AESJ-KNS Joint Workshop on Reactor Physics and Nuclear Data
Kinki University, Osaka, Japan, March 25, 201312:30 - 13:00

Registration at multi-purpose room, 2nd floor, Building No. 38,

Kinki University, Higashi-Osaka Campus
13:00 - 13:05

Opening Speech,
Kenji Ishibashi (Chairperson, Nuclear Data Division of AESJ)

Session I:

Session chair, Tokio Fukahori (Japan Atomic Energy Agency)

13:05 - 13:30

Y. Iwamoto (Japan Atomic Energy Agency),
Radiation Damage Calculation in PHITS for Materials Irradiated with
Neutrons, Protons and Deuterons over a Wide Energy Range

13:30 - 13:55

Chang Je Park (Korea Atomic Energy Research Institute),
A Study on the Photoneutron Effect for a Small Research Reactor

13:55 - 14:20

A. Kimura (Japan Atomic Energy Agency),
Neutron Capture Cross Section Measurements for Radio Isotopes using the
ANNRI in J-PARC/MLF

14:20 - 14:30

Coffee break

Session II:

Session chair, Deokjung Lee (UNIST)

14:30 - 14:55

Han Gyu Joo (Seoul National University),
Investigation of Intra-pellet Power Profile Effects on Whole Core Transport
Calculation for Power Reactors

14:55 - 15:20

Yuichiro Ban (Toshiba Corporation),
The Small Reactivity Worth Measurement in Critical Experiments- Uncertainty estimation for reactivity fluctuation -15:20 - 15:45

Myung-Hyun Kim (Kyung Hee University),
A Neutronic Design of a Hybrid Reactor for Waste Transmutation

15:45 - 15:55

Coffee breakSession III:

Session chair, Tomohiro Endo (Nagoya University)

15:55 - 16:20

Nam Zin Cho (Korea Advanced Institute of Science and Technology),
Two Formulations of Continuous-Energy Monte Carlo Local Problem inOverlapping Local/Global Iteration Methodology

16:20 - 16:45

Masato Tabuchi (Nuclear Engineering Ltd.),
Efficient Calculation Scheme with Preservation of Transmission
Probabilities in the Method of Characteristics

16:45 - 17:10

Deokjung Lee (Ulsan National Institute of Science and Technology)
Hybrid Method of MOC and MC for Efficient Neutron Transport Analysis

17:10 - 17:15

Closing Speech,
Nam Zin Cho (Korea Advanced Institute of Science and Technology)

AESJ-KNS Joint Workshop on Reactor Physics and Nuclear Data, Kinki University, Osaka, Japan, March 25, 2013

Radiation Damage Calculation in PHITS for Materials Irradiated with Neutrons, Protons
and Deuterons over a Wide Energy Range
Y. Iwamoto a , H. Iwamoto a, M. Haradaa, K. Niita b, T. Sawai aJapan Atomic Energy Agency, 2-4, Shirakatashirane, Tokai, Naka, Ibaraki 319-1195, Japanb
Research Organization for Information Science and Technology, Tokai, Naka, Ibaraki 319-1196, Japan*
Corresponding author: iwamoto.yosuke@jaea.go.jpacalculations. These particles cause the cascade damage
in a material via Coulomb scattering with a target atom.
For incidence of charged particles, Coulomb scattering
between incident particles and the target atom also
causes the cascade damage. The conditions of various
irradiations will be described by using the damage
energy to characterize the displacement cascade. This isdefined as the initial energy of target PKA or secondary
particles created by nuclear reactions, corrected for theenergy lost to electronic excitations by all of theparticles composing the cascade. The point defects andtheir clusters affect the macroscopic material properties,
such as hardness.

1. Introduction
Currently, in the design phase, there are newmaterial irradiation facilities such as the ADS Target
Test Facility (TEF-T) [1] at J-PARC and theInternational Fusion Materials Irradiation Facility(IFMIF). To evaluate radiation damage for the
structural materials, historically, displacement per atom
(DPA) is used as the unit of displacement damage
intensity.
Recently, we have developed a calculation method of
the displacement cross-sections [2] in the energy range
from 10-10 MeV to 3 GeV, including event generator
and Coulomb scattering in the Particle and Heavy Ion
Transport code System (PHITS) [3]. For the design offacilities, the database of displacement cross-sections
has been required. Although the database for J-PARC
facilities was developed [4], there is no data for protons
below 20 MeV and for deuteron at all energies due to alack of Coulomb scattering model. Neutron data is not
sufficient to estimate the radiation damage of thestructural materials.
In this work, the authors developed the database ofdisplacement cross-sections in the energy range from
10-10 MeV to 3 GeV for neutron and from 100 keV to 3
GeV for proton and deuteron using the new PHITS. It
includes 14 elemental targets, many of which arecommon structural materials at accelerator and reactor
facilities, at listed below:
6C, 27Al, 14Si, 23V, 24Cr, 25Mn, 26Fe, 28Ni, 29Cu, 41Nb,
42Mo, 74W, 82Pb, 83Bi
The effect of the newly calculated cross-sections inassessing radiation damage at a TEF-T target vessel anda test irradiation in IFMIF materials is illustrated in thepresentation as well.

Fig. 1. Overview of radiation damage calculations in PHITS.

Displacement cross-section is calculated with
Coulomb scattering using the following equation [2]:tmax dVsc(1)
V
KN NRT dt

³

td

dt

where NNRT is the number of defects produced in
irradiated material. Vsc is a universal one-parameter
differential scattering cross-section equation in reduced
notation. K is the defect production efficiency (numberof survived defects to NRT predictions) [7] introduced
by C.H.M. Broeders et al. They have shown that the
NRT model overestimates the number of displacements.
The authors therefore made database of displacement
cross-sections in addition to defect production
efficiency for 26Fe, 29Cu and 74W listed in the paper [7].

2. Radiation Damage Calculation in PHITS
Figure 1 shows overview of radiation damage
calculation in PHITS. For all incident particles, Primary
Knock on Atoms (PKAs) and secondary particles are
created by the nuclear elastic scattering and nuclear
reactions. The conservation law on the energy and themomentum is sustained in each event using nuclear
reactions, INCL4.6 [5], for high energy particles withenergies above 10 MeV and the event generator mode
[6] for low energy neutrons below 10 MeV. Thesemodels can generate the energy distribution of thesecondary particles which affect the radiation damage

3. Calculated Displacement Cross-Sections
Figure 2 shows the displacement cross-sections forcopper irradiated with proton, neutron or deuteronversus incident energy in the energy range from 0.1
MeV to 3 GeV. The defect production efficiency, Ș,
was 1 for VNRT curves. For VBCA-MD, Ș was obtained
from the paper [7]. For protons and deuterons atenergies above 20 MeV, the secondary particles createdby nuclear reaction are more dominant than PKAs

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AESJ-KNS Joint Workshop on Reactor Physics and Nuclear Data, Kinki University, Osaka, Japan, March 25, 2013

produced by nuclear elastic scattering, and contributionof Coulomb scattering for the secondary particles
increases with energy. For the proton-induced crosssections below 20 MeV, the PHITS results are in good
agreement with the experimental data. In the all cases,
the difference between VBCA-MD and VNRT increases withenergies. For neutrons at 14 MeV, protons at 1.1 GeV
and 1.94 GeV, the agreement between VBCA-MD and theexperimental data is better than the agreement between
VNRT and data [2]. For deuterons, we found that
displacement cross-sections above 20 MeV, which ismainly produced by the secondary particle, give good
agreement with the data for proton and neutron within afactor of 1.5. Finally, VNRT for the 14 elemental targets
as listed in ‘1. Introduction’ and VBCA-MD for 26Fe, 29Cu
and 74W were obtained by using the radiation damage
calculation. The cross-sections were folded into
calculated particle fluxes in PHITS to estimate DPA
values.

occur before the stopping range is reached, andsecondary particles contribute to the overall DPA value
at target depths below the range.

Fig. 3. The depth dependence of DPA for SUS316 specimen
irradiated by 400 MeV proton and 40 MeV deuteron beams.

5. Conclusions
The displacement cross-sections for common
structural materials were calculated using the radiation
damage calculation method in PHITS. The
displacement cross-sections with the defect production
efficiency gave good agreement with experimental data.
For application to the DPA calculations at 400 MeV
proton and 40 MeV deuteron, calculated cross-sections
were folded into calculated particle fluxes in PHITS.
Thus the PHITS including the displacement crosssections can be useful to calculate the DPA values inmaterials used at accelerator facilities that will be
exposed to intense primary and secondary particle
irradiation. It will also be useful at fission and fusion
reactor facilities.

Thresholddisplacement energy= 30 eVFig. 2. The displacement cross-sections of copper as afunction of incident neutron, proton or deuteron energy. K=1
for solid lines and K=equation in ref. [7] for dashed lines. The
experimental data summarized in ref. [2] are also shown.

