investigation of the effects of the resonance absorption in a fusion breeder blanket

Investigation of the effects of the resonanceabsorption in a fusion breeder blanket

Sumer Sahin*, Hacı Mehmet Sahin, Kadir Yıldız

Gazi Universitesi, Teknik Egitim Fakultesi, Besevler, Ankara, Turkey

Received 13 November 2001; accepted 20 December 2001

Abstract

In generic neutronic studies of a fusion breeder, resonance absorption is mostly neglected.

In this work, the effects of resonances on the neutronic parameters a fast and moderatedfusion blanket are investigated. In the present case, a (D,T) fusion reactor acts as an externalhigh energetic (14.1 MeV) neutron source. The fissile fuel zone, containing 10 rows in radialdirection, covers the cylindrical fusion plasma chamber. The fissile fuel is natural UO2. Fissile

zone is cooled (a) with pressurised helium gas for the fast blanket and (b) with light water forthe moderated, each of them with a volume ratio of Vcoolant/Vfuel=2 in the fissile zone. Thestudy has shown that careful resonance self-shielding calculations are indispensable for neu-

tronic studies of a moderated fusion blanket. On the other hand the omission of the resonanceself-shielding in generic studies of a fast fusion blanket can be tolerated to some degree. Fur-thermore, a correct description of the fusion neutron source spectrum has great importance

on neutronic parameters, along with the resonance self-shielding calculations. # 2002 Pub-lished by Elsevier Science Ltd.

1. Introduction

In fusion–fission (hybrid) neutronic studies, generally the resonance self-shieldingtreatment has been neglected so far. At the present status of generic studies, thissimplification may be tolerated for fast hybrid blankets to some degree. But, inthermal blankets, omission of the resonance self-shielding effects may yield totallymisleading conclusions.The purpose of this work is to investigate the resonance effects on the main inte-

gral data of a (D,T)-driven fusion hybrid blanket, for both a fast as well as in a

Annals of Nuclear Energy 29 (2002) 1641–1660

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0306-4549/02/$ - see front matter # 2002 Published by Elsevier Science Ltd.

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* Corresponding author. Tel.: +90-312-212-43-04; fax: +90-312-212-00-59.

E-mail address: [email protected] (S. Sahin).

moderated system. The neutronic parameters will be evaluated with and without aresonance treatment for the same blanket compositions for the sake of a consistentcomparison.The conventional fusion reaction delivers the external neutron source for the blankets.

Dþ T ! 4 He 3:5 MeVð Þ þ n 14:1 MeVð Þ

The fusion–fission hybrid is a combination of the fusion and fission processes. Thefusion plasma is surrounded with a blanket made of the fertile materials (U238 orTh232) to convert them into fissile materials (Pu239 or U233) by transmutationthrough the capture of the high yield fusion neutrons. This would support the enri-ched fuel supply for the existing light water reactors (LWRs). The fertile materialsmay also undergo a substantial amount of nuclear fission, especially, under theirradiation of the high energetic 14.1 MeV- (D,T) neutrons. In addition to that someof the bred fissile material burns in the hybrid blanket ‘‘in situ’’.

2. Blanket geometry

In the present work, the neutronic analysis is performed on an experimentalhybrid blanket geometry, which has been presented to the international scientificcommunity on different occasions (Sahin et al., 1984, 1986, 1998, 1999). Fig. 1 showsthe basic structure of the hybrid blanket adopted in this work. Table 1 depicts thematerial composition and the geometrical dimensions in the investigated blanket.In this concept, a line neutron source in a cylindrical cavity simulates the fusion

plasma chamber. A first wall made of stainless steel, type SS-304, surrounds thelatter. The fissile zone is made up of natural-UO2 fuel.The fuel zone is cooled with (a) pressurised helium gas coolant for a fast blanket

and (b) with light water for a thermal reactor. The volumetric ratio of coolant-to-fuel is selected as 2:1. The cladding of the fuel rods is made of stainless steel, typeSS-304, as the first wall. In the course of numerical calculations, the fissile fuel zoneis divided into 10 equidistant sub zones, which correspond to the 10 fuel rod rows inthe fissile zone in the radial direction, as shown in Fig. 1.The radial reflector is made of Li2O and graphite in the sandwich structure. This

measure reduces the neutron leakage drastically and leads to a better neutron econ-omy (Sahin et al., 1984, 1986).

