Fusion nuclear systems design and analysis

Fusion Engineering and Design 7 (1989) 369-376 North-Holland, Amsterdam

FUSION

NUCLEAR

Yoshiaki OKA’,

SYSTEMS

Kazuo FURUTA

I Deportment of Nuclear Engineering, University of Tokyo, Hongo, Bunkyo-ky

369

DESIGN

AND ANALYSIS

2 and Shunsuke KONDO

ond ’ Nuclear Engineering Tokyo 113, Jopon

Research

’

Loborotory,

Faculty

of Engineering,

Received July 1988

Conceptual design of a power-producing fusion-fission hybrid reactor was carried out based on the new concept of the blanket containing equilibrium fissile fuel. The blanket safety performance was analysed on residual heat removal and accidental criticality. The concept of a direct enrichment fusion breeder blanket using UOr powder was also presented and studied. The impact of uncertainties in neutron cross section data on design parameters such as tritium breeding ratio was analysed including the uncertainties of the secondary angular and energy distribution of neutrons. The uncertainty of the tritium breeding ratio due to cross-sections is about 6% for a commercial tokamak reactor. The errors of the design parameters due to the approximations in the multigroup transport calculation were also quantitatively estimated. The methods for the analyses were developed. The computer codes for nuclear analysis and design were developed. Those are: (1) BISON for one-dimensional transport and burnup calculation, (2) SUSD for the cross section sensitivity and uncertainty analysis, (3) TRISTAN for three-dimensional radiation transport calculation and (4) MEDUSA-IB for one-dimensional hydrodynamic calculation of the implosion and thermonuclear bum of an ion beam driven ICF target.

1. Introduction Conceptual design of a fusion power reactor system is very important in finding problems to be solved and a direction to take. The development of computer codes is also essential to quantify the design. This paper summarizes the work of the fusion reactor analysis and design from neutrouics point of view. It includes, (1) conceptual design and analysis of fusion-fission hybrid reactors for power and fissile-fuel production, (2) uncertainty analysis of the nuclear performance of fusion reactor blankets, (3) development of computer codes for nuclear analysis and design.

2. Fusion-fission

hybrid

reactor studies

A fusion-fission hybrid reactor is a fusion reactor with a blanket containing fissile or fertile material. Fusion neutrons are used in the blanket to cause fission, to produce fissile fuel from fertile or to trausmutate

toxic help were brid

radioactive waste. It is thought that the hybrids early deployment of fusion reactors. New concepts presented and studied on a power producing hyreactor and a fuel producing hybrid reactor.

2.1. Design fusion-fission centration

and safety analysis of a power producing hybrid reactor with equilibrium fissile con-

Power producing hybrids, as well as fuel producing hybrids, have the problem of power increase with fuel bumup. The problem can be mitigated by adding an equilibrium concentration of fissile material to blanket fuel. The concept also provides the possibility to attain high fuel bumup, high power density, a high tritium breeding ratio, flattened spatial power distribution and long-term operation at a constant power level without refueling [l]. The power producing tokamak hybrid reactor based on the equilibrium fissile fuel concept was designed iu order to evaluate the performance of the reactor and to identify technological problems [2]. The conceptual view of the reactor is shown iu fig. 1. It consists of three

0920-3796/89/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

370

Y. Oka, K. Furuta, 1 Toroldol 2 Pololdol 3 Inboard 4 Inboard 5 OutMard 6 OutbOard 7 ExhoUst 8 Coolont

S. Kondo

field toll field toll shield blonket blanket shield duct header

(mm)

Fig. la. Vertical section of the power producing hybrid reactor.

tokamak

kinds of blankets: an inbroad tritium breeding blanket, an outboard tritium breeding blanket and a fuel blanket. The fuel blanket is provided neither on the inboard side nor bebind the toroidal field coils because there is

Fig. lb. Transverse section of the power producing tokamak hybrid reactor.