REFERENCES

4. Displacement Production due to Protons at TEFT and Deuterons at IFMIF[1] S. Saito, Pb-Bi Target Development at JAEA, The 10th
International Workshop on Asian Network for AcceleratorDriven System (ADS) and Nuclear Transmutation
Technology (NTT), 6th and 7th December, 2012, at KURRI,
Japan.
[2] Y. Iwamoto, K. Niita, T. Sawai et al., Improvement ofRadiation Damage Calculation in PHITS and Tests for
Copper and Tungsten Irradiated with Protons and Heavy-ionsover A Wide Energy Range, Nuclear Instruments andMethods In Physics Research B, Vol.274, p.57, 2012.
[3] K. Niita et al., PHITS: Particle and Heavy Ion Transport
Code System, Ver. 2.23, JAEA-Data/Code, 2010-022, 2010.
[4] M. Harada, N. Watanabe, C. Konno et al., DPA
Calculation for Japanese Spallation Neutron Source, Journalof Nuclear Materials, Vol.343, p.197, 2005.
[5] A. Boudard, J. Cugnon, J. –C. David, S. Leray, and D.
Mancusi, New Potentialities of the Li`ege Intranuclear
Cascade Model for Reactions Induced by Nucleons and Light
Charged Particles, Physical Review C, Vol.87, 014606, 2013.
[6] Y. Iwamoto, K. Niita, Y. Sakamoto et al., Validation of
the Event Generator Mode in The PHITS Code and Its

In this section, applications of the calculated
displacement cross-sections, VNRT, to the radiation
damage calculations at TEF-T and IFMIF are described.
At TEF-T, 400 MeV protons were irradiated with the
SUS316 specimen (compositions used in thecalculations given in atomic %: 67.4Fe-18.4Cr-11.5Si1.5Mo-1Mn-0.2C, size: 0.2 cm × 4 cm × 15 cm), which
was contained within the spallation target of leadbismuth eutectic (LBE). For deuteron-irradiation test,
40 MeV deuteron beam was employed and the SUS316
specimen was contained within air. Figure 3 shows thedepth dependence of the DPA value for 400 MeV-250
kW proton into SUS316+LBE with 4,500 hours
irradiation and 40 MeV-10 MW deuteron into SUS316
with 10 hours. The DPA value is related to the energy
deposition. The depth dependence of the DPA value
exhibits a so-called Bragg peak in the case of 40 MeV
deuteron beam. For 400 MeV protons, nuclear reactions-2-

AESJ-KNS Joint Workshop on Reactor Physics and Nuclear Data, Kinki University, Osaka, Japan, March 25, 2013

Application, International Conference on Nuclear Data for
Science and Technology 2007, DOI: 10.1051/ndata:07417.
[7] C.H.M. Broeders and A.Yu. Konobeyev, Defect
Production Efficiency in Metals under Neutron Irradiation,
Journal of Nuclear Materials, Vol.328, p. 197, 2004.

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AESJ-KNS Joint Workshop on Reactor Physics and Nuclear Data, Kinki University, Osaka, Japan, March 25, 2013

A Study on the Photoneutron Effect for a Small Research Reactor
Chang Je Park∗ and Byungchul Lee
Korea Atomic Energy Research Institute, 1045 Daedeok-daero, Yuseong-gu, Daejeon, 305-353, Korea*
Corresponding author: cjpark@kaeri.re.kr

by a square control plate. The thickness of control
absorber is 3 mm and the height is 650 mm. In thereference core, the Hf metal is chosen as the control
absorber and it provides enough reactivity worth toensure a safe shutdown of reactor.

1. Introduction
A small research reactor has been designed toprovide high neutron flux toward the beam tube for cold
neutron beam research based on the HOR reactor.[1]Total 9 square fuel assemblies are loaded. In order tomanage fuel assembly easily, a single square type offuel assembly is proposed in this design. Beryllium ischosen as the reflector, which provides a bettercharacteristics of neutron moderation. However, thephotoneutron effect of Be should be scrutinizedespecially for kinetics parameter and decay heat after
shutdown. In order to control the reactor safely, thekinetics parameter such as delayed neutron yield andthe neutron generation time are very important.[2] And
the decay heat and neutron source after shutdown play
an important role to manage the reactor and to restart
the reactor, too.[3] In this study, the photoneutron effectof Be reflector is analyzed with three different computercode systems. The equilibrium core is searched by the
McCARD code [4] and the depletion analysis of fuelassembly has been done with the ORIGEN-S code[5],from which the gamma intensities are used as thesource term to estimate photoneutron in the Be reflector
by using the MCNP5 code[6].
In Section 2, the core configuration of the small
research reactor is provided. And calculation model andresults are described in Section 3. Finally, Section 4
provides conclusions of this study.

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Figure 1. Core configuration of the small research
reactorTable I. Fuel Data for the Small Research Reactor
Item
Value
U3Si2-Al
Fuel Meat Material
UMo-Al4.8 : U3Si2
U density (g/cc)
8.0 : UMo
Meat thickness (mm)0.76
Meat width of standard FA(mm)63.2
Cladding thickness (mm)0.38
Moderator channel thickness (mm)2.46
Number of plates in standard FA
20
FA size (mm)81x81x600

2. Core Configuration of Small Research Reactor

3. Analysis Results of Photoneutron Effect

The small research reactor is simply designed toenhance the thermal neutron flux at the nose of thebeam tube for cold neutron beam research by shifting
fuel assemblies toward the beam tube as shown in Fig.
1. The core fission power is 3 MW and the reflector is
Be square block which size is 81 mm x 81 mm. The
core composed of 5 standard fuel assemblies and 4
control fuel assemblies. The fuel is a typical plate typeand both the standard fuel assembly and the control fuelassembly are all the same size in a square shape. The
composition of fuel meat is U3Si2-Al and its enrichmentof uranium is 19.75 wt% U-235, which is a typicalvalue in current research reactors. As an alternative,
UMo-Al fuel is also taken into consideration, which
provides more uranium density and longer fuel cycle.
The specification of the fuel assembly is given in Table
I. Due to a single type of fuel assembly, it is a great
advantage in fuel management for flexible coreconfiguration. The control fuel assembly is surrounded

In order to analyze photoneutron effect in Be
reflector, as a first step, a core depletion calculation iscarried out to find an equilibrium core by the McCARD
code. Two types of fuels are used with different fuelcycle lengths. In the case of U3Si2 fuel, 70 days per
cycle is given and the UMo fuel takes 150 days per
cycle. The estimated discharge burnups are about
44 %U-235 and 54 %U-235 for U3Si2 fuel and UMo
fuel, respectively, which are provided in Fig. 2. Fromthe burnup data, the gamma source term is obtained up
to 3 days from the ORIGEN-S calculation for 9
different assemblies. By using total gamma intensities
in the core after shutdown, the photoneutron in the Be
reflector is calculated with the MCNP5 code. The
ENDF7u library is used to consider photoneutron effect.
The obtained total gamma intensity of the fuel region
and the average photoneutron flux in reflector region
are tabulated in Table II. Photoneutrons in Be reflector-4-

AESJ-KNS Joint Workshop on Reactor Physics and Nuclear Data, Kinki University, Osaka, Japan, March 25, 2013of U3Si2 fuel loaded core varies from 5.4E+10 n/cm2s to
3.5E+8 n/cm2s as the time passes from 1 s to 3 days.
The photoneutron fluxes of UMo loaded core aresimilar to those of U3Si2 loaded core due to similar
gamma spectra. Decay heat of Be reflector after
shutdown is also estimated from the results of thephotoneutron flux calculation. The ORIGEN-S code isused with the flux irradiation option and Fig. 3 shows
the distribution of decay heat as a function of time after
shutdown. The decay heats in Be reflector region of two
different cores are similar and as the shutdown timeincreases, the decay heat decreases from about 3E-05
W/cc to 3E-07 W/cc.
The kinetic parameter is also estimated by the same
way as proposed in Ref.[2] The MCNP5 code is used
and it is assumed that the U3Si2 fuel is fresh with asingle fuel density. The gamma rays producing
photoneutrons are produced from prompt and delayed
fission gammas, prompt and delayed capture gammas.
Ignoring delayed gammas, the effective delayed neutron
fission fraction can be estimated by the coupledneutron-photon calculation in MCNP5 code using mpn
card for the reflector materials only. From thesimulation, the delayed fractions of photoneutron fromprompt fission gamma and prompt capture gamma isestimated 0.00028, 0.00024 for U3Si2 and UMo fuels,
respectively, which are similar results compared withthat of Ref.[2]. The corresponding ratios to the effective
delayed neutron fraction are about 3.8%, 3.4% for
U3Si2 and UMo fuels, respectively.
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REFERENCES[1] H. Gibcus, P.D. Leege, F. Labohm, J. D. Vries, A.
Verkooijen, J. Valko, W. Feltes, and J. Heinecke,“Options for the Delft Advanced Neutron Source”,
IGORR 2003 – the 9th Meeting of the International
Groups on Research Reactors, March 2003, Sydney,
Australia (2003).
[2] B. Dionne and N. Hana, “Impact of Photoneutrons on
Transients for the MURR and MITR HEU and LEU
Cores", RERTR 2010 – the 32nd International Meeting on
Reduced Enrichment for Research and Test Reactors,
October 2010, Lisbon, Portugal (2010).
[3] M.S. Onegin, "Delayed Photoneutrons in the PIK Reactor",
Atomic Energy, Vol. 107, No.3, 194, 2009.
[4] H.J. Shim and C.H. Kim, McCARD: Monte Carlo Codefor Advanced Reactor Design and Analysis, User's
Manual, Ver. 1.1, Seoul National University, 2011.
[5] I.C. Gauld, O.W. Hermann, R.M. Westfall, ORIGEN-S:
SCALE System Module to Calculate Depletion, Actinide
Transmutation, Fission Product Buildup and Decay, andAssociated Radiation Source Terms, ORNL/TM-2005/39,
Ver.6, Vol.II, Sect. F7 (2009).
[6] X-5 Monte Carlo Team, MCNP - A General Monte Carlo
N-Particle Transport Code, Version 5, LA-CP-03-0245,
Los Alamos National Laboratory (2003).
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&GEC[JGCVKPVJG$G 9EE&$major input for the safety analysis and for the restart
analysis after reactor shutdown.
As a further work, a detail study on the core design data
will be performed by analyzing the reactivity feedback
coefficient and neutron detector response.