3. Numerical calculations

3.1. Calculational tools

The neutron transport calculations have been performed by solving the Boltz-mann transport equation with the SN transport codes (1) ANISN (Engle, 1970) and(2) XSDRNPM (Greene et al., 1997a).

1642 S. Sahin et al. / Annals of Nuclear Energy 29 (2002) 1641–1660

ANISN is used coupled with the 30 groups neutron transport and activity cross-section data library CLAW-IV (Al-Kusayer et al., 1988), processed with TRANSX-2 (MacFarlane, 1993). CLAW-IV represents an extended version of the Los AlamosNational Laboratory (LANL) cross section data library CLAW (Barrett et al.,1979), has point cross section linearization and resonance reconstruction toleranceof 0.5%, and all cross sections are Doppler broadened to 300 �K. The neutron crosssections are averaged over 30 energy groups using the Bondarenko (1964) fluxapproximation with a fusion, fission, 1/E, thermal weight function. The energystructure is such that it has 12, 9 and 9 neutron groups in the MeV, KeV and eVincluding thermal regions, respectively. A global resonance treatment and the group

Fig. 1. Cross sectional view of the investigated blanket (dimensions are given in centimetres).

S. Sahin et al. / Annals of Nuclear Energy 29 (2002) 1641–1660 1643

structure of the CLAW library have been done with special emphasis on fusionneutronic calculations.XSDRNPM is the integrated SN code in the SCALE SYSTEM. The latter

includes the following master neutron cross-section libraries (Jordan et al., 1997);

� the 238 groups library, derived from ENDF/B-V,� the 44 groups library, derived from ENDF/B-V,� the 27 groups library, derived from ENDF/B-IV,� the 16 groups HANSEN-ROACH (Jordan et al., 1997) library.

The resonance calculations can be performed with

� BONAMI (Greene et al., 1997b) for unresolved resonances and� NITAWL-II (Greene et al., 1997c) for resolved resonances.

Table 1

Number densities of atoms in materials and nucleides of the blanket zone

Zone Material Nuclides Dimensions(cm)

Atomic densities (1024cm�3)

Moderated blanket Fast blanket31.3% fuel 31.3% fuel62.6% H2O 62.6% He6.1% SS-304 6.1% SS-304(by volume) (by volume)

Cavity 0–300First wall SS-304 12C 300–301.3 7.873–4 7.873–41

Si 6.734–4 6.734–4Cr 1.728–4 1.728–4Fe 5.926–2 5.926–2Ni 8.055–3 8.055–3

Fuel Nat- UO21H 301.3–313.8 4.178–2

+ Coolant 16O 3.312–2 1.223–2(H2O or He) Si 4.107–5 4.107–5

Cr 1.054–3 1.014–312C 4.802–5 4.802–5Fe 3.614–3 3.614–3Ni 4.913–4 4.913–4235U 4.369–5 4.369–5238U 6.075–3 6.075–3

Tritium breeding zone Li2O6Li 313.8–325.8 4.638–3 4.638–37Li 329.8–334.8 5.704–2 5.704–216O 340.8–344.8 3.084–2 3.084–227Al 3.014–3 3.014–3

Reflector Graphite 12C 325.8–329.8 1.128–1 1.128–1334.8–340.8344.8–360.8

1 Read as 7.873.10�4.Fuel cell geometry: hexagonal lattice; cladding outer diameter: 0.93 cm; cladding thickness 0.0463 cm;cladding material: SS-304; theoretical density of fuel 10.96 g/cm3; sintering density of fuel 80%.


The cell calculations are then performed with the CSAS control module (Landerset al., 1997), which first produces the resonance self-shielded weighted cross-sections(if requested) to be used in the SN code XSDRNPM.The cell-weighted cross-sections are then used in the blanket calculation with the

SN code XSDRNPM, following the cell calculations.Within the framework of the present investigations, one can assume that calcula-

tions with 238 groups-resonance treated cross-sections will have the highest precision,and will represent the benchmark in this work.In the course of all transport calculations with ANISN and XSDRNPM, the

integration of the angular neutron flux has been done in S8–P3 approximation byusing Gaussian quadrature (Sahin et al., 1991a). The numerical output of thetransport calculations have further been processed with the help of the auxiliarycode ERDEMLI (Sahin et al., 1991b) to evaluate specific information for this work.