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no space for thick helium coolant piping to accessthe fuel blanket. The fuel blanket cover ratio to the whole surface of first wall is roughly 38%. The number of toroidal field coils is 14 and the blanket is divided into the same number of sectors by the toroidal field coils. The inboard and outboard tritium breeding blankets are tube-in-shell type in which coolant tubes pass through the tritium breeding material in a structural shell. The thickness of the blanket is 40 cm inboard and 38 cm outboard. Natural Liz0 is used as tritium breeding material. The produced tritium is purged into helium purge gas and recovered continuously. The fuel blanket consists of pressure tubes arranged in 3 stages and 2 rows. Each pressure tube contains a bundle of 199 fuel pins. The fuel pin of 8 mm diameter at 1.8 m in length is like that of GCFR’s (Gas Cooled Fast Reactors) and the surface of cladding is roughened for the promotion of heat transfer. U-Pu mixed carbide containing 12% plutonium discharged from LWRs is used as fuel. Helium coolant enters the pressure tube from the bottom end, rises along the fuel pin bundle and goes out from the top end. The fuel pin is the vented type and volatile FP are purged into the coolant. Austenitic type 316 stainless steel is used as structural and cladding material because we have had much experience with its use and the irradiation data has been accumulated comparatively well. Blanket exchange is carried out in the following manner. The fuel blanket modules between the toroidal field coils are pulled out linearly together with the shield. The outboard tritium breeding blanket modules are next detached from the shield, rotated around the totoidal axis and pulled out. The inboard tritium breeding blanket modules are finally detached from the shield and pulled out linearly. New blanket modules are loaded in the opposite way. The major parameters of the reactor are summarized in table 1. The tokamak employed here is nearly the same dimensions as FER (Fusion Experimental Reactor) of JAERI. The details of the nuclear and thermal hydraulic design are described in ref. [2]. The same problem due to residual heat arises in a hybrid reactor as in a fission reactor. Especially for power producing hybrids, this problem is more serious than for other hybrid concepts, because a large amount of fission products (FP) accumulated in the blanket generate much decay heat. Analysis ‘of blanket safety is very important. Calculation of the residual heating rate after reactor shutdown showed that FP decay heat contributes to most of the residual heat within a short cooling time among%ther source of heat due to delayed neutron and the decay of the actinides and activation

Y. Oka, K. Fututa,

S. Kondo

Table 1 Design parameters of the power producing reactor

tokamak hybrid

Basic parameters

Major radius Plasma radius Aspect ratio Fist wall radius Average neutron wall loading Operation mode Number of TF coils Number of tritium breeding blanket modules Tritium breeding material Hybrid

blanket

Number of canisters Fuel Structural material Fuel rod diameter/pitch Number of fuel rod/canister Heavy metal inventory Power

5.3 m 1.2/1.9 m 4.4/2.8 1.35 m 1 MW/m’ continuous 14 28 (inboard) 14 (outboard) Li,O 658 (“0.88pu0.12)c

316 S.S. 8.0/11.1 mm 199 117 ton

output

Thermal power Gross electric power Net electric power

2786 MWt 879 MWe 627 MWe

products. Transient thermal analysis was performed for emergency reactor shutdown, loss of coolant flow accident, loss of coolant accident and local blockage accident. As a result of calculations it became clear that the required conditions for residual heat removal were less severe than for GCFRs because of the lower power density. However, the complexity of a hybrid reactor will make it necessary to take several measures in order to satisfy thesec conditions. Reactivity analysis for loss of coolant accident, steam ingress accident and blanket melt down accident showed that accidental criticality is not probable for this design. 2.2. Concept and nuclear performance ment fusion breeder blanket using lJ0,

of direct powder

enrich-

The conventional studies on fuel producing hybrids were based on fuel reprocessing after removal from the blanket. Reprocessing, however, is expensive and adds to the cost of the bred fuel for fission burner reactors. A new concept is presented for direct enrichment of fissile fuel in the blanket of a fusion-fission hybrid reactor [3]. The enriched fuel produced by this method can be used in fission reactors without reprocessing. The outstanding feature of the concept is the powdered