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Figure 2. Burnup of the small research reactor at theequilibrium core (%U-235)

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4. Conclusions

Figure 3. Decay heat in the Be reflector after shutdown

In this study, the small research reactor is suggested
with two types of fuels, U3Si2 and UMo. From thedepletion calculation, the equilibrium core is searchedand some reactor parameters are obtained including thedischarge burnup. By use of burnup data of each
assembly, the photoneutron effect in Be reflector has
been investigated through two code systems, the
ORIGEN-S and the MCNP5 code systems. Among
several important parameters to be checked, it isobtained decay heat after shutdown and delayed neutron
fraction in this study. For two types of fuels, the similar
decay heats are estimated and the absolute level is low
as expected. The delayed neutron fraction due tophotoneutron is also obtained based on the previous
approaches and there is not so large difference from thereference. These photoneutron data will be utilize as an

Table II. Photoneutron Flux in Be Reflector andGamma Intensity in the Core Region
U3Si2

Time
after
shutdown

Avg. flux(n/cm2s)

1s
10 s

UMo

5.35E+10
3.85E+10

Gamma
intensity(photon/s)
9.41E+17
7.89E+17

5.07E+10
3.64E+10

Gamma
intensity(photon/s)
9.44E+17
7.93E+17

100 s1000 s1 hours
10 hours

2.29E+10
9.80E+09
5.21E+09
9.07E+08

5.81E+17
3.90E+17
2.80E+17
1.57E+17

2.02E+10
9.37E+09
5.02E+09
8.86E+08

5.86E+17
3.95E+17
2.86E+17
1.63E+17

2 days3 days

3.69E+08
3.52E+08

9.89E+16
8.47E+16

4.02E+08
3.67E+08

1.04E+17
8.90E+16*Relative error < 0.1-5-



Avg. flux(n/cm2s)AESJ-KNS Joint Workshop on Reactor Physics and Nuclear Data, Kinki University, Osaka, Japan, March 25, 2013

Neutron capture cross section measurements for radio isotopes
using the ANNRI in J-PARC/MLF
A. Kimuraa*, T. Fujiib, S. Fukutanib, M. Furusakac, K. Furutakaa, S. Gokoa,1, H. Haradaa, F. Hiragac, J. Hori a,
M. Igashirad, T. Kamiyamac, T. Katabuchid, T. Kina1, K. Kinoc, F. Kitatania, Y. Kiyanagic, M. Koizumia,
M. Mizumotod, S. Nakamuraa, K. Takamiyab, Y. Tohaa
Nuclear Science and Engineering Directorate, Japan Atomic Energy Agency, Tokai-mura, Naka-gun, Ibaraki,319-1195, Japanb
Research Reactor Institute, Kyoto University, 2-1010, Kumatori-cho, Sennan-gun, Osaka, 590-0494, Japanc
Graduate School of Engineering, Hokkaido University, Kita-ku, Sapporo, Hokkaido, 060-8628, Japand
Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo,152-8550, Japan
Present address: 1 Japan Nuclear Energy Safety Organization, 2 Kyusyu University*
Corresponding author: kimura.atsushi04@jaea.go.jp
The 244Cm sample for Ȗ-ray measurements contained
0.6 mg of curium oxide. Its isotopic enrichment was
90.1 mole%, and its main activity was 244Cm 1.8 GBq.
The 246Cm sample contained 2.1 mg of curium oxide.
Its isotopic enrichment was 59.4 mole% with a 27.5
mole% contamination of 244Cm, and its main activities
were 246Cm 12.1 MBq and 244Cm 1.7 GBq. To fulfill
the safety regulations at MLF, each sample was sealed
in an aluminum case 9 mm in outer diameter, weighing
280 mg, and having 0.5-mm-thick walls.
Each sample was put in a bag of fluorinated ethylene
propylene (FEP) films and attached to a sample holder.
Random timing pulses were fed into every pre-amplifier
from a random pulse generator in order to make a deadtime correction. The total measuring time was about 64
hours for the 244Cm sample and about 94 hours for the246
Cm sample. For the background estimation, Ȗ-ray
measurements with an empty aluminum case and an
empty FEP bag were also carried out for 48 hours and44 hours, respectively.

1
Introduction
Accurate data of neutron-capture cross sections areimportant in detailed engineering designs and safety
evaluations of innovative nuclear reactor systems [1-2].
Especially, neutron-capture cross sections of minor
actinides (MAs) and long-lived fission products(LLFPs) have attracted attention in the field of nuclear
systems such as transmutation of radioactive waste andvarious innovative reactor systems. However, accurate
measurements of these cross sections are very difficult
due to high radioactivity of these samples.
To overcome the difficulty, the Accurate NeutronNucleus Reaction measurement Instrument (ANNRI)
has been developed by the collaboration of Hokkaido
University, Tokyo Institute of Technology, and JAEA.
The ANNRI is located on the Beam Line No. 04 of thematerials and life science experimental facility (MLF)
in the Japan Proton Accelerator Research Complex (JPARC) [3]. A series of neutron capture cross-section
measurements have been started using the ANNRI [4].
The results for 244 and 246Cm and 237Np were reported inRefs. [5] and [6]. As an example of neutron-capture
cross-section measurements, a brief view of themeasurements for 244 and 246Cm will be presented.

3
Results and Discussion
Pulse-height spectra gated at the first resonance of244
Cm and 246Cm are shown in Fig. 1. The spectra wereobtained by subtracting off-resonance spectra from onresonance spectra. Eight and five Ȗ-ray emissions wereobserved in the 244Cm(n, J) and 246Cm(n, J) reactions,
respectively. In the spectrum for the 244Cm resonance,
the252- and 381-keV Ȗ-rays have already been studiedin other reactions. The other six Ȗ-rays were not known
until now. In the spectrum for the 246Cm resonance, all
the five prompt Ȗ-rays are previously unknown.
The dead time of the data acquisition system wascorrected using the random timing pulses. The
backgrounds due to scattered neutrons were estimatedusing the capture J-ray yields for the empty FEP bag
sample and the empty aluminum sample. Correction
factors for neutron self-shielding and multiple
scattering were calculated with the Monte Carlosimulation code MCNP. The neutron spectrum
determined by measuring 478-keV Ȗ-rays emitted in
10
B(n,ĮȖ) reactions. Relative cross sections were

2
Experimental Procedure
The measurements of prompt J rays emitted in theneutron-capture reactions have been performed with anarray of germanium (Ge) detectors in the ANNRI.
The array of Ge detectors is composed of twenty-two
Ge crystals and located on the flight length of 21.5 m as
described in Ref. [4]. The pulsed neutron beam wascollimated to a 7 mm diameter at the sample position.
The energy-integrated neutron intensities at the sample
position are 4.5×106 n/s/cm2 in the neutron energy
range of 1.5-25 meV at a beam power of 120 kW. In
the experiments, J-PARC was operated at a repetition
rate of 25 Hz, a power of 120 kW and in the "doublebunch mode", in which each proton pulse consists of
two bunches (each with a width of 100 ns) at intervalsof 600 ns.

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AESJ-KNS Joint Workshop on Reactor Physics and Nuclear Data, Kinki University, Osaka, Japan, March 25, 2013

deduced by using the TOF spectra, the deduced
backgrounds, these corrections and the neutron
spectrum. Contributions from chemical and isotopic
impurities were obtained and subtracted by broadening
the evaluated values of JENDL-4.0 with SAMMY[9]and by normalizing the broadened values to the relative
cross sections at the strongest resonances. The crosssections for 244Cm and 246Cm were derived bynormalizing the relative cross sections to the evaluatedvalues in JENDL-4.0 using the resonance area of thefirst resonance of 240Pu.

4Conclusions
The series of neutron capture cross-section
measurements have been started using the ANNRI. The
results gave accurate data for the neutron capture crosssections of 244Cm and 246Cm in the resonance region.
This achievement also shows the effectiveness of the
ANNRI for the measurement of neutron capture crosssections of highly radioactive samples.
The authors would like to thank the accelerator andtechnical staff at J-PARC for operation of theaccelerators and the neutron production target and forthe other experimental supports.
Present study includes the result of "Study on nuclear
data by using a high intensity pulsed neutron source foradvanced nuclear system" entrusted to Hokkaido
University by the Ministry of Education, Culture,
Sports, Science and Technology of Japan (MEXT).
This work is supported by JSPS KAKENHI(22226016 and 22760675).
REFERENCES[1] NEA/WPEC-26, Uncertainty and target accuracy

assessment for innovative systems using recent
covariance data evaluations, ISBN 978-92-64-99053-1,
2008.

Fig. 1 The pulse-height spectra gated at the firstresonance of 244Cm (a) and 246Cm (b). Asterisks (*)
indicate previously unknown J rays.