3.2. Comparison of pertinent cross sections in different libraries

The cross sections will play the major role in transport calculations. Hence, it isuseful to compare the most pertinent cross sections, listed in the selected datalibraries.

Fig. 2. Fission cross section of 235U for the selected libraries. 1: 30 groups Claw-IV library; 2: 238 groups

ENDF/B-V library; 3: 44 groups ENDF/B-V library; 4: 27 groups ENDF/B-IV library; 5: 16 groups

HANSEN-ROACH library.


Fig. 2 shows the fission cross sections of 235U for different libraries. The resonancestructure is well represented in the 238-group library. All other sets can approximatethe resonances only very roughly. Fission cross sections have comparable values inthe energy range of 0.1 MeV <E<10 MeV in all sets. The agreement between thelibraries for <1 eV is also quite good. This energy region is not important for fastassemblies, but it becomes very important for thermal assemblies.Fig. 3 shows the fission cross sections of 238U for different libraries. Similar con-

siderations apply for resonances, as above. Fission cross sections have comparablevalues in the energy range of 0.1 MeV <E in all sets. Below 0.1 MeV, differences incross sections become important, and one can observe a complicated resonance struc-ture. But all cross sections remain below mbarn range. Their contribution to neutronbalance will be lower than other errors in a numerical calculation, and hence negligible.Figs. 4 and 5 show the fission spectrum of 235U and 238U for different libraries,

respectively. Fission spectra w are plotted in w/�U for the sake of a group-indepen-dent presentation and a consistent comparison (Sahin et al., 1991c). There is prac-tically no difference in w between different libraries.Fissile and fusile breeding rates are among the most important data in fusion

breeder studies. Fig. 6 shows the 238U(n,�) reaction, which produces 239Pu. Reso-nance absorption in 238U plays the key role in fissile breeding. The 238-group libraryhas a fine resonance description. All other libraries have a very broad resonancestructure. The differences outside the resonance region become moderate.

Fig. 3. Fission cross section of 238U for the selected libraries. (Legend: as Fig. 2.)


Fig. 4. Fission spectrum of 235U for the selected libraries. (Legend: as Fig. 2.)

Fig. 5. Fission spectrum of 238U for the selected libraries. (Legend: as Fig. 2.)


Fig. 7 shows the main fusile breeding reaction 6Li(n,�)T cross sections. There isonly one broad resonance around 270 keV, covered by a number of energy groups.Differences between the libraries remain only on minor grade.

3.3. Calculation modes

Following calculation modes which have been used, which couple the SN codewith the selected library:

� Blanket calculations with homogenized fuel zone usingmode (1) ANISN and CLAW-IV library without resonance treatment for thecell geometry.

� Blanket calculations using XSDRNPM, supplied with resonance self-shieldedand cell weighted cross-sections in the fuel zone following an appropriateresonance treatment for the cell geometry first with BONAMI and then withNITAWL-II using the following data libraries:mode (2) the 238 groups ENDF/B-V library,mode (3) the 44 groups ENDF/B-V library,mode (4) the 27 groups ENDF/B-IV library,mode (5) the 16 groups HANSEN-ROACH library.

Fig. 6. 238U(n,�) reaction for the selected libraries. (Legend: as Fig. 2.)


The calculation mode (2) with the highest energy group number will represent thebenchmark in the course of the present study.

� Blanket calculations with homogenized fuel zone using XSDRNPM using thefollowing data libraries without resonance treatment for the cell geometry:mode (6) the 238 groups ENDF/B-V library,mode (7) the 44 groups ENDF/B-V library,mode (8) the 27 groups ENDF/B-IV library,mode (9) the 16 groups HANSEN-ROACH library.