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371

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form in which UO, fuel is placed in the reactor blanket, where it is irradiated to requisite enrichment for use as fuel in a burner reactor, e.g. 3%. After removal from blanket, the powder is mixed to homogenize the eruichment. Fuel pellets and assemblies for fission reactors are then fabricated from the powder without reprocessing. The powder is easily produced from purification and de-oxidization of yellow cake, U,O,. In current industrical practice, UO, is deoxidized in a fluidized bed, to produce UO, already in the form of powder. The concept of irradiating UO, in powder eliminates the problems of spatial nonuniformity in fissile enrichment and of radiation damage of fuel clad, encountered in other direct enrichment concepts that assume the irradiation of prefabricated fertile fuel. Powder mixing for homogenization brings the additional benefit of removing volatile fission products. Also, burnable poison can be added, as necessary, after irradiation. There is also the eventual possibility of refueling the powder from the fusion reactor blanket under operation, when the technology of powder transportation is well developed. The disadvantage of the method would be its requiring full remote fabrication of the fuel elements for fission burner reactors, but this difficulty should quickly diminish with the rapid progress seen today in remote-handling technology. The effect of the residual fission products on the reactivity of the fission reactor was estimated to be cancelled if the fissile content is increased only 10%. It does not impose severe penalty on the exposure time in the fusion blanket. An extensive neutron& parameter survey showed that the optimum blanket arrangement for this emichment concept was one presenting a fission-suppressing configuration. The volume fractions of the blanket were 1% natural UO, fuel, 9% natural Li,O, 50% beryllium moderator, 30% helium coolant and 10% structural Table 2 Principal parameters of the fusion breeder Major radius Neutronic load on first wall Fusion power Total thermal power Gross electric power Power required for RF heating, pumping and system support Net electric power Production rate of 3% enriched U-PuO, fuel Blanket coverage: 0.9,

5.0 m 1.0 MW/m2 370 M-w 490 Mwt 147 MWe 147 MWe OMWe

23 t/p Plant factor: 0.9.

312

Y. Oka, K. Furuta, S. Kondo / Furion nuclear systems design

stainless steel. The thickness of the blanket was about 50 cm. The blanket consisted of beryllium blocks traversed by small tubes providing seperate channels for UO, and Li,O. The average enrichment of the UO, powder reaches 3% after 0.56 MW yr/m2 exposure. It is only 7 months to attain this level of exposure with the assumed neutron wall loading 1 MW mm2. The principal parameters of the fusion breeder are summarized in table 2. The size of the tokamak device is similar to INTOR. The reactor will produce 23 tons of 3% plutonium-enriched UO, powder every year. The thermal support ratio (client LWR power to fusion breeder power) would be about 13. The power generated by the fusion breeder would be wholly consumed in the plant for supporting radio frequency heating, for coolant pumping and for other purposes, leaving no net power available for out-of-plant consumption.

3. Uncertainty analysis fusion reactor blankets

of the nuclear

performance

of

In the nuclear design of fusion reactors, it is necessary to assess design parameters such as the tritium breeding ratio (TBR), nuclear heating rate, and shielding performance. These parameters are obtained by neutron transport calculation, and the accuracy of the numerical results is determined by uncertainties in cross-section data as well as approximations assumed in the calculation. We developed the methods for the cross-section sensitivity and uncertainty analysis of the nuclear performance of fusion reactor blankets. We also developed the method for estimating the errors of the numerical solution of the transport equation. The errors and tmcertainties of design parameters such as TBR were quantitatively estimated. 3.1. Cross section sensitivity and uncertainty

