Development of Burn-up Calculation Systemfor Fusion-Fission Hybrid Reactor
M. Matsunaka, S. Shido, K. Kondo, H. Miyamaru, I. Murata
Division of Electrical, Electronic and Information Engineering,
Graduate School of Engineering, Osaka University,
Yamada-oka 2-1, Suita, Osaka 565-0871, Japan
A fusion- ssion hybrid reactor which is a fusion reactor with a blanket region containing
nuclear fuel. In our group, a calculation system for analysis of fusion- ssion hybrid reactor
has been developed and transport and burnup calculations were carried out for various hybrid
energy systems with three-dimensional ITER model. The burnup calculation system consistsof a general-purpose Monte Carlo code MCNP-4B, a point burnup code ORIGEN2 and someother postprocessing codes developed by us, which process the calculated results. In order toevaluate collapsed cross section for burnup as precise as possible, making of collapsed cross section
process was postprocessed using not tally function but neutron track length data of the MCNP
calculation directly. We are using a modi ed version of MCNP-4B so as to output all neutrontrack length data in the blanket region. JENDL-3.3 pointwise data and JENDL Activation Cross
Section File 96 were used as base cross section libraries. From the calculation results for a reactor
type employing a water cooled uranium cycle, fusion- ssion hybrid reactor is surely feasible fromthe standpoint of neutronics design. Further calculation and analysis are planned to improve
hybrid reactor performance of LLFP transmutation and so on.

1 Introduction
A fusion- ssion (FF) hybrid reactor system is a concept of combining nuclear fuel with fusion
reactor. Neutrons can be well multiplied by ssion in the nuclear fuel loaded in the fusion
reactor blanket even for a relatively lower plasma condition. Tritium is thus bred so as to attainits self-suciency. Then enough energy multiplication is expected and moreover it is possible totransmute or to burn the nuclear waste such as long-lived ssion products (LLFP) and minor
actinides (MA) by surplus high energy neutrons.
In our group, a calculation system for the analysis had been developed to investigate theperformance of FF hybrid reactor that is feasible at present. Such feasible FF hybrid reactor
is expected to have the following characteristics, i.e., low plasma condition, subcriticality andtritium self-suciency. Target parameters considered are thus tritium breeding ratio (TBR),
keff , power density, energy multiplication factor in accordance with the changes of material
composition due to burnup. Transmutation ability of long-lived ssion products and minor
actinides is also evaluated. The author's group has performed a lot of neutronics analysis withthe calculation system for various types of FF hybrid reactors1) . Through a long experience
to use the system, it was found that the system used previously had a problem in the making
process of collapsed cross sections for burnup2) . The objectives of this work is to modify theburnup calculation system to make the cross section set for burnup very strictly with a special
postprocess procedure. Also, as an example of the hybrid reactor analysis, the calculation results
for a reactor type employing a water cooled uranium cycle is brie y described.

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2 Calculation System
2.1 Development of Calculation SystemBurnup calculations for FF hybrid reactor had been performed in the author's group so far
with a calculation system combining general-purpose Monte Carlo code MCNP-4B3) with point
burnup code ORIGEN24) . However, it was found from the experiences previously that thecalculation system had a problem on making one-group cross sections for burnup calculation.
The one-group cross section set was made by the tally function of MCNP. Tally function is known
to be a useful function for users to estimate neutron ux, reaction rate, and so on. However thenumber of tallies available for users is too small to compute collapsed cross sections for all thenuclei included. Thus the calculation system was planned to be modi ed to improve making
procedure of the one-group cross sections for burnup.
There were three options to improve the calculation system as follows. (1)Postprocessing
to make one-group cross section using the calculated neutron spectrum by the MCNP tally.
This option was very easy to apply and faster computation can be expected. But it would
spoil continuous treatment of neutron energy. (2)Modi cation of MCNP to make one-groupcross section directly or to remove the limit of the number of tallies available. But drastic
modi cation of MCNP is actually unreal, and increase of the number of tallies will expand thecomputation time extremely. (3)Extracting neutron transport data and postprocessing of it.
This is the most strict procedure and was nally adapted in the present study. This option
required a little modi cation of MCNP with a slight increase of the computation time. But ittakes a longer time required to make collapsed cross sections in the postprocessing.
Figure 1 shows the current burnup calculation procedure. One burnup cycle consists ofthe following four steps: 1) Criticality calculation by KCODE of MCNP, 2) Neutron transport
calculation by modi ed MCNP, 3) Making of ORIGEN library from neutron track length dataand evaluated nuclear data libraries, and 4) Burnup calculation by ORIGEN for each blanketcells. The whole burnup calculation of the FF hybrid system is completed by repeating thisburnup cycle.

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Material List of Cells for Burnup?

Input Processing

HH888HHBurnup Cycle:
88
HHj
8
- MCNP Input Files
ORIGEN Input Files ?
Criticality Calculation?
Checking k - Terminates
when k 1?
Transport Calculation?
Track Length and Energy Data of Neutron EvaluatedCross Section?
88Libraries
Making of collapsed 8
ef f

ef f

Cross Section?