[2] G. Aliberti, G. Palmiotti, et. al., Nuclear data sensitivity,
uncertainty and target accuracy assessment for future nuclear
systems, Annals of Nuclear Energy, 33 (2006), pp. 700-733.
[3] M. Igashira, Y. Kiyanagi, et. al., Nuclear data study at JPARC BL04, Nucl. Instrum. Meth. Phys. Res. A, 600 (2009),
pp. 332-334.
[4] T. Kin, K. Furutaka, et. al., Development of a 4ʌGermanium Spectrometer for Nuclear Data Measurements at
J-PARC, the 2009 NSS-MIC Conf. Rec., Orland USA, Oct.
25-31, 2009 (2009), pp. 1194 -1197.
[5] A. Kimura, et al., Neutron-capture cross-sections of244
Cm and 246Cm measured with an array of large germanium
detectors in the ANNRI at J-PARC/MLF, J. Nucl. Sci.
Technol., 49 (2012), pp. 708-724.
[6] K. Hirose, et al., Cross-section measurement of 237Np (n,J) from 10 meV to 1 keV at Japan Proton Accelerator
Research Complex, J. Nucl. Sci. Technol., 50 (2013), pp. 188200.
[7] K. Kino, et. al, Measurement of energy spectra and spatial
distributions of neutron beams provided by the ANNRI
beamline for capture cross-section measurements at the JPARC/MLF, Nucl. Instrum. Methods. Phys. Res. A, 626(2011), pp. 58 -66.
[8] K. Shibata, et. al., JENDL-4.0: A New Library for Nuclear
Science and Engineering, J. Nucl. Sci. Technol. 48 (2011), pp.
1-30.
[9] N. M. Larson, Updated Users’ Guide for SAMMY:
Multilevel R-Matrix Fits to Neutron Data Using Bayes’
Equations, ORNL/TM-9179/R7, Oak Ridge National
Laboratory (2006).
[10] M. S. Moore , G. A. Keyworth, Analysis of the Fission
and Capture Cross Sections of the Curium Isotopes, PhysicalReview C, 3 (1971), pp. 1656 -1667.

The obtained neutron-capture cross sections for 244Cm
and 246Cm are shown in Fig. 2 together with thosemeasured by Moore[10] and with JENDL-4.0(broadened with SAMMY). The resonances of 244Cm ataround 7.7 and 16.8 eV and of 246Cm at around 4.3 and15.3 eV were observed in the capture reactions for the
first time. The uncertainties of the obtained crosssections are 5.8% at the energy of the first resonance of244
Cm and 6.6% at that of 246Cm.

Fig. 2 Deduced neutron capture cross sections of 244Cm(a) and 246Cm (b) and comparison to those measured by
Moore[10] and broadened JENDL-4.0[8].

-7-

AESJ-KNS Joint Workshop on Reactor Physics and Nuclear Data, Kinki University, Osaka, Japan, March 25, 2013

G

Investigation of Intra-pellet Power Profile Effects on Whole Core Transport Calculation forPower Reactors
Yeon Sang Jung and Han Gyu Joo*
Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744, Korea
joohan@snu.ac.kr

term on the right hand side. This was no problem for theflat power cases, but not for the nonuniform profile
cases. With this consideration, the heat conduction
equation was discretized in this work with the volumescheme which can preserve the heat generation rate ofeach mesh explicitly. On the other hand, thetemperature and burnup dependent thermal properties of
UO2 fuel pins, e.g., thermal conductivity and gap
conductance, should be assigned properly by using
measured data.Here the thermal conductivity correlation
taken from the data for the NRC’s FRAPCON 3.4
code[4] was used and the gap conductance data fortypical OPR1000 fuel pins obtained from the Koreanfuel vendor were used.

1. Introduction
The purpose of the whole core transport calculation
incorporating multi-physics phenomena which canoccur in a power reactor is to attain high fidelity in thecore behavior prediction. All the physical phenomena
occurring in a reactor should be adequately modeled insuch high fidelity realistic simulations. One of the real
phenomena that can be overlooked in the whole corecalculation is the nonuniform heat generation withineach pellet which results from the rim effect. It is
initially caused by the spatial resonance self-shielding
effect that would result in edge peaked fissile Plutonium
buildup production in burned pellets. In addition to theincreased peripheral absorption due to the resonanceself-shielding of U-238 in the region of lower
temperature, the nonuniform power profile effectshould be properly incorporated in the core calculation
for properly representing the Doppler effect. In aprevious work by Mastumoto et al. for the single pincell level calculation[1], it was confirmed that the rightprofile for the pellet leads to smaller power defects thanthe predicted values obtained with a flat profile. In thiswork, the effect of intra-pellet power profiles on thewhole core transport calculation is investigated for an
operating pressurized water reactor (PWR) with thedirect whole core transport code nTRACER[2].
2. Incorporation of Intra-pellet Power Profiles in
Whole Core Transport Calculations

Fig. 1. Intra-pellet Power and Temperature Profiles ofBurned Fuels

Because of the spatial self-shielding due to U-238
resonance absorption, more fissile plutonium isotopes
are built up at the periphery of a fuel pellet as the fueldepletes. This would lead to a higher heat generation
rate at the rim of burned fuels as illustrated in Fig. 1. As
a consequence, the interior fuel temperature is reduced
while the pellet surface temperature is not muchaffected. Recently, the effect of the temperature profileon the effective cross sections was examined[3], but theconsistent incorporation of power and temperature
profiles in actual core calculations was not considered.

2.2. Resonance Self-shielding Calculation with Nonuniform temperature profiles
The temperature profile obtained from the heat
conduction calculation is used in the subsequent
resonance self-shielding calculation to generate
effective multigroup cross sections. Here the selfshielded cross section for the resonance energy range isevaluated with the sub-group method for the direct
whole core transport calculation. The limitation of theconventional subgroup method requiring a uniform
temperature is mitigated by the temperature dependent
subgroup formulation of nTRACER[5] where thenumber density of resonance isotopes is adjusted suchthat the resulting macroscopic cross sections canrepresent the temperature dependency properly in the
nonuniform temperature profile cases.

2.1. Fuel Conduction Calculation with Intra-pellet
Power Profiles
In the fuel conduction calculation, the finite
difference method with the point scheme is adopted
widely. The point scheme, however, is not aconservation scheme meaning that it cannot guarantee
the conservation of the energy specified as the source-8-

AESJ-KNS Joint Workshop on Reactor Physics and Nuclear Data, Kinki University, Osaka, Japan, March 25, 2013

G
Fig. 3 shows the difference in the reactivity
decrement at a higher power level from the HFP
condition between the two calculations. Here larger
under-prediction is observed at higher burnup becauseof the increased rim effect with more plutonium buildup.
From these results, the Doppler power coefficients werealso calculated and are compared in Table 3 for thethree burnup levels. The reduction in Doppler power
coefficient observed at EOC1 is about 5% which is not
negligible. And it will be larger in the subsequent reload
cycles.

3. Effects of Intra-pellet Power Profiles
In order to investigate the effects of intra-pellet power
profiles, nTRACER was applied to the depletioncalculation of the initial core of Yonggwang Nuclear
Unit 3(YGN3C1) and to the Doppler power coefficient
calculations.
3.1. Effect on OPR1000 Depletion Calculations
As shown in Fig. 2 which provides the critical boron
concentration data obtained with and without theconsideration of intra-pellet power profiles as well as
the measured ones, essentially no difference is foundbetween the two calculation cases. It implies that the
impact of the intra-pellet power profile during thenormal power operation is marginal.

Table 1. Effect of Intra-Power Power Profile on
Doppler Power Coefficients of YGN3C1
Burnup,
MWD/TU

Doppler Power Coefficient,
pcm/% power
IPPP1)

Flat Profile

Error, %

0

-9.44

-9.52

0.86

6

-8.36

-8.58

2.65

13

-8.52

-8.98

5.48

1)

Intra-Pellet Power Profile, IPPP

4. Conclusions
The thermal feedback treatment with intra-pellet
power profiles was incorporated in the direct wholecore transport code nTRACER and was applied to thepower reactor calculations. In the depletion calculation,
only marginal effect was observed. A notable increaseof about 5% is, however, observed in the Doppler
power coefficient at EOC1. Since stronger effect should
be observed in the following cycles where the fuelburnup is higher, estimation of the power profile effectin the reload cycles is underway.

Fig. 2. Effect of Intra-Pellet Power Profile on
YGN3C1 Core Depletion
3.2 Effect on Doppler Power CoefficientsThe Doppler power coefficient is expected to beover-predicted (in absolute magnitude) with the flat
power profile scheme because the average fueltemperature will be higher than the actual value for anedge-peaked power profile. Thus it would lead to anunder-prediction of reactivity with the increasing core
power level. This effect was examined for the YGN3C1
core by performing the core calculation at higher power
levels as shown in Fig. 3. The coolant temperature wasmade unchanged by adjusting the core flow rate.

Acknowledgement
This work was supported by MEST of Korea throughNRF Grant No. 2009-0083414.
References[1] H. Matsumoto, M. Ouisloumen and T. Takeda, “Spatially
Dependent Self-Shielding Method with Temperature Profile
for Two-Dimensional Code PARAGON,” J. Nucl. Sci. Tech.,43, 1311-1319, 2006.
[2] Y.S. Jung, “nTRACER V1.0 Methodology Manual,”
SNURPL-CM-001(10), Seoul National University Reactor
Physics Laboratory, 2010.
[3] C.H. Lim, Y.S. Jung and H.G. Joo, “Incorporation of
Resonance Upscattering and Intra-Pellet Power Profile in
Direct Whole Core Calculation,” Proc. KNS Spring Meeting,Jeju, Korea, May 17-18, 2012.
[4] K.J. Geelhood, W.G. Luscher, C.E. Beyer and M.E.
Flanagan, “FRAPCON-3.3: A Computer Code for the
Calculation of Steady-State, Thermal-Mecanical Behavior of
Oxide Fuel Rods for High Burnup, ” NUREG/CR-7022, Vol.1,
NRC, 2011.
[5] Y.S. Jung, U.C. Lee, and H.G. Joo, “Examination of
Temperature Dependent Subgroup Formulations in Direct
Whole Core Transport Calculation for Power Reactors,” Proc.
ICAPP, Chicago, IL, USA, June 24-28, 2012.