analysis

The variance of the response due to the cross section uncertainty can be evaluated by using the covariance matrix of the cross-sections and the sensitivity coefficients of the response to the cross-sections. The sensitivity coefficient is calculated using the first-order perturbation theory. The uncertainty of the secondary neutron energy distribution (SED) and the secondary neutron angular distribution are very important for fusion neutronics analysis. It had not been well considered by the conventional methods. We developed the methods and formats to express SAD/SED uncertainties. The computer code

system, SUSD, was developed for the analysis [4]. The uncertainties of the ‘Li and 7Li cross-section with SAD/SED were evaluated based on IENDG3PRl. The uncertainty of the tritium breeding ratio, the nuclear heating rate and fast neutron leakage flux were analysed on four types of blanket concepts which were used in the blanket comparison selection study (BCSS) of ANL. Details of the analysis are described in ref. [5]. The major result was as follows: (1) The relative standard deviation (RSD) due to the cross-section uncertainty was 2-4% in TBR, 2-34; in the neutron heating and lo-20% in the fast neutron leakage flux from the inboard shield. (2) The uncertainties in SAD/SED had the same order of contribution to the error as that of the excitation function. The type of reactions contributing the error was also clarified. 3.2. The errors of the nuclear performance calculated the multigroup discrete ordinates transport method

by

The numerical solution of the transport equation has the errors associated with the computational method. As for deterministic methods to solve the transport equation, the primary sources of such errors include: (1) incomplete convergence of iterative solution, (2) discretization of space variables, (3) Legendre polynominal expansion of the transfer cross-sections, (4) discretization of angular variables, and (5) multigroup approximation. Emprical estimation of the errors is costly and very time consuming, where calculation is repeated by varying the order of approximations and the results are compared with each other. We developed the method for estimating the errors. It was based on the perturbation theory and was applied to the first three sources of the errors. We estimated the errors of the discrete ordinates transport calculation, such as ANISN, for fusion neutronics problem. The details of the study are described in refs. [6] and [7]. The blanket models were the same as those for the cross-section sensitivity uncertainty analysis. The errors of the tritium breeding ratio and the fast neutron leakage flux from the inboard shield were analysed. The results are listed in table 3 together with the errors due to cross-section uncertainty. The errors associated with iteration, round-off, spatial discretization and P, expansion of the transfer cross-sections were calculated using the perturbation theory. The convergence criterion was 10m3 (point) and 5 x lo-’ (volume). The mesh spacing was 1 cm and the diamond difference

Y. Oka, Table

K. Furuta,

S, Kondo

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3

Comparison

of errors

and tmcertaintics

(in !%) of TBR

and fast neutron

leakage

flux

estimated

Design

parameter:

TBR

Blanket

type

Li/Li

Li,O/H,O

Li/Li

Li,O/H,O

f 5.4

k5.8

k26

*34

Cross-section Iteration

Spatial

uncertainty

‘)

and round-off

0.003

discretixation

Angular

discretixation

P, expansion Multi-group

’ Twice

of the standard

0.02

flux

for fusion

reactor

0.04

0.02

Point convergence <10-s Mesh clcm

- 0.14

3.5

3.2

< 0.1

< 0.09

< 0.5

< 0.3

S6

0.31

6.1

9.1

P3

1.6

-0.8

blankets

Order of approxtmation

-0.19

0.67 approximation

Leakage

factor l/3-1/4

factor l/2-1/3

spacings

42-group

deviations

scheme was used. The order of P, expansion was 4. Those errors were generally small. The errors of tritium breeding ratio associated with the P, expansion of the scattering cross-sections was found to be less than 1%. The errors associated with the cross-section uncertainty were the largest for the tritium breeding ratio. The errors attributed to the multi-group approximation were estimated by comparing the calculations by BISON with multi-group cross-sectionsand MCNP with the continuous energy cross sections. BISON is the one-dimensional transport and bumup calculation code developed by us [8]. The transport calcualtion scheme is the same as that of ANISN. The neutron flux of the multigroup BISON calculation agreed well with that of the continuous energy MCNP calculation in the blanket. In the reflector and shield the fast neutron leakage flux was, however, greatly underestimated by the multigroup BISON calculation as shown in the last row of the table 3. The energy group structure and the selfshielding factors take a very important role for the accuracy for multigroup calculation. The details of the result are described in ref. [7]. 4. Computer code development for nuclear analysis Several computer codes were developed for the design and analysis of fusion reactors. The features of the codes are described briefly in the followings. The codes except TRISTAN are available from BSIC (Radiation Shielding Information Center) of OBNL, OECD/NEA data bank and Nuclear Data Center in Japan.

