Nuclear heating calculation for the high flux test module in IFMIF
Daisuke Kaku, Tao Ye, and Yukinobu Watanabe
Department of Advanced Energy Engineering Science, Kyushu University,
Kasuga, Fukuoka 816-8580, Japan
Corresponding email: watanabe@aees.kyushu-u.ac.jp

The PHITS code is applied to neutronics calculations for the high flux test module in IFMIF. The
calculated neutron energy spectrum and heating rate show reasonably good agreement with the previous
result of the conceptual nuclear design. These physical quantities are calculated using different high-energy
nuclear data libraries (LA150, NRG-2003, and JENDL/HE-2004), and the similarities and differences are
discussed. The validity of the KERMA approximation and the sensitivity of the Li(d,xn) neutron source
term to heat production calculation are examined.
1. Introduction
The International Fusion Materials Irradiation Facility (IFMIF) 1) is composed of an accelerator-driven
deuteron-lithium neutron source for irradiation tests of fusion reactor candidate materials. Neutrons up to
about 55 MeV will be produced by two 125 mA beams of 40 MeV deuterons bombarding a thick target offlowing liquid lithium. So far, conceptual nuclear designs of the IFMIF have been performed mainly usinga code McDelicious developed in Forschungszentrum Karlsruhe (FZK)2,3). In detailed design of the IFMIF,
more accurate estimation will be required on behaviors of fast neutrons with energies up to 55 MeV inmaterials. Several high-energy particle transport codes such as MCNPX4) and PHITS5) are widely used forvarious accelerator applications in combination with the latest high energy nuclear data libraries. Therefore,
it is worthwhile to test to what extent these codes and high energy nuclear data libraries are applicable to
IFMIF neutronics calculations.
The PHITS code5) is chosen for calculations of nuclear heating in the high flux test module (HFTM) in
the IFMIF. The main purpose of this work is to examine the applicability of the PHITS code to IFMIF
neutronics calculations. Neutron energy spectrum and nuclear heating over the HFTM are calculated andcompared to FZK results. Furthermore, the sensitivity of three nuclear data libraries (LA1506), NRG20037),
and JENDL/HE-20048)) to nuclear heating and the validity of KERMA approximation are discussed.
Influence of the d-Li reaction source term is investigated on nuclear heating using differential thick target
neutron yield data of the Li(d,n) reaction measured recently in Tohoku University9).
2. Calculation procedure
The high flux test module (HFTM) is placed downstream behind the flowing liquid lithium target,
forming the highest neutron radiation region. The HFTM consists of a steel container housing a numebr of
irradiation rigs that contain encapsulated irrradiation specimens.
The PHITS code is used for IFMIF-HFTM neutronics calculations. The details of the PHITS code aredescribed in ref. 5).
In the present calculation, a simplified HFTM configuration is adopted as in the previous FZK work2).
The geometrical configuration is depicted in Fig.1. The HFTM part is composed of a rectangular block 20 x
5 x 5 cm3 filled with Eurofer with a mass denisty of 6.24 g/cm3, which is 80% of the normal density to takeaccount of the space occupied by colling gas.
Each of two deuteron beams impinges on the lithum target with 10º declination angle in verticaldirection. Fig.1 illustrates the lithium target (26 x 2.5 x 20 cm3) filled with lithium at 0.512 g/cm3 and its
back plate (26 x 0.18 x 20 cm3) filled with Eurofer at 7.8 g/cm3 density. The PHITS code can calculate
neutron production from the Li(d,xn) reaction in the lithium target using the QMD model10) in priciple, but
a preliminary result does not show reasonable agreement with experimental results. Thus, the differential
thick target neutron yields (TTY) calculated by the McDelicious code2) are used as the source term in thepresent work. The source term is assumed to be a surface source placed at a distance correspoding to therange of deuteron in lithium, although it is a volume source in practice. The tilt angles of ±10º of incident
deuteron beam are taken into account so that the direction of neutron emission at 0º coincides with that of2006 Symposium on Nuclear Data

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the incident deuteron beam. It should be noted that scattering of neutrons from lithum layer between thesurface neutron source and the back plate is neglected because the calculated TTY data are used as theneutron source term.

Fig.1 Geometrical configuration of the lithium target and HFTM

3. Results
3.1 Applicability test of the PHITS code to IFMIF neutronics calculation
Energy distribution of the average neutron flux in the HFTM calculated by the PHITS code is comparedwith the FZK result obtained by the McDelicious code2) in Fig.2. The former reproduces the latter well,although there is a slight difference in the energy range between 10 and 25 MeV. The difference might bedue to that in the neutron source term, because the surface neutron source is assumed in the present work as
mentioned in sect. 2. Table 1 shows comparisons of the average neutron and gamma fluxes, the average dpa
rate, the total heat production, and the average heat production density. The present calculation shows
agreement with the FZK result within about 10 %. Thus, this benchmark test indicates that the PHITS code
is applicable to neutronics calculations for thermal-hydraulic design of the HFTM.