Fig. 3. Reactivity Under-prediction with Flat Power
Profile in YGN3C1-9-

AESJ-KNS Joint Workshop on Reactor Physics and Nuclear Data, Kinki University, Osaka, Japan, March 25, 2013

The Small Reactivity Worth Measurement in Critical Experiments- Uncertainty estimation for reactivity fluctuation Yuichiro Ban a , Kenichi Yoshioka b, Hironori Kumanomido b
Isogo Nuclear Engineering Center, Power Systems Company, Toshiba Corporation, 8 Shinsutita-cho, Isogo-ku,
Yokohama, 235-8523
bPower & Industrial Systems Reserch & Development Center, Power Systems Company, Toshiba Corporation, 4-1,
Ukishima-cho, Kawasaki-ku, Kawasaki, 210-0862*
Corresponding author: yuichiro.ban@toshiba.co.jpapile oscillator. For these reason, the sample jerk method
is advantageous for reducing experimental costs andtime for critical experiments
The specifications of the sample driving device areshown below:z Maximum load
: 5kg,z Maximum withdrawal speed : 500mm/s,
z Maximum stroke: 1000mm.

1. Introduction
A small reactivity worth measurement plays
important role in reactor physics experiments. However,
the measurement uncertainty of the small reactivity
depends on phenomena fluctuation e.g., critical waterlevel. The reduction of the uncertainty and the accurate
estimation of the uncertainty are required.
There are several measurement methods forreactivity worth, e.g., difference of critical water level
method[1], pile oscillator method[2],[3], foil activation
method[4] and so on. Although the pile oscillator
method is suitable for small reactivity measurement, it
requires an expensive equipment and complex
procedure to deduce reactivity from measured data.
We proposed “sample jerk method” as a robust
measurement method for small reactivity worth. We
have already developed a sample driving device andused for sub-criticality measurements[5]. In order toimprove the measurement uncertainty of the sample
jerk method due to a fluctuation, we developed a new
estimation method based on stochastic process ofneutron.
In this paper, a small reactivity worth measurement
and its uncertainty estimation are described.

2.2 Uncertainty estimation for reactivity fluctuation
The reactivity meter can be estimated by the inverse
kinetic method (IK method)[6] as shown following
equation:/ dn(t ) /U E¦ Om Cm (t ) . (1)n(t ) dtn(t ) mThe reactivity has a fluctuation due to stochastic
process of neutron. As previously mentioned, it isimportant to accurately estimate the reactivity
uncertainty.
There is a correlation among the fission sources
between generations. Therefore, we have to evaluate
the uncertainty with correlation.
A Monte Carlo code simulates a stochastic process ofneutron like an actual phenomenon. Therefore, anestimation method of Monte Carlo code is valuable inevaluating the reactivity uncertainty. The MVP code[7]uses Ueki method[8] to evaluate the real variance of
eigenvalue as shown following equation:
1
2 N 1 N
V2
cov>k i , k i @  ¦ ¦ cov>k i , k j @. (2)N
N i 1 j i 1
The first term denotes a variance of i-th generation
eigenvalue. The second term denotes a correlation of
between generations. We apply Ueki method toevaluation the reactivity uncertainty as shown following
equation:1
2 N 1 N
V2cov>U i , U i @  ¦ ¦ cov>U i , U j @ . (3)N
N i 1 j i 1

2. Methods and Results
In this section, some of the measurement techniques
are described. This measurement technique is consistedof sample jerk method with a sample driving device anda reactivity meter. Additionally, we describe the resultsof critical experiment.
2.1 Sample jerk method
The sample jerk method is similar to pile oscillator or
source jerk method. The procedure of sample jerk
method is as follows:
1. An critical state with a sample,
2. Withdrawal of the sample from critical core,
3. Increase of the count rate of neutron detectors,
4. Measurement of reactivity worth with using thereactivity meter.
As shown above, the sample jerk method is not need a
lot of procedure. The sample worth measurement can be
carried out in a short time. Additionally, the sample jerk
method is not need a sample oscillation. The
experiment equipment can be miniaturized relative to

2.3 Experimental results
We carried out reactivity measurements by the
sample jerk method in LWR-type critical facility,
Toshiba Nuclear Critical Assembly (NCA). In theseexperiments, core consists of a uniform grid-plate, 2.0
wt% fuel rods and sample as shown Table 1. The
sample is located in the center of core.

-10-

AESJ-KNS Joint Workshop on Reactor Physics and Nuclear Data, Kinki University, Osaka, Japan, March 25, 2013

Table 1 Specification of experiments
Fuel rod pitch [cm]1.52
Fuel enrichment[wt%]2.0
Sample MaterialNi

3. Conclusions

In this paper, we propose the sample jerk method fora small reactivity worth measurement and apply Ueki
method to critical experiment. The sample jerk method
is advantageous for reducing experimental costs andtime for critical experiments
We carried out critical experiments for reactivity
worth measurement in the deference of critical waterlevel method and the sample jerk method. The result
revealed that the sample jerk method can reduce themeasurement uncertainty.
The Ueki method can consider the influence ofcorrelation between neutron generations. We applied tothe estimation of reactivity uncertainty for criticalexperiment. The influence of correlation is less than
0.1 ¢. However, the influence becomes more importantfor small worth measurement. Therefore, this technique
is useful for small worth measurement.
As shown above, we propose the valuable method forsmall worth measurement in critical experiment.

We measured some times to confirm thereproducibility. The results of critical experiments areshown Table 2. The uncertainty results in Table 2 areestimated from the maximum difference of eachexperiment result. Eq.(3) is not used in this results. As
shown Table2, the results of both methods areagreement within the experiment uncertainty. The
uncertainty of sample jerk method is smaller than thatof the deference of critical water level method, because
the uncertainty of the critical water level has no effecton the measurement uncertainty of sample jerk method.
Therefore, the sample jerk method is suitable for small
sample worth.
Table 2 Confirmation of the reproducibility
Deference of
Measurement
critical water
Sample jerk
methodlevel
Sample worth[¢]3.73±0.40

3.77±0.10

REFERENCES

An estimation of reactivity uncertainty is importantto evaluate the sample worth in any measurement
method. Figure 1 shows the reactivity of reactivity
meter in a critical state. We estimate the uncertainty ofreactivity by using Eq.(3) as shown Table 3. By
considering the covariance, the uncertainty is increased
three times. The influence of correlation is less than
only 0.1 ¢. However, the influence becomes more
important for small worth measurement. Therefore, thistechnique is useful for small worth measurement.

[1] T. Kikuchi, K. Yoshioka, Y. Maru, Critical
Experiments on Simulated BWR High-Burnup 9x9 AType Fuels, Proc. Physor96, Sep.16-20, 1996, Mito,
Japan.
[2] Y. Yamane, et. al., The Determination of CoupledCore Reactor Kinetic Parameters Through Frequency
Response, Nucl. Sci. Eng., Vol.76, pp.232-245, 1980.
[3] S. Okajima, et. al., Analysis of Doppler EffectMeasurement in FCA Cores Using JENDL-3.2 Library,Proc. Physor96, Sep.16-20, 1996, Mito, Japan.
[4] K. Yoshioka, et. al., Critical Experiments on
Reduced-Moderation
BWR:BARS–
Reactivity
Coefficients Measurements-, ICAPP ’03, May.4-7,
2003, Córdoba, Spain.
[5] S. Gunji, et. al., Sample driving machine for reactor
physics experiments – Application to sub-criticality
measurement based on noise analysis-, AESJ2008,
March.26-28, 2008, Osaka, Japan.
[6] Z. Akcasu, et. al., Mathematical Method in Nuclear
Reactor Dynamics, Academic Press, New York, p.8897, 1971.
[7] Y. Nagaya, et. al., MVP/GMVPII: General Purpose
Monte Carlo Codes for Neutron and Photon Transport
Calculations based on Continuous Energy andMultigroup Methods, JAERI-1348, 2005.
[8] T. Ueki, et. al., Error Estimations and Their Biases
in Monte Carlo Eigenvalue Calculations, Nucl. Sci.
Eng., Vol.125, pp.1-11 1997.

2

Reactivity[¢]

1
0
-1
-2
1500

1600
1700
Data series

1800

Fig. 1 Reactivity in critical state
Table 3 Estimation reactivity in critical state
Estimation method(Confidence interval:95%)

Notconsideringcovariance

Consideringcovariance:
Eq.(3)

Reactivity[¢]-0.010±0.019-0.010±0.061* The uncertainties are variance of the averagereactivity. Not variance of the each reactivity.

-11-

AESJ-KNS Joint Workshop on Reactor Physics and Nuclear Data, Kinki University, Osaka, Japan, March 25, 2013

A Neutronic Design of a Hybrid Reactor for Waste Transmutation
M. Tariq Siddique and Myung-Hyun Kim*
Department of Nuclear Engineering, Kyung Hee University, 446-701, Rep. of Korea
mhkim@khu.ac.kr
1. Introduction
A fusion-fission hybrid reactor concept is an
attractive and efficient solution for burning of highlevel waste including transuranic(TRU) isotopes andfission products (FP). This study was initiated to
explore the possibility of a hybrid reactor fortransmutation of long-lived isotopes separated fromPWR spent fuels [1] [2]. A concept of hybrid reactor
for waste transmutation (Hyb-WT) is proposed whichbased on a low power Tokamak (less than 150 MWt)and annular ring shaped reactor core with multiple
zones of metal fuel (TRU 60 w/o, Zr 40 w/o) and FP.
Performance of design concepts were measured bymany indices such as TRU and FP mass burned per fullpower year, support ratio, reduction in TRU and FP
toxicity and tritium breeding ratio. A variety ofcomputational tools (codes) have been used for hybrid
reactor design studies because of absence ofspecifically designed tool. MCNPX [3] andMONTEBURNS [4] codes are compared for theevaluation of Hyb-WT performance parameters. The
differences among three most popular cross section
libraries ENDF/B-VII, JEFF3.1.2 and JENDL3.2 arealso evaluated.