Numerical results are discussed in the sections below:

3.4. Neutron spectra

As differentiated quantities, neutron spectra have the greatest importance. Reso-nance effects will occur mainly in the fissile fuel zone. Figs. 8 and 9 show the neutronspectra in the middle of the fissile fuel zone of the moderated and fast blanket,respectively.The fusion neutron source peak around 14 MeV is described clearly by the modes

(1), (2) and (6). On the other hand it is smeared by other modes with 16, 27 and 44neutron energy groups. This will cause an important deficiency for fusion neutroncalculations.

Fig. 7. The 6Li(n,�)T cross sections for the selected libraries. (Legend: as Fig. 2.)


The effects of resonance structure on neutron spectrum are described only with thefine 238-group library [modes (2) and (6)] properly. All other modes with coarsegroup structure were not able to evaluate the neutron spectrum in the resonanceenergies adequately. This may be tolerated to some degree for fast blankets genericstudies, where the neutron flux density begins to decline strongly below keV region,as shown in Fig. 9. But it cannot be tolerated for moderated blankets, where theneutron fluxes in the thermal and resonance regions become very important. Inmoderated blankets, the omission of the resonance self-shielding effects leads to anunderestimation of the neutron flux densities. One can read in Fig. 8, just before theresonance region, that the 238-group library without resonance treatment [mode (6)]calculates the neutron fluxes at 300 keV �20% lower than in mode (2). In theresonance region, one can recognize easily the exaggerated flux sinks in the reso-nance energies in mode (6). Below the resonance region, the flux underestimationincreases to 32.5% at 6 eV, and to 36.5% in thermal energies around 0.05 eV. Thiswill have a direct impact on neutron economy and related neutron reaction rates.

3.5. Fission heating density

As an intermediate differential/integral quantity, fission heating density in themoderated and fast blanket is depicted in Figs. 10 and 11, respectively. In the mod-erated blanket (Fig. 10) when compared with the benchmark mode (2), all other

Fig. 8. Neutron spectrum in the centre of the fuel zone of the moderated blanket with different calcula-

tion modes 1, 2, 3, 4, 5, 6, 7, 8, 9 denote the respective calculation mode.


modes underestimate the absolute values of the fission energy release intolerablylow. Qualitatively, modes with condensed neutron groups, but with resonancetreatment [(3), (4), (5)] are describing the geometrical shape of the fission heatingfunction quite as good. The same applies also for the fine group library (238 groups),but without resonance calculation (6). Libraries of coarse group structure andwithout problem-specific resonance treatment [(1), (7), (8), (9)] fail to calculate thefission heat function in a moderated blanket, neither qualitatively nor quantitatively.In the moderated blanket, thermal fission in 235U is dominating over the fast fis-

sion in 238U. The former decreases towards the left and right sides of the fissile zonedue to the thermal neutron leakage. This phenomenon is well described with reso-nance treatment [modes (2), (3), (4), (5)] and also with the fine group calculationeven without resonance treatment (6), but it is totally ignored using libraries ofcoarse group structure without resonance treatment [(1), (7), (8), (9)], due to thestrongly underestimation of the thermal fission in 235U.In such a fast blanket with an external source, fission heating density has a con-

tinuously decreasing character (Fig. 11). When compared with the benchmark mode(2), the fine group library gives the closest results, even by omission of the resonancetreatment in mode (6) (�1.4% lower), followed by the mode (1) (�4.9% lower).Resonance effects are only minor on the fission heating density. Although othermodes may reflect the qualitative nature quite well, they underestimate the absolute

Fig. 9. Neutron spectrum in the centre of the fuel zone of the fast blanket with different calculation

modes. (Legend: as Fig. 8.)


values of the fission heat by �15–20% below. This quantitative error is caused dueto the failure of the group structure of the related libraries to describe the fusionsource neutron spectrum around 14 MeV correctly.In a fusion blanket, a uniform energy production density would be desirable due

to significant advantages from an engineering point of view with respect to a simplerfuel management scheme (better fuel utilization), higher total power output, andlower temperature and radiation damage gradients throughout the blanket. A verysimple measure for spatial energy uniformity can be given by the peak-to-averagefission power density ratio � in the blanket. One can follow in Tables 2 and 3 thedeviation behaviour of � for different calculation modes from the benchmark [mode(2)] fairly comparable with those deviations as it was observed for the respectedcalculation modes in the case of fission heating density in Figs. 10 and 11, both formoderated and fast blankets, respectively.