3.2 Analysis of nuclear heating in the HTFM
The spatial distribution of nuclear heating rate in the HFTM is calculated for the case where each of two
deuteron beams (2 x 125mA) impinges on the lithium target with 10º declination angle in horizontal
direction. It should be noted that the beam incidence with horizontal declination is adopted in the latest
IFMIF design3). In fig.3, the result is presented as a three-dimensional plot sliced in half at x=0. The size ofeach boxel (i.e., an elementary cubic segment) is 0.5 x 0.5 x 0.5 cm3. The highest heating rate of 27 W/cm3
is obtained in the vicinity of the surface region. The spatial distribution is also plotted along the depth into
HFTM (i.e., z-axis) in Fig.4. It is found that the total heating rate is attenuated linearly with the depth andthe dependence of neutron and gamma heating upon the depth is different.
Nuclear heating for other fusion reactor candidate materials (F82H, V4Ti4Cr, SUS304, and SiC) is also
calculated in the same way using the PHITS code. For the sake of simplicity, the geometrical model usedconsists of a rectangular block 20 x 5 x 5 cm3 filled with each material with the same mass density as thenormal density, in order to see rough estimation of the dependence of nuclear heat production on materials.
The result is shown in Table 2. The neutron and photo heat and their sum are almost same among threeiron-based materials (Eurofer, F82H, and SUS304), while the total heat production for SiC, is much smaller
than the other materials because the amount of photon heat released in the HFTM is considerably small.

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14

13

10

2

Flux (n/cm /MeV/s)

10

12

10

11

FZK result
PHITS calculation

10

10

10

0

10

20

30

40

50

Neutron Energy (MeV)

Fig.2. Comparison of neutron energy spectra in the HFTM between the present PHITS calculation andthe FZK result2)

Fig.3. Three-dimensional spatial distribution of nuclear heating rate calculated by assuming deuteron beamincidence with horizontal declination600

total heatneutron heat
photon heat

550
500

Heat(W)

450
400
350
300
250
200
150
100
0

1

2

3

4

5

z-axis [Depth Direction] (cm)Fig.4.

Spatial distribution of the heating rate produced in the HFTM along z-axis

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Table 1. Physical parameters of the HFTM and results of neutronics calculations. The result of the FZK
work is take from ref.2) for comparison.
Parameter
Size
VolumeMaterial
Material Density
Average Neutron Flux
Average Neutron Energy
Average Gamma-ray Flux
Average dpa rate
Total Heat Production
Average Heat Production Density

Table 2.

FZK work

Present work
20 x 5 x 0.18 cm3500 cm3
Eurofer (Fe-88.9%, Cr-9.6%,C-4.9%, ....)
6.24 g/cm3
142
5.86 x 10 n/cm /s
6.40 x 1014 n/cm2/s
7 MeV
7 MeV
14
2
2.63 x 1014 γ/cm2/s
2.33 x 10 γ/cm /s
29 dpa/fpy
31 dpa/fpy
7.0 kW
7.5 kW
14 W/cm3
15 W/cm3

Total heat production in the HFTM for different materials

material

Eurofer

F82H

V4Ti4Cr

SUS304SiC

Total heating (kW)
Neutron (kW)

9.94
4.05

9.50
3.93

9.70
6.33

10.70
4.70

6.10
5.48

Photon (kW)

5.89

5.57

3.37

6.00

0.62

4. Discussion
4.1 Sensitivity of nuclear data library to calculation of nuclear heating and neutron flux
The neutronics calculations were performed using the PHITS code with three nuclear data libraries(LA1506), NRG20037), and JENDL/HE-20048)) in order to see how nuclear data libraries influencecalculations of neutron flux and nuclear heating. As presented in Fig.5 and Table 3, the neutron fluxes arealmost identical among three calculations, while the total heating rates are largely different (up to 50%).
Table 3 indicates that the difference in the total heating rates is due to that in the heat generated by neutrons.
This can be easily explained from the fact that the heating numbers of 56Fe (i.e., kerma factors) included in
the libraries are obviously different, particularly in the high energy range above 20 MeV, as seen in Fig.6.
2

LA150
JENDL/HE-2004
NRG2003

13

2

Flux (n/cm /MeV/s)

10

14

10

10

12

11

Heating number (MeV/collision)

10

10

56

1

10

Fe
LA150
JENDL/HE-2004
NRG2003

0

10

-1

10

-2

10

-3

10

-4

10

50MeV

-5

10

-6

0

10

20

30

40

50

Neutron Energy (MeV)

Fig.5. Comparison of the calculated neutron fluxes
in the HFTM.