)LJ*HRPHWU\RIIXVLRQ̽ ILVVLRQK\EULG
Table 2. Geometrical parameters of Tokamak design.
Major radius Ro (m)3Minor radius a (m)0.7
Fusion Power Pfus (MW) max.
150
Neutron source (#/s-1) max.
6.7u1019
1.8
Elongation N
0.5
Triangularity G
Aspect ratio
4.3
Plasma volume (m3)47.6

3. Comparison of MONTEBURNS and MCNPXMONTEBURNS use one group cross sections [4]whereas MCNPX use 63 group cross sections [7] fordepletion calculations which is the major difference
between two code systems. To evaluate its effect on hybrid
reactor design study depletion and toxicity variations of
TRU and FP, k-eff and tritium breeding were calculated for
Hyb-WT using MONTEBURNS and compared withMCNPX 2.6. ENDF/B-VII library was used for both codes.

2. Concept of Hyb-WT
The geometry and material composition of hybrid
reactor for waste transmutation (Hyb-WT) are shown in
Fig.1 and Table 1 respectively.
Table 1. Material composition of Hyb-WT
Material andvolume fraction

Thickness
(cm)

MCNPX
MONTE

1.00

First WallODS Steel (MA957): 70%,
He-gas: 30%

TRU zone
Vol % per
Fuel
Assembly

TRU: 3.56%, Zr: 7.04%, LiPb:
59.91%, SiC: 4.45%, Clad ODS
steel: 9.98%, Na-Bond: 15.06%

45

FP zoneI-129: 0.5%, Cs-135: 1.7%, Tc99: 0.8%, SiC: 2.5%, C: 78%,
He-gas:16.5%

30

600

5

500
400

0.95

keff

300
200

0.90

Diff. (pcm)

Zone

100
0

0.85

0

The Hyb-WT is based on a low power Tokamak (150
MW max) as a neutron source of fast neutrons. The
geometrical parameters of Tokamak design are shown intable 2. The TRU core was designed at 2,000 MWth fission
power level [2] [5]. The material composition for TRU and
FP are assumed to be same with those of spent fuel from
1,000 MWe PWR with 10 years cooling time [6].

200

400

600

800

1000

-100
1200

Time (Days))LJ&RPSDULVRQRINHIIFDOFXODWHGZLWK0&13;
DQG0217(%8516IRU+\E:7

-12-

AESJ-KNS Joint Workshop on Reactor Physics and Nuclear Data, Kinki University, Osaka, Japan, March 25, 2013

Table 4: Transmutation performance parameters of Hyb-WT
predicted by ENDF/B-VII, JEFF312 and JENDL32.

)LJ7ULWLXPEUHHGLQJFDOFXODWHGE\0&13;DQG
0217(%8516RYHUWKHLUUDGLDWLRQF\FOHIRU+\E:7

The comparison of k-eff variation over the irradiation
cycle for MONTEBURNS and MCNPX is shown in Fig. 2.
The difference between two k-eff values is almost zero atthe beginning of cycle and increased with time. The
maximum difference was observed to be 488 pcm at theend of cycle. It shows that MONTEBURNS slightly
overestimate the TRU transmutation.
There is very small difference in TRU mass depletion,
the maximum % difference for TRU mass is 0.12% at
the end of cycle and it also reflect slightly higher
estimation of TRU transmutation by MONTEBURNS.
A big difference between MCNPX andMONTEBURNS tritium breeding calculation isobserved as shown in Fig. 3. MCNPX calculates 13.24
kg tritium breeding whereas MONTEBURNS predicts
5.89 kg, over the irradiation cycle. It suggests that thedata for Li-7 may not be considered for tritium breedingin MONTEBURNS as tritium production cross section
for Li-7 is not negligible above 2 MeV.

NeutronLibrary

ENDF/
B-VII

TRU
JEFF3
12

JEND
L32

ENDF
/B-VII

FP
JEFF3
12

JENDL
32

Inventory (T)FP Mass
Produced (kg)
Mass-burned(kg)(kg/fpy)% massburned/yr
Support Ratio
for 100%
availability
Ingestion
Toxicity
Reduction
Inhalation
Toxicity
Reduction

16.68

16.68

16.68

2.51
162.852.51
162.892.51
162.832250.42250.52249.7251.55254.51222.67746.724.48%

746.76
4.48%

746.5
4.47%

83.47
3.32%

84.45
3.36%

73.89
2.94%

2.99

2.99

2.99

2.09

2.12

1.85

4%

4%

4%

11%

11%

11%

8%

8%

8%

13%

13%

11%

5. Conclusions
MONTEBURNS may not be a better option forhybrid reactor design study especially for tritium
breeding calculation. There is no significant difference
between ENDF/B-VII and JEFF312 calculated
performance parameters of Hyb-WT. JENDL32 shows
significant difference from ENDF/B-VII for FP
transmutation and k-eff value estimation. May be
JENDL33 or JENDL4 calculations match closely with
ENDF/B-VII because of improved cross section values.
The preliminary study of Hyb-WT shows great
potential of fusion energy for waste transmutation. It iscompletely new and evolving technology it may require
a comprehensive design and performance analysis over
its life time which will be pursued for its practicalapplication.

4. Neutronic Analysis of Hyb-WT
Table 3 and 4 shows the summary of neutronicparameters and TRU and FP transmutation performance
calculated using ENDF/B-VII, JEFF312 and JENDL32.
The JEFF312 and JENDL32 resulted in overestimatedk-eff values as compared to ENDF/B-VII even thoughsimilar TRU compositions and number densities areused. Because of different k-eff values the required
fusion power and consequently the TBR is different forthree libraries even though the tritium mass prediction
by three libraries is not significantly different. The TRU
transmutation performance of Hyb-WT predicted bythree libraries is similar except the slightunderestimation of TRU mass transmutation by
JENDL32 but it significantly underestimates the FP
transmutation.

REFERENCES[1] M. T. Siddique and M.H. KIM, “Preliminary Neutronic
Performance Evaluation on a Conceptual Design for a
Transmutation Fusion Blanket,” Trans. Am. Nucl. Soc.,
Vol.105, 2011 ANS Winter Meeting, Washington D.C., USA,
Oct.30-Nov.3, 2011.
[2] M. T. Siddique and M. H. KIM, “Preliminary Feasibility
Study of a Low Power Hybrid Reactor,” Proc. of KSTAR
conference, Muju Deogyusan Resort, Korea, Feb. 22-24, 2012.
[3] D. B. Pelowitz, “MCNPX User’S Manual Version 2.6.0,”
Los Alamos National Laboratory, 2008.
[4] R. Holly, I. David, and H. R. Trellue, “User ’ s Manual,
Version 2.0 for MONTEBURNS, Version 5B,” 1999.
[5] M. T. Siddique and M. H. Kim, “A Feasibility Study on a
Clean Power Fusion Fission Hybrid Reactor,” Fusion Energy
Conference 2012, San Diego, CA-USA, Oct. 8-13, 2012, pp.
1–8.
[6] H. Condé, “Introduction to ADS For Waste Incinerationand Energy Production,” The Impact of Nuclear Science onLife Science, 2001.
[7] J. S. Hendricks, G. W. Mckinney, M. L. Fensin, M. R.
James, R. C. Johns, J. W. Durkee, J. P. Finch, D. B. Pelowitz,
L. S. Waters, M. W. Johnson, and F. X. Gallmeier, “MCNPX
2.6.0 Extensions LA-UR-08-2216,” 2008.

Table 3: Major neutronic parameters of Hyb-WT predicted by
ENDF/B-VII, JEFF312 and JENDL32 library.
Cross-section
ENDF/BJEFF312
JENDL32
LibraryVII
Fusion Power
14-83
12-81
10-77
(MW)
Range of keff
0.97133 0.976060.98071variation
0.857030.860840.86595
TBR
1.46
1.53
1.68
H3 Mass (kg)
11.67
11.59
11.86

-13-

AESJ-KNS Joint Workshop on Reactor Physics and Nuclear Data, Kinki University, Osaka, Japan, March 25, 2013

Two Formulations of Continuous-Energy Monte Carlo Local Problem
in Overlapping Local/Global Iteration Methodology
YuGwon Jo and Nam Zin Cho*
Korea Advanced Institute of Science and Technology (KAIST)
291 Daehak-ro, Yuseong-gu, Daejeon, Korea 305-701*
nzcho@kaist.ac.kr

problem (FKP) formulation and compares the two
formulations.