nuclear

313

4.1.

BISON

BISON (Bumup of Isotopes and One-dimensional transport) is a one-dimensional transport and bumup calculation code [8,9]. The one-dimensional Boltzmann transport equation is solved by the discrete ordinates method in order to obtain neutron and gamma-ray flux. Transport calculation of BISON is based on the one-dimensional discrete ordinates code ANISN but some of the options of ANISN such as buckling search for fission reactor analysis were removed. BISON becomes a very compact code. The production-depletion equations for nuchdes such as U, Th and Li are solved by the Bateman’s method using the obtained flux. The calculated atomic densities are used to obtain new flux in the next time step. The procedure is repeated for the blanket-life time. Other nuclear performances such as heating rate and radiation damage rate, are also easily calculated by BISON. Two kinds of nuclear data libraries are required for BISON calculation. One is a group-independent crosssection library for the transport calculation, and the other is a nuclear data library for bumup calculation. The libraries for the purpose are provided and called BISON library. They are, (1) the coupled neutron and gamma-ray cross-section library with 42 neutron and 21 gamma-ray energy group structure up to P5 Legendre scattering terms and (2) the bumup library for U-Pu and Th-U fuel cycle calculation and Li-T fusion fuel calculation. The revised version, BISON 1.5, supports the capability of adjoint calculation [8]. It is also a part of the

374

Y. Oka, K. Furu~a,

1

1

SEAOR

S. Kondo

1

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uncertaintyanalysis.

SUSD code system for sensitivity and uncertainty analysis. The data input has been simplified by free format. BISON has frequently been used for the design and analysis of fusion reactors and fusion-fission hybrid reactors. The change of nuclear performance with fuel bumup is easily calculated by the code. The nuclear design of all the conceptual fusion reactors and the hybrid reactors was carried out using BISON at the Nuclear Engineering Research Laboratory of the University of Tokyo. 4.2. SUSD

SUSD (Sensitivity and Uncertainty with Secondary Distributions) is a code for sensitivity-uncertainty analysis including the effect of secondary neutron angular distribution (SAD) and secondary neutron energy distribution (SED) [4]. The role of SUSD is schematically shown in fig. 2. The forward and adjoint flux are calculated by ANISN, BISON and DOT 3.5. GROUPR and ERRORR are the modules of the NJOY code system which was developed at Los Alamos Scientific Laboratory. They are used for the generation of the group-cross sections and the group covariance matrix, respectively. PUFF-2 is the module similar to ERRORR. We have newly developed GROUPSR and SEADR. GROUPSR is used for generating SAD partial

systems

design

transfer matrix for SAD sensitivity analysis. SEADR is used for preparing the multigroup SAD/SED covariante matrices. The code stores the moment matrix and the sensitivity coefficients. The calculation can be restarted using the data. The variance and standard deviation of detector responses and design parameters can be obtained using the covariance matrices and the sensitivity coefficients. The code was used for estimating the uncertainty of TBR, etc. as described in section 3. 4.3.