ORIGEN Cross-Section Library PP

PPPPq?
Burnup Calculation? Files
ORIGENOutput)
making MCNP Input Files HHH
HHHj

88
8888

Output Processing?

Calculation Result Files
Figure 1: Flow Chart of Burnup Calculation

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2.2 Making of Collapsed Cross Sections

In the ORIGEN code, cross section libraries for several types of nuclear reactor are prepared.
However, those are not applicable to the present calculation, because FF hybrid reactor will be
operated under subcritical condition and hence the energy spectrum varies depending on eachcon guration of nuclear fuel. It is thus needed to replace cross section values of the libraries
attached in ORIGEN with the ones suitable for the present subcritical system. The ORIGEN
code requires collapsed (one-group) cross-sections of (n,g), (n,2n), (n, ), (n,p), (n,gx) and (n,2nx)
for activation products (including stable nuclei) and Fission products, and requires those of (n,g),(n,2n), (n,3n), (n,f), (n,gx) and (n,2nx) for actinides. (n,gx) and (n,2nx) mean cross sections of(n,g) and (n,2n) producing isomers.
As described above, in the present study, modi ed version of MCNP-4B was used to get all
neutron transport data in the blanket cells. The data exported from a transport calculation andstored in a le are track-length (DLS), particle weight (WGT) and neutron energy (ERG). DLS,WGT and ERG are variable names of MCNP. Track-length is neutron ying distance between
events, that is, reaching cell boundary and occurring of collision, as shown in Fig. 2.
Material Nuclide33JJ1HYHHHH
  1 0HH HHjJ+ J]J 0 HHj11 JJ0Neutron
Track-Length

Cell Boundary
Figure 2: Neutron Track Length

The collapsed cross section is evaluated by the following equations.
Z(E )dE =PDLSi 1 WGTi
NP S 1 V OLiR

 (RE ) 1 (E )dE
(E )dEP
1 WGTi 1  (ERGi)
Pi= i DLSi DLSi 1 W GTi

 coll =where:
collE
 (E )
(E )
DLSi
W GTi
ERGi
NPSV OL

Collapsed Cross-Section
Neutron Energy
Energy Dependent Cross-Section
Energy Dependent Neutron Flux
Track-Length of Neutron Track i
Weight of Neutron Track i
Energy of Neutron Track i
History Number
Cell Volume

The cross sections of ORIGEN library are replaced by coll . Point-wise data of (E ) isdirectly used from evaluated nuclear data libraries of JENDL-3.3 and JENDL Activation Cross
Section File 965) . The library for LMFBR contained in ORIGEN was also referred for minor
nuclei as not contained in both of JENDL-3.3 and JENDL Activation Cross Section File 96.

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3 Calculation Results
With the developed calculation system, various calculations have been carried out so far6; 7) .
In the present paper, as a typical example, brief results of a water cooled uranium cycle aredescribed.
3.1 Calculation Model and Condition

Figure 3 shows cross sections of calculation geometry and tables 1 and 2 show calculation
conditions. The 3-dimensional ITER8) model (18 degree sector model) and physics parameters
derived from the plasma conditions already achieved at JT-60 of JAEA9) were employed.
The blanket was divided into 5 sections radially and each section was divided into 6 layers (30cells total). The material composition of fuel cell and breeder cell are shown in table 3. Li2 ZrO3
was selected as breeding material, and loaded into breeder cell with beryllium. 6 Li enrichment
was 30 %. Fuel cell consists of structural material SS316, natural UO2 and reprocessed PuO2 as
nuclear fuel and water as coolant.
There were two transmutation cells in second layer. 5 long-lived ssion products (LLFP) of93 Zr, 99 Tc, 107 Pd, 129 I and 135 Cs were loaded into transmutation cells with moderator.
In the present calculation, the period of burnup is 5 years and the plant factor is 70 %. Eachyear includes ve burnup cycles and a cooling cycle of 100 days. Each burnup cycle lasts 53 days.

CentralSolenoidVacuum
Vessel888- 888Plasma
31 HYH TF Coil
HH 0Blanket 9  PF Coils
00
Divertor 0@@R

Table 1: Main parameters for calculations
based on JT-60 and ITER
Plasma parameters
Major radius (m)6.2
Minor radius (m)2.1
Plasma volume (m3)884
Plasma temperature (keV) 19
Con nement time (s)1.1Electron density (m03)
4.821019
Fusion power (MW)646
neutron yield (n/s)
2.221020
Neutron wall load (MW/m2 ) 0.40
(average)
Blanket parameters
Total thickness (m)Total volume (m3 )0.38265Figure 3: Cross Section of the Calculation
Model

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Table 2: Material loading arrangement
First Wall side
1st layer
Breeder
2nd layer
Breeder3
3rd layer
Fuel
4th layer
Fuel
5th layer
Breeder
6th layer
Breeder
Vacuum Vessel side
*two of ve regions are replaced
to FP transmutation cell

Table 3: Material composition
Composition of fuel (%)
Reprocessed Pu
Natural UO2
Water
SS316