3.6. Main blanket parameters

The most pertinent integral neutronic data for the moderated and fast blankets,are shown in Tables 2 and 3, respectively. The comparison of the integral data withthe benchmark calculation [mode (2)] can be summarized as follows:

Fig. 10. Fission energy density in the fuel zone of the moderated blanket with different calculation modes.

(Legend: as Fig. 8.)


� Neutron reactions above a threshold energy in fast neutron groups are lesssensitive to resonance treatment, such as 7Li(n,�n’)T and 238U(n,f ), [seemodes (2) and (6)]. This is not surprising because these reactions lie above theresonance region.

� Neutron reactions in the resonance and thermal energy groups are sensitiveto resonance treatment, such as 6Li(n,�)T, 235U(n,f ) and 238U(n,�), depend-ing on the resonance structure.

� Reaction rates in a moderated blanket are more sensitive to resonance treat-ment than in a fast blanket.

The following sections contain further comments on the integral data, individually.

3.3.1. Tritium productionDirect resonance effects on lithium isotopes will be nil or only minor. The

7Li(n,�n’)T reaction has no resonances. The 6Li(n,�)T reaction has only one broadresonance in the upper energies around 270 keV (see Fig. 7). A fine resolution in neu-tron group structure can describe these cross sections properly. Hence, deviations inTBR values are caused due to the differences in the neutron spectra, which are depen-dent on all parameters of the blanket system, including resonances in fission fuel.

Fig. 11. Fission energy density in the fuel zone of the fast blanket with different calculation modes.

(Legend: as Fig. 8.)


Table 2

Integral neutronic data for the moderated blanketa

Calculation

type

(1) (2) (3) (4) (5) (6) (7) (8) (9)

T6 0.297 (�47.7%) 0.568 0.490 (�13.7%) – – 0.441 (�22.3%) 0.281 (�50.5%) – –

T7 0.080 (2.5%) 0.078 0.042 (�46.2%) – – 0.078 (0.0%) 0.041 (�47.4%) – –

TBR total 0.377 (�41.6%) 0.646 0.532 (�17.6%) – – 0.519 (�19.6%) 0.322 (�50.1%) – –235U(n,f) rate 0.098 (�75.7%) 0.404 0.356 (�11.9%) 0.357 (�11.6%) 0.338 (�16.3%) 0.277 (�31.4%) 0.127 (�68.5%) 0.084 (�79.2%) 0.077 (�80.9%)238U(n,f) rate 0.088 (�18.5%) 0.108 0.086 (�20.3%) 0.084 (�22.2%) 0.059 (�45.4%) 0.098 (�9.2%) 0.072 (�33.3%) 0.069 (�36.1%) 0.045 (�58.3%)

Total fission

rate

0.186 (�63.6%) 0.512 0.442 (�13.6%) 0.441 (�13.8%) 0.397 (�22.4%) 0.375 (�26.7%) 0.199 (�61.1%) 0.153 (�70.1%) 0.122 (�76.1%)

238U(n,�) rate 0.950 (76.3%) 0.539 0.468 (�13.2%) 0.470 (�12.8%) 0.437 (�18.9%) 0.729 (35.2%) 0.761 (41.2%) 0.832 (54.3%) 0.780 (44.7%)

� 1.486 (16.1%) 1.280 1.290 (0.8%) 1.282 (0.2%) 1.294 (1.1%) 1.291 (0.9%) 1.362 (6.4%) 1.424 (11.2%) 1.382 (8.0%)

M 3.727 (�55.9%) 8.447 7.433 (�12.0%) 7.247 (�14.2%) 6.634 (�21.4%) 6.448 (�23.6%) 3.905 (�53.8%) 3.162 (�62.5%) 2.723 (�67.7%)

k1 0.359 (�52.8%) 0.761 0.761 (0.0%) 0.760 (0.1%) 0.761 (0.0%) 0.685 (�10.0%) 0.443 (�41.7%) 0.347 (�54.4%) 0.337 (�55.7%)

L 0.028 (�15.1%) 0.033 0.026 (�21.2%) 0.023 (�30.3%) 0.019 (�42.4%) 0.031 (�6.1%) 0.022 (�33.3%) 0.018 (�45.5%) 0.014 (�57.6%)

a Normalization is made for one 14.1 MeV incident neutron into the blanket.