Fig. 2. The role of SUSD for the cross section sensitivityand

nuclear

TRISTAN

TRISTAN was developed to solve the transport equation in three-dimensional (X, Y, Z) geometry [lO,ll]. The solution technique is the method of direct integration. It is a type of the method of characteristics based on analytical integration along the radiation trajectories in several directions. The method is suitable for the radiation shielding problems because of its exactness in the treatment of the streaming term of the transport equation. TRISTAN uses multi-group crosssections and conservation of radiation flux restored by a balance equation. It also contributes to the high accuracy of the calculation. Numerical integration of double-differential cross-sections is applied to represent, precisely, the anisotropic scattering instead of using the Legendre polynominal expansion. TRISTAN includes several techniques such as separation of the flux into the scattered and unscattered components. The principal features that enhance the applicability of TRISTAN is the utilization of stratification of angular mesh and an adjoint solution to reduce the required computational time. The accuracy of TRISTAN was verified by comparing with the results of the Monte Carlo code MCNP. The comparison was also carried out with the experimental values of the fission neutron streaming through a 1.5 m long annular air duct in water [ll]. The result is depicted in fig. 3 together with the calculation by other Japanese three-dimensional transport codes, PALLAS and ENSEMBLE. The calculation of TRISTAN showed the most satisfactory agreement with the experiment. Further verification of the code is being carried out by analysing our fusion neutron streaming benchmark experiment for iron and polyethylene which is funded from the Grant in Aid for Fusion Research of the Japanese Government [12,13]. 1 4.4.

MEDUSA-IB

MEDUSA-IB is a one-dimensional hydrodynamic code for implosion and thermonuclear bum calculation

Y. Oka,

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50 from

100 duct

K. Fun&,

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of an ion-beam driven ICF target [14,15]. Plasma-hydrodynamics of MEDUSA-IB are based on the onedimensional, two-temperature, Lagrangian code, MEDUSA, which was developed at Culham Laboratory in UK for laser fusion. MEDUSA-IB, however, includes multigroup X-ray, alpha-particle and neutron transport models. Temperature dependence of ion-beam energy deposition is also considered. This enables the code to carry out accurate simulation of the fusion target behavior. Estimation of radiation spectrum from a fusion target is very important for fireball calculation in a surrounding buffer gas and for ICF reactor cavity design. Effects of radiation, alpha-particle and neutron transport on fusion yield and radiation spectra were clarified from the analysis using the code [15]. The analysis of a bare 1 mg DT target ignition showed that only neutron transport slightly decreases fusion yield. The analysis of a reactor-size hollow single shell target containing 4.2 mg DT fuel (UTLIF target) showed that radiation and alpha-particle transport, temperature dependence of ion beam stopping and the equation of states decreased fusion gain when they were considered accurately. Neutron transport slightly increased the gain. The momentum deposition of the ion beam and alpha-particles had very slight effects. The results are summarized in the table 4. The code was used for the design of our conceptual light ion-beam fusion reactor, UTLIF [16].

150 mouthkm)

Fig. 3. Comparison of the experimental Ni-58 (n, p) Co-58 reaction rates in the annular duct with the calculation by the Japanese three-dimensional transport codes, TRISTAN, PALLAS and ENSEMBLE. Table 4

Effect of transport models and equation of states on fusion yield of UTLIF target No.

Term Transport model Radiation

1 2 3 4 5 6 I 8

EOS Alpha

Neutron

on on off IG all deposit off off F-D on off off F-D on on off F-D on on on F-D on on off F-D With H+ momentum deposition on on off F-D Without temperature effects on H+ beam stopping on on off F-D Without alpha-particle momentum deposition

EOS: equation of states, F-D: Fermi-Dirac, IG: ideal gas

Released energy from target (MJ) Radiation

Gain

Neutron

Total

689.6 536.6 405.6 355.2 386.0 386.3

863.2 675.3 510.0 444.0 483.2 482.9

237.1 185.5 140.1 121.9 132.7 132.7

137.2 71.5 71.0 76.9 72.9

Charged particle 36.4 138.7 26.9 17.8 20.3 23.7

98.5

24.9

492.1

615.5

169.1

71.0

19.6

362.3

452.9

124.4

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5. summary

The results of the study on the fusion reactor systems design and analysis are briefly reviewed. They are (1) design of the fusion-fission hybrid reactors, (2) uncertainty of the nuclear performance of the fusion reactors, and (3) computer code development for nuclear analysis. The design and analysis of fusion nuclear systems will take a more important role than in the past for the development of fusion reactors.