2006 Symposium on Nuclear Data

10

-4

10

-3

10

-2

10

-1

10

0

1

10

10

2

10

Neutron Energy (MeV)

Fig.6. Total heating number of 56Fe

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Table 3. Comparison of calculated heating rates among three nuclear data libraries (LA150,
JENDL/HE-2004, and NRG-2003)
Nuclear data library
Total heating rate (kW)
Neutron heating rate (kW)Photo heating rate (kW)
Ratio to LA150

LA150
7.6
3.4
4.2
1

JENDL/HE-2004
11.2
6.7
4.5
1.47

NRG-2003
8.4
4.4
4.0
1.1

4.2. Validity of KERMA approximation
As neutron energy increases, production of light ions, such as protons and deuterons with relatively
high kinetic energy, becomes prominent. With an increase in the kinetic energy, the range becomes long,e.g., the range of 50 MeV protons is 5.3 mm in Eurofer with the mass density 6.24 g/cm3. Therefore, it isexpected that the KERMA approximation assuming local energy deposition becomes worse. The PHITS
code has a feature to deal with transport of light ions in matter using the continuous slowing down
approximation. This means that the spatial spreading of the energy deposited by light ions can be taken into
account beyond the KERMA approximation in the present calculation. It should be noted that the KERMA
approximation is adopted for heavy recoils because the range is quite short. In the preceding work in FZK2),
the KERMA approximation was used in calculations of heat production. Therefore, it is of interest to
examine quantitatively the validity of the KERMA approximation in the HFTM design.
The calculation condition is same as mentioned in sect. 2, except that neutrons enter in the direction
perpendicular to the surface xy-plane of the HFTM. The PHITS calculation is implemented under the full
KERMA approximation with the total heating numbers included in the nuclear data library, which is called
the PHITS-KERMA calculation hereafter, and compared with the normal PHITS calculation mentioned insect. 3. First, the total heat production is calculated by varying the depth along the neutron incident
direction. The result is shown in Fig.7. Both the results are in good agreement for thickness over 1 mm. The
KERMA approximation tends to overestimate because the light ions generated by neutron-induced
reactions are likely to escape from the HFTM volume. Next, the neutron energy dependence is examined.
In the calculation, mono-energetic neutrons impinge on the HFTM with different thicknesses of 1, 5, and
10 mm, respectively. Fig.8 presents the ratios of the total heat production calculated under the full KERMA
approximation to the normal PHITS calculation. The ratios increase with increasing neutron energy andreducing thickness, and thus the KERMA approximation becomes worse and worse. Since the maximum
energy of the source neutron in the IFMIF is about 55 MeV and the thickness of the HFTM is 25mm,
however, the KERMA approximation is found to be valid in the heat production calculation in the HFTM.
Finally, the spatial distributions of total heat production are compared between the two cases in Fig. 9. It isfound that the difference appears slightly in the vicinity of the surface because most of generated light ionsare expected to escape from the front surface.

Heat (MeV/source)-1

10

PHITS-KERMA
PHITS

-2

10

-3

10

-4

10

0.01

0.1

1

10

Thickness(mm)Fig. 7. Comparison of the total heat production between the full KERAM approximation and the normal
PHITS calculation

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3.0
2.8

Ratio of KERMA to PHITS

2.6

Target Thickness
10mm
5mm
1mm

2.4

ratio

2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8

20

40

60

80

100

120

140

160

Neutron Energy(MeV)

1.25x10-3

1.20x10-3

1.15x10-3

1.10x10-3

1.05x10-3

1.00x10-39.50x10-49.00x10-4

3

Heat(MeV/cm /source)

Fig.8. Ratio of the total heat production calculated under the full KERMA approximation to the normal
PHITS calculationz mesh: 1mm
PHITS-KERMA
PHITS

0.0

0.5

1.0

1.5

2.0

z-axis(depth directioin), cm

Fig. 9.

Spatial distribution of total heat production

4.3. Sensitivity of the d-Li neutron source
The McDelicious neutron spectra used as input in the PHITS calculations mentioned early are comparedwith the recent experimental data of differential thick target neutron yields measured by Baba andco-workers9) in Fig.10. It is shown that the McDelicious calculation overestimates the production ofneutrons with energies below 5 MeV at 0º and the spectral shape is different from the observation at thehigh-energy end. Consequently, it is of interest to see how this difference affects the calculated neutron flux
and heat production rate in the HFTM. In Fig.11, the PHITS result using the experimental data as theneutron source term is compared with that using the McDelicious neutron spectra. There is no appreciable
difference between the two calculations. However, it will be necessary to improve the overestimation seenin Fig.10 by re-evaluating the cross section data for the d + 7Li reaction.