T6,6Li(n,�)T rate; T7,

7Li(n,�n’)T rate; TBR, tritium breeding ratio; �, peak-to-average fission power density ratio; M, blanket energy multiplication; L, radial neutron

leakage fraction.

[Numbers in parentheses indicate the deviations from the benchmark mode (2)].

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Table 3

Integral neutronic data for the fast blanketa

Calculation

type

(1) (2) (3) (4) (5) (6) (7) (8) (9)

T6 1.080 (�5.1%) 1.139 0.985 (�13.5%) – – 1.075 (�5.6%) 0.921 (�19.1%) – –

T7 0.150 (2.7%) 0.146 0.094 (�35.6%) – – 0.146 (0.0%) 0.094 (�35.6%) – –

TBR total 1.230 (�4.3%) 1.285 1.079 (�16.0%) – – 1.221 (�5.0%) 1.015 (�21.0%) – –235U(n,f) rate 0.014 (�17.6%) 0.017 0.014 (�17.6%) 0.014 (�17.6%) 0.013 (�23.5%) 0.014 (�17.6%) 0.011 (�35.2%) 0.011 (�35.2%) 0.011 (�35.2%)238U(n,f) rate 0.136 (�3.5%) 0.141 0.118 (�16.3%) 0.115 (�18.4%) 0.096 (�31.9%) 0.141 (�0.0%) 0.117 (�17.0%) 0.114 (�19.1%) 0.095 (�32.6%)

Total fission

rate

0.150 (�5.0%) 0.158 0.132 (�16.4%) 0.129 (�18.3%) 0.109 (�31.0%) 0.155 (�1.9%) 0.128 (�19.0%) 0.125 (�20.9%) 0.106 (�32.9%)

238U(n,�) rate 0.319 (29.1%) 0.247 0.194 (�21.5%) 0.206 (�16.6%) 0.188 (�23.9%) 0.309 (25.1%) 0.257 (4.0%) 0.263 (6.5%) 0.242 (�2.0%)

� 1.406 (1.1%) 1.390 1.394 (0.3%) 1.374 (�1.1%) 1.335 (�3.5%) 1.391 (0.07%) 1.399 (0.6%) 1.380 (�0.7%) 1.342 (�3.4%)

M 3.461 (�3.9%) 3.602 3.189 (�11.5%) 2.835 (�21.3%) 2.547 (�29.3%) 3.532 (�1.9%) 3.114 (�13.5%) 2.778 (�22.8%) 2.498 (�30.6%)

k1 0.307 (�11.3%) 0.346 0.360 (4.1%) 0.345 (�0.3%) 0.363 (4.9%) 0.313 (�9.5%) 0.316 (�8.7%) 0.309 (�10.7%) 0.324 (�6.3%)

L 0.076 (�2.6%) 0.078 0.066 (�15.3%) 0.059 (�24.4%) 0.058 (�25.6%) 0.078 (0.0%) 0.066 (�15.3%) 0.059 (�24.4%) 0.058 (�25.6%)

a Legend: same as in Table 2.

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Table 2 includes the tritium production in 6Li (T6) and in7Li (T7) in the moder-

ated blanket. T6 constitutes �88% of the total TBR. Tritium is produced mainly inthe lower neutron energies. Mode (2) can evaluate the thermal neutron spectra witha high precision in a fine energy resolution as well as under consideration of reso-nance effects in heavy nuclides (see Fig. 8). For neutron spectral reasons, T6 isstrongly underestimated without resonance treatment, even with the same 238-groupstructure, namely in mode (6).Comparison of T7 in modes (2) and (3) with (6) and (7) shows, respectively, that