References

[8]

[9] [lo]

[ll]

PI Y. Oka, K. Furuta and S. An, Concept and nuclear

PI 131

[41

PI

performance of power-producing fast fission blankets for fusion-fission hybrid reactors using equilibrium fissile fuel, J. Nucl. Sci. Technol. 19 (1982) 166-168. K. Furuta, Y. Oka and S. An, Design and safety of power producing fusion-fission hybrid reactor, Nucl. Engrg. Des. Fusion 1 (1984) 255-263. Y. Oka, T. Kasahara and S. An, Concept and nuclear performance of direct-enrichment fusion breeder blanket using UOa powder, J. Nucl. Sci. Technol. 22 (1985) 165-173. K. Furuta, Y. Oka and S. Kondo, SUSD, A computer code for cross section sensitivity and uncertainty analysis including secondary neutron energy and angular distributions, UTNL-R-0185 (March 1986) (in Japanese), ORNL/TR-88/18 (English translation, 1988). K. Furuta, Y. Oka and S. Kondo, A cross-section sensitivity and uncertainty analysis on fusion reactor blankets with SAD/SED effect, Nucl. Engrg. Des/Fusion 3 (1986)

[12]

[13]

(141

[15]

287-300.

161K. Furuta, Y. Oka and S. Kondo, Development of method based on perturbation theory for estimating and correcting errors in numerical solution of transport equation, J. Nucl. Sci. Technol. 24 (1987) 173-180. [71 K. Furuta, Y. Oka and S. Kondo, Accuracy of multi-group

[16]

nuclear

systems

design

transport calculation in D-T fusion neutronics, J. Nucl. Sci. Technol. 24 (1987) 333-339. K. Furuta, Y. Oka and S. Kondo, BISON 1.5, A onedimensional transport and bumup calculation code, Nuclear Engineering Research Laboratory, University of Tokyo Report, UTNL-R-0203 (February 1987). K. Furuta, Y. Oka and S. An, BISON, A one-dimensional transport and bumup calculation code, UTNL-R-0141 (September 1982). T. Ida, Y. Oka, S. Kondo and Y. Togo, TRISTAN, A three dimensional radiation transport calculation code by the direct integration method, UTNL-R-0204 (March 1987). T. Ida, S. Kondo, Y. Togo and Y. Oka, Development of radiation transport code in three dimensional (X, Y, Z) geometry for shielding analysis by direct integration method, J. Nucl. Sci. Technol. 24 (1987) 181-193. Y. Oka et al., Measurement of fast neutron streaming with plastic track recorders registering recoil protons, in: Proceedings of the Topical Conference on Theory and Practices in Radiation Protection and Shielding, April 22-24, 1987, Knoxville (American Nuclear Society, 1987) pp. 93-102. Y. Oka et al., Fusion neutron streaming benchmark experiment and the analysis by the three-dimensional transport calculation code, TRISTAN, submitted to Intemational Symposium on Fusion Nuclear Technology, April, 1988, Tokyo. M. Uchida, Y. Oka and S. An, MEDUSA-IB, A one-t& mensional implosion and bumup calculation code for ion beam driven inertial confinement fusion target, UT’NL-R0168 (October 1984). M. Uchida, Y. Oka, M. Akiyama and S. An, Simulation of multigroup X-ray, alpha-particle and neutron transport in ion beam driven ICF target, J. Nucl. Sci. Technol. 22 (1985) 683-696. H. Madarame et al., A conceptual design of light ion beam fusion reactor-UTLIF (2), Nucl. Engrg. Des. Fusion 1 (1984) 387-407.