review & editing. Ryoji Hiwatari: Validation, Writing – re­view & editing. Youji Someya: Validation, Writing – review & editing.
Yoshiteru Sakamoto: Validation, Writing – review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.

4. Concluding remarks

Acknowledgments

We evaluated the effect of the nuclear reaction heat from the 6Li(n,α)
T reaction on the tritium containment performance of Li rods via
simulation. The temperature of the Li rods for the HTTR (GTHTR300)
increased by 36 K (46 K) in the hollow portions and Zr pebble regions via
the nuclear reaction heat of the 6Li(n,α)T reaction, and the amount of
leaked tritium decreased by 31.8% (37.1%) for the temperature in­crease. This is because the tritium absorption performance of the Zr
improved more than the deteriorated tritium containment performanceof the Al2O3 layer. Considering the effect of the moderator temperature,
the nuclear reaction heat would decrease the tritium leakage under only
high-temperature operation in the HTGR (e.g., over 900 K for theHTTR). If the He coolant was circulated in the region where the Li rods
were loaded, the tritium leakage could decrease even further due to thecooling in the Al2O3 layer.
Currently, hydrogen absorption experiments using Ni-coated Zr have
yet to be completed to measure the hydrogen absorption performance.
These experiments must be completed to verify this study. We expectthat tritium can be rapidly absorbed by Ni-coated Zr at hightemperatures.
Only the 6Li(n,α)T reaction was considered here, but other nuclear
reactions in Li rods can occur by neutron irradiation. For example, 28Al
atoms are produced by neutron reactions in the Al2O3 layer and havestrong radioactivity for their short half time, which may change thetemperature distribution. Therefore, other reactions must be consideredto evaluate their tritium containment performance. In addition, an
experiment using an Li rod test unit with a heater should be conducted toconfirm the effects of reaction heat on the tritium containment
performance.
The temperature distribution and tritium containment performancefor the Li rods can be influenced by the interaction of each layer ofmaterials with the neutron flux and irradiation damage. It was reported
that hydrogen diffusion was retarded for tungsten because of the trap­
ping effect caused by radiation defects (Hatano et al., 2013). However, it
was also reported that hydrogen diffusion was enhanced by irradiation
for Al2O3 (Macaulay-Newcombe and Thompson, 1998). Regarding
thermal conductivity, more defects and vacancies were observed in
LiAlO2 by neutron irradiation (Devaraj, 2021) so that thermal conduc­tivity may decrease. The influence of irradiation has not been well un­derstood at present. However, due to the short operation period for thetritium production (360 days) and low neutron flux in the HTGR, serious
problems may not occur via irradiation. We should conduct an irradia­
tion test in the HTTR to check the influence of neutron irradiation.

This work was supported by JSPS (Japan Society for the Promotionof Science) KAKENHI Grant-in-Aid for Scientific Research (B)JP18H01200 and JP21H01065, and cooperative program with BA (The
Joint Implementation of the Broader Approach Activities in the Field ofFusion Energy Research) reactor design team in Japan.
References
R. Hiwatari, Research frontier of tritium for fusion reactor -toward the Demo reactor- (2);Basic concept of tritium fuel balance required for DEMO, J Atomic Energy Society
Japan [in Japanese] 60 (8) (2018) 52.
Asaoka, Y., Okano, K., Yoshida, T., Tomabechi, K., 1996. Requirements of Tritium
Breeding Ratio for Early Fusion Power Reactors. Fusion Tech. 30 (3P2A), 853–863.
Gierszewski, P., 1989. Tritium supply for near-term fusion devices. Fusion Eng. Des. 10,
399–403.
Matsuura, H., Kouchi, S., Nakaya, H., Yasumoto, T., Nakao, Y., Shimakawa, S., Goto, M.,
Nakagawa, S., Nishikawa, M., 2012. Performance of high-temperature gas-cooled
reactor as a tritium production device for fusion reactors. Nucl. Eng. Des. 243,
95–101.
Matsuura, H., Okamoto, R., Koga, Y., Suganuma, T., Katayama, K., Otsuka, T., Goto, M.,
Nakagawa, S., Ishitsuka, E., Tobita, K., 2019. Li-rod structure in high-temperature
gas-cooled reactor as a tritium production device for fusion reactors. Fusion Eng.
Des. 146, 1077–1081.
Nakaya, H., Matsuura, H., Katayama, K., Goto, M., Nakagawa, S., 2015. Study on amethod for loading a Li compound to produce tritium using high-temperature gascooled reactor. Nucl. Eng. Des. 292, 277–282.
T. Nakata, et al., Nuclear Design of the Gas Turbine High Temperature Reactor(GTHTR300), JAERI-Tech (2002) 2002-066.
Katayama, K., Ushida, H., Matsuura, H., Fukada, S., Goto, M., Nakagawa, S., 2015.
Evaluation of Tritium Confinement Performance of Alumina and Zirconium for
Tritium Production in a High-Temperature Gas-Cooled Reactor for Fusion Reactors.
Fusion Sci. Tech. 68 (3), 662–668.
S. Saito, et al., Design of High Temperature Engineering Test Reactor, JAERI-1332(1994).
Koga, Y., Matsuura, H., Ida, Y., Okamoto, R., Katayama, K., Otsuka, T., Goto, M.,
Nakagawa, S., Nagasumi, S., Ishitsuka, E., Shimazaki, Y., 2018. Study on lithium rod
test module and irradiation method for tritium production using high temperature
gas-cooled reactor. Fusion Eng. Des. 136, 587–591.
Izumino, J., Katayama, K., Matsuura, H., Fukada, S., 2018. Study on hydrogen absorptionin Zr powder used for tritium confinement in a production system of tritium forfusion reactors with a high-temperature gas-cooled reactor. Nucl. Mat. Energy 17,
289–294.
Matsuura, H., et al., 2021. The T-containment properties of a Zr-containing Li rod in ahigh-temperature gas-cooled reactor as a T production device for fusion reactors.
Fusion Eng. Des. 169, 112441.
Katayama, K., Izumino, J., Matsuura, H., Fukada, S., 2018. Evaluation of hydrogen
permeation rate through zirconium pipe. Nucl. Mat. Energy. 16, 12–18.
Nagasumi, S., et al., 2017. Study on Tritium Production Using a High-Temperature GasCooled Reactor for Fusion Reactors: Evaluation of Tritium Outflow by NonEquilibrium Diffusion Simulations Fusion Sci. Tech. 72, 753–759.
Y. Someya, et al., Development of water-cooled blanket concept with pressure tightness
against in-box LOCA for JA DEMO, Fusion Eng. Des. 146 (2019) 894-897.
Maruyama, So, Fujimoto, Nozomu, Sudo, Yukio, Murakami, Tomoyuki, Fujii, Sadao,
1994. Evaluation of core thermal and hydraulic characteristics of HTTR. Nucl. Eng.
Des. 152 (1-3), 183–196.
KAWAMURA, Yoshinori, NISHIKAWA, Masabumi, TANAKA, Kenichi,
MATSUMOTO, Hiroyuki, 1992. Adsorption Characteristics of Water Vapor on
Gamma-Lithium Aluminate. Journal of Nucl. Sci Tech. 29 (5), 436–444.
Y. Nagaya, et al., MVP/GMVP Version 3: General Purpose Monte Carlo Codes for Neutronand Photon Transport Calculations Based on Continuous Energy and Multigroup
Methods, JAEA-Data/Code (2017) 2016-018.
OKUMURA, Keisuke, MORI, Takamasa, NAKAGAWA, Masayuki, KANEKO, Kunio, 2000.
Validation of a Continuous-Energy Monte Carlo Burn-up Code MVP-BURN and Its