T7 is practically not affected by resonance treatment. On the other hand, a compar-ison of T7 in mode (2) with (3) or that one in mode (6) with (7) shows that it isunderestimated severely by the 44 groups library due the smearing of the fusionsource spectrum in case of a broad first neutron group (8.187–20 MeV). As one cansee in Fig. 8, that the blanket neutron spectra in modes (3) and (7) do not show thetypical fusion source neutron peak. This fact underestimates T7 by almost a factorof 2. In mode (1), despite a modest group number of 30, T7 could be calculatedexcellently, because the source neutron peak is described fairly authentically. How-ever, T7 constitutes only �12% of the TBR. Therefore, a proper resonance treat-ment and furthermore an authentic description of the fusion neutron source areboth required to assess the tritium breeding in a moderated blanket.In the fast blanket, T6 constitutes �88% of the TBR, too. However, neutron

spectrum calculations show only minor variations between different modes, as canbe seen in Fig. 9. Compared to the benchmark [mode (2)], both the fine group cal-culations [mode (6)] (238 groups) without resonance treatment and the coarse groupcalculations (1) (30 groups) with a global resonance treatment are able to calculateT6 quite well (underestimation by �5%). On the other hand 44 group calculationswith [mode (3)] or without resonance treatment [mode (7)] underestimate T6severely. These comparable deviations in T6 and also in T7 with modes (3) and (7)are caused by an improper description of the fusion neutron source, and are practi-cally independent on the resonance treatment. By an appropriate description of thefusion neutron source, both modes (1) and (6) would deliver excellent results for T7and useful values for the total tritium breeding.

3.3.2. Fission reactionsIn a moderated blanket, fission reactions in 235U are dominant over those in 238U,

Table 2, and in a fast blanket vice versa, Table 3. As one can see in Fig. 2, that theresonances in 235U(n,f) below the keV region become very important. Comparedwith the benchmark (2), important underestimation of the integral 235U(n,f) rate inthe moderated blanket appears in the calculations with lower group libraries [modes(3), (4), (5)] despite a resonance treatment in the latter, mainly due to the incorrect-ness in the input of the fusion source spectrum. An omission of the resonancetreatment leads to an incredible underestimation in the 235U(n,f) rate [modes (1), (6),(7), (8), (9)].In the moderated blanket, also the integral 238U(n,f) rate is affected strongly, both

by resonance treatment and group structure. Fission in 238U occurs mainly in theMeV range. Here, the fusion source spectrum becomes more important than the


resonance treatment, as it can be seen in the corresponding 5th reaction line inTable 2. Total fission and fission neutron production rates show similar behaviouras the dominating 235U(n,f) reaction rate.In the fast blanket, the integral 235U(n,f) rate is underestimated with lower group

libraries [modes (3), (4), (5)] even more than in the moderated blanket despite theresonance treatment. Deviations from the benchmark (2) increase by omission ofresonance calculation, but not at the same level as in the moderated blanket. On theother, the integral 238U(n,f) rate is practically not affected by resonances. Anappropriate definition of the fusion neutron source spectrum becomes the mainrequirement. Among the lower group libraries, best results for the integral 238U(n,f)rate in the fast blanket is obtained with the CLAW-IV library, mode (1).In a fusion reactor, total power output is to be calculated with the help of the

energy multiplication (M), which is defined as the ratio of the nuclear heat produc-tion in the blanket to the incident fusion neutron energy. CLAW-IV contains thetotal nuclear energy release data, but SCALE system libraries do not. For the sakeof a consistent comparison between different libraries, only the dominant con-stituents of the nuclear heat production are considered which is the fission energy,followed by the exothermic 6Li heating:

M ¼200� < � ��f > þ4:784 � T6 � 2:467 � T7

14:1þ 1

< ��f >: Total integral fission rateThe contribution of other energy release reactions will be minor and is neglected

in this comparative study.The deviations in M between different calculation modes both for moderated and

fast blankets have a similar behaviour as those in the total integral fission rate, asexpected and shown in Tables 2 and 3, respectively.