6.2
40.6
36.7
16.5

Composition of breeder (%)
Li2 ZrO3
Be6 Li enrichment (%)

1090303.2 Validation of Postprocessing

Table 4 shows validity con rmation result of the present making procedure of collapsed crosssection. These 10 nuclei are especially signi cant when estimating the performance of FF hybrid
reactor. The value in the table is the ratio of one-group cross section evaluated by the present
procedure to FM option in MCNP. As shown in the table, present making procedure can besuciently trusted.
Table 4: Validity Con rmation Result of the Present Collapsed Cross-Section Making Procedure
Ratio of Calculated Cross-Section (this method3 / MCNP Tally33 )(n,g)(n,2n)
(n,p)
(n, )
93 Zr
9.998E001 1.000E+00 9.998E001
1.000E+00
99 Tc
1.000E+00 1.000E+00 1.000E+00
1.000E+00
107 Pd9.999E001 9.997E001 1.000E+00
1.000E+00
129 I
9.998E001 1.000E+00 1.000E+00
1.000E+00
135 Cs
9.998E001 1.000E+00 1.000E+00
1.000E+00(n,g)(n,2n)(n,3n)(n,f)
232 Th
9.999E001 9.998E001 9.999E001
1.000E+00
233 U
9.977E001 1.000E+00 1.000E+00
9.993E001
235 U
1.000E+00 9.999E001 9.998E001
9.997E001
238 U
1.000E+00 1.000E+00 1.000E+00
9.996E001
239 Pu9.998E001 1.000E+00 9.999E001
1.000E+00*One-group cross-section estimated by the present procedure*One-group cross-section estimated by dividing the calculated reaction rate by thecalculated total ux

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3.3 Burnup Calculation Results

The present burnup calculation system c an estimate parameters such as e ective multiplication factor (kef f ), power density in fuel cell, neutron ux and changes of nuclide numberdensity. In the present paper, three most signi cant parameters on discussing feasibility of FF
hybrid system are selected.
Figure 4 shows tritium breeding ratio (TBR) and energy multiplication factor and table
5 indicates transmutation performance of 5 LLFPs over the whole burnup period. The mostimportant restriction is to ensure the TBR to be over 1.05 during the operation of fusion reactor.
Figure 4 shows that the TBR is always over 1.2 throughout the burnup period of 5 years. Theenergy multiplication factor is about 10, however decreasing monotonously to around 8. Theseresults indicates that this type of FF hybrid system is feasible. But the results for transmutation
performance is not so excellent. Some of them show even a negative result, meaning increase ofLLFP. Practically, transmutation ratios of 99 Tc, 107 Pd and 129 I are acceptable for performancein the transmutation cell and in the whole blanket as well. However, the amount of 93 Zr and135 Cs are inversely increased compared to their initial inventory. This result suggests further
investigation especially for LLFP transmutation performance.

TBR
Energy Multiplication Factor

1.4

TBR

16141.2

121

100.8

80.6

60.440.22000200

400600800 1000 1200 1400 1600 1800
burnup days
Figure 4: Burnup calculation results for TBR and Energy generation

Energy Multiplication Factor

1.6Table 5: Transmutation Performance for LLFP (%)(decreased percentage per initial load)
93 Zr 99 Tc 107 Pd
129 I
135 Cstransmutation cell 0.9 201586blanket total-2 11
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4 Summary
A general-purpose transport and burnup code system for precise analysis of the fusion ssion
hybrid reactor has been developed. One group cross sections for burnup are updated in eachburnup cycle, which is the most strict method to collapse cross sections. The present calculation
system enables to perform precise neutronics analysis of subcritical systems such as a fusion
ssion hybrid reactor. However, at the moment, one dicult problem is still left, i.e., it takes a
lot of computation time to calculate one-group cross section set.
From the present calculation results carried out with the newly developed calculation system,
it is suggested that FF hybrid reactor is surely feasible from the standpoint of neutronics design.
Further calculation and analysis are nevertheless needed to improve hybrid reactor performance
including nuclear waste transmutation performance.

References
1) I. Murata, et. al., Fusion Eng. Des., 75-79 (2005) 871-875
2) I. Murata, et. al., to be published in the Proc. of the 24th Symposium on Fusion Technology,Warsaw, Poland, September 2006.
3) J. F. Briesmeister (Ed.), MCNP-A General Monte Carlo N-Particle Transport Code, Version
4B, LA-12625-M, 1997.
4) A. G. Cro , Nucl. Technol. 62 (1983) 335-352.
5) http://wwwndc.tokai-sc.jaea.go.jp/nucldata/ .
6) S. Shido, et. al., Proc. of the 2005 Symposium on Nuclear Data, JAEA-Conf 2006-009, P.169.
7) M. Matsunaka, et. al., to be published in the Proc. of the 24th Symposium on Fusion Technology, Warsaw, Poland, September 2006.
8) http://www.naka.jaea.go.jp/ITER/FDR/ .
9) http://www.jaeri.go.jp/jpn/open/press/980625jt-60/index.html (in Japanese).

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