5. Summary
The PHITS code was first applied to neutronics calculations for the high flux test module (HFTM) in
the IFMIF neutron source facility. The calculated neutron energy spectrum and nuclear heating were ingood agreement within 10% with the previous result by the FZK group. This indicates the applicability of
the PHITS code to neutronics calculations for the HFTM. The calculation using different nuclear datalibraries, LA150, NRG-2003, and JENDL/HE-2004, showed that the neutron fluxes are almost identical,
while the heating rates have a large discrepancy, reflecting the difference in the heating numbers includedin these libraries. In addition, it was confirmed that the KERMA approximation is reasonably good in
calculating the heating rates in the HFTM unless one discusses the heat generated within the small size less2006 Symposium on Nuclear Data

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than 1 mm. Finally, the sensitivity of the Li(d,xn) neutron source term to nuclear heating in HFTM was
examined, because there are some discrepancies between the McDelicious neutron spectra used in this workand the recent experimental data of differential thick target neutron yields. The heating calculation with theexperimental data showed no remarkable difference from that with the McDelicious neutron spectra.
The PHITS code employs the quantum molecular dynamics (QMD) model10) to describe nuclear
reactions that may take place in heavy-ion transport processes in matter. Its application to deuterontransport calculation is not necessarily successful. In addition, there are some discrepancies between the
McDelicious calculation and experimental data as mentioned in sect. 4. Thus, we plan to study
deuteron-induced reactions with particular focus on neutron production, aiming at further upgrading of
IFMIF neutronics calculations.
Finally, our IFMIF-HTFM neutronics calculation will be linked with thermal-hydraulic design that isbeing performed by the Kyushu University group11,12) in the future.

-1

(a)

-1

10

Flux (1/sr/MeV/μC/source)

Flux (1/sr/MeV/μC/source)

10

-2

10

-3

10

0 degreenormalized neutron spectraC
M Delicious
Tohoku Univ.

-4

10

(b)

-2

10

20 degree
normalized neutron spectraC
M Delicious
Tohoku Univ.

-3

10

-4

0

10

20

30

40

10

50

0

10

Neutron Energy (MeV)

20

30

40

50

Neutron Energy (MeV)

Fig. 10. Comparisons of calculated and measured thick target neutron yields from lithium at the deuteronincident energy of 40 MeV. The emission angles are 0 degree (a) and 20 degree (b), respectively. The
experimental data are taken from ref.9)

10

15

10

14

10

13

10

12

10

11

Heat(kW)

2

Flux(1/cm /MeV/s)c

M Delicious Tohoku
7.6
7.8

c

Use of M Delicious data
Use of Tohoku U. data
0

10

20

30

40

50

Neutron Energy(MeV)

Fig.11. Comparison of average neutron fluxes and total heat production between the PHITS calculation
with the McDelicious neutron source term2) and that with the experimental data9)2006 Symposium on Nuclear Data

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Acknowledgements
The authors wish to thank K. Niita for his helpful instruction for use of the PHITS code. They
acknowledge K. Kosako for his useful discussion on the heating numbers included in nuclear datalibraries. They are also grateful to A. Shimizu, T. Yokomine, and S. Ebara for their cooperation andencouragement.
References[1] H. Matsui, “Present status and future prospects of the IFMIF project”, in Proceedings of the 23rd
Symposium on Fusion Technology, Sept. 20-24, 2004, Venice, Italy.
[2] S.P. Simakov, et al., “IFMIF neutron source term simulation and neutronics analysis of the high flux
test module”, Report FZKA 6743, Karlsruhe (2002).
[3] U. Fischer, et al., Fusion Eng. Des. 81, 1195-1202 (2006).
[4] L.S. Waters(Ed.), MCNPX Uers's Manual, Version 2.3.0, LA-UR-02-2607 (2002).
[5] H. Iwasa, K. Niita, and T. Nakamura , J. Nucl. Sci. and Technol., 39, 1142-1151 (2002).
[6] M.B.Chadwick, et al., Los Alamos National Laboratory report LA-UR-99-1222 (1999).
[7] A. J. Koning, et al., in Proceedings of the International Conference on Nuclear Data for Science andTechnology, Santa Fe, USA, September 26-October 1, pp.422-425 (2004).
[8] Y. Watanabe, et al., in Proceedings of the International Conference on Nuclear Data for Science andTechnology, Santa Fe, USA, September 26-October 1, pp. 326-331 (2004).
[9] M. Hagiwara et al., J. Fusion Sci. & Technol., 48, 1320 (2005).
[10] K. Niita, et al., Phys. Rev. C 52, 2620 (1995).
[11] S. Ebara, S. Nagata, H. Irisa, T. Yokomine, and A. Shimizu, Fusion Eng. Des. 81, 887-891 (2006).
[12] S. Ebara, T. Yokomine, and A. Shimizu, Fusion Eng. Des. 82, 61-72 (2007).

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