CRediT authorship contribution statement
Yuki Koga: Conceptualization, Methodology, Software, Writing –original draft, Writing – review & editing. Hideaki Matsuura:
Conceptualization, Supervision, Project administration, Funding acqui­sition, Validation, Writing – review & editing. Kazunari Katayama:
Validation, Writing – review & editing. Teppei Otsuka: Validation,
Writing – review & editing. Minoru Goto: Validation, Writing – review
7

Y. Koga et al.

Nuclear Engineering and Design xxx (xxxx) xxx

Application to Analysis of Post Irradiation Experiment. J. Nucl. Sci. Tech. 37 (2),
128–138.
Shibata, K., et al., 2011. JENDL-4.0: A New Library for Nuclear Science and Engineering.
J Nucl. Sci. Tech. 48 (1), 1–30.
Schulz, B., Wedemeyer, H., 1986. PREPRARATION, CHARACTERIZATION AND
THERMAL DIFFUSIVITY OF γ-LiALO2. J. Nucl. Mat. 139, 35–41.
Fink, J.K., Leibowitz, L., 1995. Thermal conductivity of Zirconium. J. Nucl. Mat. 226 (12), 44–50.
P. Auerkari: VTT Manufacturing Technology, VTT Tiedotteita – Meddelanden – Research
Notes 1792, Espoo, (1996), 14.
Faubert, Francis M., Springer, George S., 1973. Measurement of the thermal conductivityof helium up to 2100◦ K by the column method. J. Chem. Phys. 58 (10), 4080–4083.
Powell, R.W., Tye, R.P., Hickman, M.J., 1965. THE THERMAL CONDUCTIVITY OF
NICKEL. Int. J. Heat Mass Transfer 8 (5), 679–688.
T. Otsuka, et al., T-containment performance of Li rod in high-temperature gas-cooled
reactor for T production: (1) Hydrogen absorption properties of Ni coated Zircaliy-4
co-existing with Li oxide, Annual Meeting 2020 of AESJ (in Japanese).

Kleykamp, Heiko, 1999. Enthalpy and heat capacity of LiAlO2 between 298 and 1700 K
by drop calorimetry. J. Nucl. Mat. 270 (3), 372–375.
Chase M. W. Jr., NIST-JANAF Themochemical Tables, Fourth Edition, J. Phys. Chem.
Ref. Data, Monograph 9 (1998) 1-1951.
Goto, M., et al., 2018. Nuclear and thermal feasibility of lithium-loaded high temperature
gas-cooled reactor for tritium production for fusion reactors. Fusion Eng. Des. 136,
357–361.
Hatano, Y., Shimada, M., Alimov, V.Kh., Shi, J., Hara, M., Nozaki, T., Oya, Y.,
Kobayashi, M., Okuno, K., Oda, T., Cao, G., Yoshida, N., Futagami, N., Sugiyama, K.,
Roth, J., Tyburska-Püschel, B., Dorner, J., Takagi, I., Hatakeyama, M., Kurishita, H.,
Sokolov, M.A., 2013. Trapping of hydrogen isotopes in radiation defects formed intungsten by neutron and ion irradiations. J. Nucl. Mater. 438, S114–S119.
Macaulay-Newcombe, R.G, Thompson, D.A, 1998. Ion beam analysis of deuteriumimplanted Al2O3 and tungsten. J. Nucl. Mater. 258-263, 1109–1113.
Devaraj, A., et al., 2021. Neutron irradiation induced changes in isotopic abundance of6
Li and 3D nanoscale distribution of tritium in LiAlO2 pellets analyzed by atom probe
tomography. Mater. Charact. 176, 111095.

8