1. Introduction
The direct whole-core transport calculation without
homogenization (in either multigroup deterministic orcontinuous-energy Monte Carlo method) is not yet
tractable for routine use with current computing power.
As an alternative to the direct approach, an overlapping
local/global (OLG) iteration scheme [1, 2] wasintroduced, in which the local problem based on amultigroup deterministic method or a continuousenergy Monte Carlo method is embedded in the partial
current-based coarse-mesh finite difference (p-CMFD)
global problem.
As an illustration, Fig. 1 shows a half-assembly
overlapping local problem (defined by green dot-dashedlines), to which the following neutron transport
equation is applied:

2. Two Formulations of Continuous-EnergyMonte Carlo Local Problem
2.1 Eigenvalue Problem (EVP) with Albedo Boundary
Condition [1, 2]
When a Monte Carlo particle is about to cross aboundary surface, it is reflected with a new weightcorrected by albedo Ƚ. This is enabled by the “albedoto-weight” conversion device developed in a Monte
Carlo depletion study [3], and it is almost trivial to
implement the method in an existing Monte Carlo code.
2.2 Fixed-k Problem (FKP) with Incoming Partial
Current Boundary Condition: M (r , E , :)  V t (r , E )M (r , E , :)

³

d :c

k

local

1

³

d
dE cV s (r , E c o E , :c  :)M (r , E c, :c) 

F (E)
4S

In this problem formulation, incoming partial currentJJ  (in angular bins) and k local k global are
given from the previous local/global iteration. In eachgeneration j, we consider N histories such thatN N sj  N jf , j 1, 2, ,
(2)
BC

(1)

³ d :c³ ddE cQV (r, E c)M (r, E c, :c) .
fwhere N is user input, N sj is the number of histories
sampled from the incoming boundary source and N jf isthe number of histories taken from the fission sourcebanked in generation j-1 and obtained as
N jf

Fig.1. Half-assembly overlapping local problem in 1-D
problemN sj1  N jf1 §§§ QV f V t···¨¨ floor ¨
wgti,col  [ ¸ ¸ ¸ ,¨ k global¸ ¸ ¸¸¨¨¨©
¹¹¹© col ©

¦ ¦
i 1

N sj

From a global solution in the OLG iteration scheme,(i) M r or J r at the local problem boundary and (ii)N  N jf .

(3)
(4)

Note that QV f is divided by k global in Eq. (3).

k global become available at each iteration. In Ref. [1], inthe case of deterministic local problem, a fixed-source
problem formulation is used in that M BC M  andAfter several generations are discarded, the subnodep-CMFD parameters [1, 2] are tallied based on collision
estimators for next global calculation.

k local k global are used to solve Eq. (1). This may bealso termed as a “fixed-k problem (FKP)” formulation
with incoming angular flux boundary condition.
In the case of continuous-energy Monte Carlo local
problem, Refs. [1] and [2] describe an eigenvalue
problem (EVP) formulation with albedo boundary
condition D J  J  given, but k local is unknown. As
another formulation, this paper presents a fixed-k

3. Numerical Results
The two formulations of continuous-energy Monte
Carlo local problem in the OLG methodology are tested
and their performances are compared in the 1-D thermal
reactor problem [1] shown in Fig. 2. The Monte Carlocalculations are performed by the in-house researchcode McSLAB [4], which considers at the present time
three major interactions (elastic scattering, capture,-14-

AESJ-KNS Joint Workshop on Reactor Physics and Nuclear Data, Kinki University, Osaka, Japan, March 25, 2013

fission) with resolved resonances and isotropic
scattering in the center-of-mass system taken into
account.

8

Fixed-k Problem
Eigenvalue Problem

rRMSE of power distributions (%)

7
6
5
4
3
2
1
0
1

2

3

4

5

6

78.63
70.89

62.56
73.90

68.00
73.92

63.32
74.45

69.75
77.77

48.92
73.28

1. N.Z. Cho et al., “Overlapping Local/Global Iteration
Framework for Whole-Core Transport Solution,”
PHYSOR 2012, Knoxville, TN, USA (2012); see also
Nucl. Sci. Eng., accepted (2013).
2. Y.G. Jo and N.Z. Cho, “Refinement of Overlapping
Local/Global Iteration Method Based on Monte
Carlo/p-CMFD Calculations,” M&C 2013, Sun Valley,ID, submitted (2013).
3. S. Yun and N.Z. Cho, “Monte Carlo Depletion under
Leakage-Corrected Critical Spectrum via Albedo
Search,” Nucl. Eng. Technol., Vol.42, p.271 (2010);
http://www.kns.org/jknsfile/v42/JK0420271.pdf.
4. Y.G. Jo, “McSLAB – A Continuous-Energy Monte
Carlo Code for Neutronics Analysis in Multi-SlabGeometry,” Korea Advanced Institute of Science andTechnology (KAIST), in progress.

global k

1.244

1.240

1.236

1.232

1.228
1

2

3

4

5

6

6

References

Fixed-k Problem
Eigenvalue Problem
Reference05

In addition to the eigenvalue problem (EVP)
formulation, this paper describes the fixed-k problem(FKP) formulation of the continuous-energy Monte
Carlo local problem to be embedded in the overlapping
local/global (OLG) iteration methodology. The two
formulations are tested on a simplified but typicalthermal reactor problem. The test results indicate thatthe rRMSEs of power distributions converge faster in
EVP than in FKP, when the maximum computing times
for local calculations are similar.
In contrast to EVP, the computing times in FKP vary
widely among local problems, depending on the local
problem characteristics and its environment. Therefore,
it will be difficult to achieve good load balance inparallel computation of local problems with FKP.

As the OLG iteration progresses, k global and relativeroot mean square errors (rRMSE) of subnode averaged
power distributions of the two formulations arecompared in Figs. 3 and 4, respectively.

1.248

4

4. Conclusions

Table I. Computing times (min, Intel Xeon X5670 single
processor running at 2.93 GHz) of local problems at
the 6-th OLG iteration
1

3

Fig.4. Comparison of rRMSEs of subnode averaged power
distributions in two formulations

To render the longest running time among local
problems similar in the two formulations, ͷ ൈ ͳͲସ
histories for EVP and ͸Ǥͷ ൈ ͳͲସ histories for FKP per
generation are selected and 50/500 inactive/active
generations are used for each local calculation.
Homogenized parameters are generated in two groups
for global subnode p-CMFD calculation, whileboundary conditions for local problems are modulated
in 45 energy groups and four angular bin partial
currents. For the reference whole-core calculation,ʹǤͷ ൈ ͳͲହ histories per generation and 200/3000
inactive/active generations are used.
Table I shows the computing times of local problems
in the two formulations at the 6-th OLG iteration. Notethat in EVP the Monte Carlo particle is reflected at aboundary surface (with adjusted weight) and tracked
further until it is absorbed, while in FKP the particle is
not tracked further when it crosses such a surface.

Local
Problem
FKP
EVP

2

OLG iteration number

Fig.2. 1-D thermal reactor with UO2 and MOX fuelassemblies

7

OLG iteration number

Fig.3. Comparison of global k’s in two formulations-15-

AESJ-KNS Joint Workshop on Reactor Physics and Nuclear Data, Kinki University, Osaka, Japan, March 25, 2013

Efficient Calculation Scheme with Preservation of Transmission Probabilities
in the Method of Characteristics
Masato Tabuchi a,b , Naoki Sugimura a, Akio Yamamoto b, Tomohiro Endo ba
Nuclear Engineering Ltd., Tosabori Nishi-ku, Osaka, Japan, 550-0001b
Nagoya University, Furo-cho, Chikusa-ku, Nagoya-shi, Aichi, Japan, 464-8603*
Corresponding author: mtabuchi@neltd.co.jp
1. Introduction

the present model, the macroband method based on theequidistant ray tracing is assumed.
The equation for preservation of the transmission
probability in a segment is described as follows:

In the method of characteristics (MOC) [1],parameters for the ray tracing, which mean azimuthal
angle division, polar angle division and ray separation
width, are important in the viewpoint of computationalburden and accuracy. Although faster calculation can be
performed with coarser ray tracing parameters,
accuracy would be degraded because of thediscretization error. In particular, for a strong absorbercell such as high Pu content MOX, very detailed ray
tracing is required to obtain an accurate result. In orderto improve the calculation efficiency, in this study, an
efficient calculation scheme to reduce discretization
error due to the ray separation is discussed.

D
1

6t
sin T

³ exp  Ds t dt
1

(1)

2 exp  D~s

(2)

In Eq. (2), the coordinate system in a segment, which
is normal to the direction of ray trace, is normalized as 1 to 1. An example of the length distribution of pathlines, which means s t in Eq. (2), is shown in Fig. 1.

2. Calculation ModelIn most of the ordinary MOC calculation codes,
equidistant ray tracing is used. However, in thisapproach, a ray trace may cover geometrical
discontinuous points, e.g. intersects of regions, hence
large discretization error would be caused in suchsituation. In order to avoid this issue, the macroband
method was developed in the previous study [2, 3]. In
the macroband method, a calculation domain is divided
into “macroband”, boundaries of which consists oftangential and intersect points in the calculationgeometry. Then each macroband is divided into
“segment” and the path lines are drawn at the center ofthe segments. The discretization error due to the ray
separation is expected to be reduced, since no segments
include discontinuous points with the macroband
method. Moreover, in the AEGIS code [4], nonequidistant ray tracing in each macroband based on theGauss-Legendre quadrature set is adopted to reduce
numerical integration error. In this study, theimprovement of the ray tracing is discussed by anotheraspect. The present study focuses on preservation of thetransmission probabilities in each segment. The
transmission probability is an important parameter,
since it represents the effective neutron attenuation.
However, it is difficult to generally and rigorously
estimate the transmission probability, since theprobability depends on not only the total cross section
but also geometrical shape of a segment. In order toeasily estimate the transmission probability, in thisstudy, length distribution of path lines in a segment isassumed to obey a linear function. For the derivation of

s(t)
-1

1

t

Fig. 1. An example of the length distribution
When the length distribution of path lines is assumed
to be a linear function as shown in Eq. (3), the effective
length to preserve the transmission probability can beobtained as Eq. (4):stEt  J

(3)

·
1 § 1
~
sinh DE ¸¸ (4)s J  ln¨¨D © DE¹
Furthermore, using a special function defined as Eq.
(5), Eq. (4) can be rewritten as Eq. (6):1 §1·ln¨ sinh x ¸x ©x¹~s J  EL DE

Lx

Since L x is the odd function ( L  x
the following relationship is satisfied:

-16-

(5)
(6)

 L x ),AESJ-KNS Joint Workshop on Reactor Physics and Nuclear Data, Kinki University, Osaka, Japan, March 25, 2013J   E L  DE

J  EL DE

3. Verification(7)

In order to confirm the accuracy of the present
method, some verification calculations are performed.
As the conventional method, the macroband method
based on the Gauss-Legendre quadrature set, which is
explained in the first paragraph, is assumed, and theaccuracy is compared between the conventional and thepresent methods. Four types of 17 x 17 fuel assemblies
listed as follows are assumed for the verification, and kinfinity values are evaluated by the AEGIS code.