3.3.3. Fissile fuel breedingThe fissile fuel production reaction is 238U(n,�) 239Pu. One can see in Fig. 6 that

neutron capture in 238U occurs mainly in the resonance energy region. There-fore, resonance calculations are indispensable for an assessment of the breedingperformance.A comparison of the modes (2) and (6) in Table 2 shows that the fissile breeding in

the moderated blanket is strongly overestimated by an omission of resonance selfshielding. Greatest deviation from the benchmark is observed with mode (1). Arough description of the fusion neutron spectrum underestimates the fissile breeding,as in the cases of modes (3), (4) and (5). On the other hand, these adverse errorscancel each other to some degree in and modes (7), (8), (9) so that the latter despite avery poor neutron source description, end up with relatively lower error values thanmode (1).In the fast blanket calculations, similar error behaviour appears, as shown in

Table 3. Resonance based errors are lower and neutron source based are higher thanin the moderated blanket. Purely by accident, these adverse errors almost cancel


each other so that modes (7), (8) and (9) give very close results to the benchmark (2)for fissile breeding in the fast blanket.

3.3.4. Criticality and leakageA hybrid blanket must be always subcritical throughout the lifetime of the fusion

breeder. For reactor safety keff values must be calculated in a reliable manner. Forthat reason k1 values of the fuel cell have been calculated with all calculationmodes. Omission of the resonance self-shielding with a fine group structure [modes(2) and (6)] underestimates k1 by �10% for both moderated and fast blankets.Alone group reduction has practically no effects on the k1 values of the moderatedblanket and only minor effects on the fast blanket [modes (3), (4) and (5)]. Omissionof the resonance self-shielding with a broad group structure [modes (1), (7), (8) and(9)] underestimates k1 only by �10% for the fast blanket, and dramatically for themoderated blanket (�50%). Hence, reactor safety requires careful calculation ofresonance effects.This relatively low neutron leakage fraction has only moderate effects on neutron

economy. However, it has primary importance for the shielding of superconductingmagnets in a magnetic fusion driver. It is also important for the biological shieldingof all reactor types. In the moderated blanket, omission of the resonance self-shielding alone with a fine group structure [modes (2) and (6) in Table 2] causes aminor underestimation of L, namely �6%. Group reduction with a smearing of thefusion source underestimates the leakage to a higher degree [modes (3), (4) and (5)].By broad neutron group structure, omission of the resonance self-shielding leads toa higher underestimation than by fine groups [modes (1), (7), (8) and (9)].In the fast blanket, resonance shielding practically does not affect the neutron leakage

[compare modes (2), (3), (4), (5) with (6), (7), (8), (9) respectively]. On the other hand,smearing of the fusion source underestimates the leakage greatly [modes (3), (4), (5), (7),(8) and (9)]. Whereas a proper simulation of the fusion source can assess the leakage outof a fast blanket very good despite broad neutron group structure [mode (1)].

5. Conclusions and recommendations

A series of calculations has been carried out to estimate the effects of resonanceself-shielding in fusion–fission (hybrid) blanket calculations. The main conclusionsare as follows:

1. For neutronic studies of a moderated fusion blanket careful resonance self-shielding calculations and cross section weighting must precede the neutrontransport calculations. Otherwise, evaluated blanket data would be com-pletely unreliable.

2. For generic studies of a fast fusion blanket resonance self-shielding calcula-tions have relatively less significance. However, data based reactions mainlyat lower energies would still lead to misleading conclusions, such as fissilebreeding, fission on nuclear fuel, criticality.


3. A further output of this work is the paramount importance of the fusionneutron source spectrum, along with the resonance self-shielding, in calcu-lating the main neutronic parameters. A correct description of the fusionneutron source spectrum over several neutron energy groups is essential tocalculate fission reaction rates, fission heating density, fusile and fissilebreeding rates and neutron leakage accurately. The cross section data setmust have a fine energy resolution between the energies 13 and 15 MeV inorder to fit the fusion neutron source spectrum properly.

Acknowledgements

This work is dedicated to the memory of the beloved Professor Dr. Dieter Emen-dorfer (1927–2001)—doctoral advisor of Professor Sumer Sahin—UniversitatStuttgart, Institut fur Kernenergetik, Stuttgart, Germany. It has been supported bythe Research Fund of the State Planning Organisation of Turkey, Gazi University,Project: # 95 K 120 370 and the Research Fund of the Gazi University, Projects: #07/2001–15 and # 07/2001–17.

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investigation of the effects of the resonance absorption in a fusion breeder blanket

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