Therefore, only the absolute value of E should beconsidered, and L x can be considered only in therange of positive x . Fig. 2 shows the distribution of
L x for positive x . As shown in Fig. 2, L x is amonotonically increasing function, and the range of its
values is between 0 and 1.
㻝㻚㻜

㻸㻔㼤㻕

㻜㻚㻤

- 4.8 wt% UO2 fuel (‘UO2’)- 4.8 wt% UO2 fuel with RCC insertion (‘RCC’)- 10.0 wt% Gd bearing 4.8 wt% UO2 fuel (‘GD’)- 4.0, 8.0, 12.0 wt% Pu-total MOX fuel (‘MOX’)

㻜㻚㻢
㻜㻚㻠
㻜㻚㻞
㻜㻚㻜
㻝㻚㻜㻱㻙㻜㻠

㻝㻚㻜㻱㻙㻜㻞

㻝㻚㻜㻱㻗㻜㻜

㻝㻚㻜㻱㻗㻜㻞

In this verification, these geometries are called as‘UO2’, ‘RCC’, ‘GD’ and ‘MOX’ respectively. The
calculation conditions are as follows. In order toevaluate the discretization error due to the ray
separation, divisions for azimuthal and polar angles are
set to be detail.

㻝㻚㻜㻱㻗㻜㻠

㼤

Fig. 2. Distribution of L x for positive x
As described above, the effective length to preserve
the transmission probability can be obtained by Eq. (6).
The first term of the right hand side of Eq. (6) isequivalent to the average length of a segment, since J
represents the intercept of the length distribution andthe coordinate system in a segment is normalized as -1
to 1. The second term of the right hand side of Eq. (6)consists of a multiplication of E and L x , which canbe both regarded as positive values. Therefore, theeffective length always becomes shorter than the
average length of a segment to preserve thetransmission probability.
In the actual implementation, D , E , J and L xshould be estimated to obtain the effective length.
Although D can be estimated before the transport
sweep, a large amount of memory would be necessary
in some cases. Therefore, D should be estimatedduring the transport sweep. On the other hand, if E andJ are estimated during the transport sweep, additional
calculation cost would be significantly increased.
Therefore, these values should be estimated before thetransport sweep. These values can be easily estimatedby drawing some additional lines in a segment during
the ray tracing. Finally, L x should be tabulated before
the transport sweep, since L x includes logarithm andhyperbolic sine functions, which need muchcomputational time to be calculated. By adopting theabove scheme, the calculation model of the present
study can be implemented without significant additionalcost, and the efficiency of the MOC calculation is
expected to be improved.

- Energy group: 172 groups (XMAS structure [5])- Azimuthal angle division: 128 for 2ʌ
- Polar angle division: 3 for ʌ/2 (TY-quadrature [6])- Ray separation width: vary between 0.01 and 0.35cm
- Scattering order: P0 (transport correction)
It should be noted that the actual ray separation
widths are different from the input values, since widthsof macrobands are different from each other. Therefore,
input value means the maximum ray separation width.
The above condition of the ray separation widths (0.01
to 0.35 cm in input values) corresponds to about 0.01 to
0.12 cm in average ray separation widths.
The calculation results are shown in Figs. 3 to 6.
These figures show the trends of k-infinity differences
against the ray separation. The results in theconventional method with 0.01 cm width are used as
the reference results. As described above, the actual ray
separation widths are not equal to the input values.
Therefore, the average ray separation width is used as
the horizontal axis in Figs. 3 to 6.
In the conventional method, the differences of kinfinity become larger when the ray separation widths
become coarser. The maximum difference is more than
0.1 %ǻk/k, and the trends of the differences have
oscillation-like behaviors in some cases. On thecontrary, in the present method, although thedifferences become slightly larger for coarser ray
separation width, the maximum difference is smaller
than 0.05 %ǻk/k. Furthermore, the oscillation-likebehaviors in the present method are not remarkable
compared with those in the conventional method.
From these results, the effectiveness of the present
method can be confirmed. Since the accuracy is not-17-

AESJ-KNS Joint Workshop on Reactor Physics and Nuclear Data, Kinki University, Osaka, Japan, March 25, 2013㻰㼕㼒㼒㼑㼞㼑㼚㼏㼑㻌㼛㼒㻌㻷㻙㼕㼚㼒㼕㼚㼕㼠㼥㻌㼇䂴㼗㻛㼗㼉

greatly decreased for coarse ray separation width in thepresent method, efficiency of the MOC calculation is
expected to be improved by the present method.

4. Summary
In this study, an efficient calculation scheme for
MOC is investigated. The equation for the effective
length of a path line is derived based on an assumptionthat the lengths are linearly distributed in a segment. By
using the effective length, the transmission probabilities
in each segment can be preserved. Through theverification calculations, the accuracy of the present
method can be confirmed, and efficiency of the MOC
calculation is expected to be improved by the present
method.

㻜㻚㻞㻑㻯㼛㼚㼢㼑㼚㼠㼕㼛㼚㼍㼘㻌㻹㼑㼠㼔㼛㼐㻜㻚㻝㻑㻼㼞㼑㼟㼑㼚㼠㻌㻹㼑㼠㼔㼛㼐

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REFERENCES㻜㻚㻝㻞[1] J. R. ASKEW, A Characteristics Formulation of the
Neutron Transport Equation in Complicated Geometries,
AEEW-M 1108, U. K. Atomic Energy Authority, 1972.
[2] E. A. Villarino, R. J. J. Stammler, A. A. Ferri, J. J. Casal,
HELIOS: Angularly Dependent Collision Probabilities,
Nuclear Science and Engineering, Vol.112, p.16, 1992.
[3] T. Ushio, T. Takeda, M. Mori, Neutron Anisotropic
Scattering Effect in Heterogeneous Cell Calculations of Light
Water Reactors, Journal of Nuclear Science and Technology,
Vol.40, p.464, 2003.
[4] A. Yamamoto, T. Endo, M. Tabuchi, N. Sugimura, T.
Ushio, M. Mori, M. Tatsumi, Y. Ohoka, AEGIS: an advanced
lattice physics code for light water reactor analyses, Nuclear
Engineering and Technology, Vol.42, p.500, 2010.
[5] E. Sartori, Standard Energy Group Structures Of Cross
Section Libraries For Reactor Shielding, Reactor Cell andFusion Neutronics Applications: VITAMIN-J, ECCO-33,
ECCO-2000 and XMAS, JEF/DOC-315, Revision 3, NEA,
Data Bank, Gif-sur-Yvette Cedex, France, Dec. 11, 1990.
[6] A. Yamamoto, M. Tabuchi, N.Sugimura, T. Ushio, M.
Mori, Derivation of optimum polar angle quadrature set forthe method of characteristics based on approximation error for
the Bickley function, Journal of Nuclear Science andTechnology, Vol.44, p.129, 2007.

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Fig. 3. Verification results for UO2
㻜㻚㻞㻑㻯㼛㼚㼢㼑㼚㼠㼕㼛㼚㼍㼘㻌㻹㼑㼠㼔㼛㼐㻜㻚㻝㻑㻼㼞㼑㼟㼑㼚㼠㻌㻹㼑㼠㼔㼛㼐

㻜㻚㻜㻑
㻙㻜㻚㻝㻑
㻙㻜㻚㻞㻑
㻜㻚㻜㻜

㻜㻚㻜㻞
㻜㻚㻜㻠
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㻜㻚㻜㻤
㻜㻚㻝㻜
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Fig. 4. Verification results for RCC㻜㻚㻞㻑㻯㼛㼚㼢㼑㼚㼠㼕㼛㼚㼍㼘㻌㻹㼑㼠㼔㼛㼐㻜㻚㻝㻑㻼㼞㼑㼟㼑㼚㼠㻌㻹㼑㼠㼔㼛㼐

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㻜㻚㻜㻠
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㻭㼢㼑㼞㼍㼓㼑㻌㻾㼍㼥㻌㻿㼑㼜㼍㼞㼍㼠㼕㼛㼚㻌㼃㼕㼐㼠㼔㻌㼇㼏㼙㼉㻜㻚㻝㻞㻰㼕㼒㼒㼑㼞㼑㼚㼏㼑㻌㼛㼒㻌㻷㻙㼕㼚㼒㼕㼚㼕㼠㼥㻌㼇䂴㼗㻛㼗㼉

Fig. 5. Verification results for GD㻜㻚㻞㻑㻯㼛㼚㼢㼑㼚㼠㼕㼛㼚㼍㼘㻌㻹㼑㼠㼔㼛㼐㻜㻚㻝㻑㻼㼞㼑㼟㼑㼚㼠㻌㻹㼑㼠㼔㼛㼐

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Fig. 6. Verification results for MOX-18-

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