B-VI, EFF-1 and EFF-2 beryllium data evaluations for neutron transport calculations

ELSEVIER

Fusion Engineering and Design 28 (1995) 624 635

Fusion Engineering and Design

Benchmark analyses of the ENDF/B-VI, EFF-1 and EFF-2 beryllium data evaluations for neutron transport calculations U. Fischer, E. Wiegner Association KfK-Euratom, Kernforschungszentrum Karlsruhe, Institut f~r Neutronenphysik und Reaktortechnik, PO Box 36 40, D-76021 Karlsruhe, Germany

Abstract

The beryllium data evaluations by Perkins et al. (ENDF/B-VI), Field et al. (EFF-2) and Young and Stewart (EFF-1) are analysed with regard to their use in neutron fusion applications. There are considerable differences in the secondary energy and angle distributions with a strong impact on the neutron transport in beryllium. For EFF-2 and ENDF/B-VI data there are severe discrepancies with measured double-differential cross-sections at several energies and angles. A preference for the EFF-1 beryllium data can be deduced from the analysis of transmission experiments on spherical beryllium assemblies with measurements of the neutron leakage spectra. Owing to compensation effects the calculated neutron multiplication factors of beryllium are not very sensitive to the different beryllium data evaluations.

1. Introduction

Beryllium is the most favoured neutron multiplier candidate for solid breeder blankets of both "next step" fusion machines (e.g. ITER) and demonstration power reactors. Hence there is a need for high-quality nuclear data suitable for describing 14 MeV neutron transport phenomena in beryllium. Several beryllium data evaluations are available, which, in principle, are appropriate for this purpose: the L L N L evaluation by Perkins et al. [ 1], incorporated into the ENDF/B-VI data library and selected for the Fusion Evaluated Nuclear Data Library FENDL, the recent evaluation by Field et al. (University of Birmingham, UK) [2], performed for the European Fusion File EFF-2, the L A N L evaluation by Young and Stewart [3], adopted in the EFF-1 data file,

and the evaluation of Shibata [4], performed for the Japanese Evaluation Nuclear Data Library JENDL-3. All of these data evaluations provide double-differential (n, 2n) cross-sections, but using very different approaches for constructing them. This has resulted in very different secondary energy (SED) and angle (SAD) distributions, which have a strong impact on the neutron transport in beryllium. Apart from this there is a significant difference in the (n, 2n) cross-section, which around 14MeV neutron incidence energy is about 10% higher in the L A N L evaluation than in the others. In this paper, we analyse the quality of the ENDF/BVI, EFF-1 and EFF-2 beryllium data evaluations with regard to their use in neutron transport calculations. The analysis involves the following three stages. First,

0920-3796/95•$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0920-3796(94)00342-4

U. Fischer, E. Wiegner / Fusion Engineering and Design 28 (1995) 624 635

SED and SED/SAD data, processed from the underlying nuclear data files at 14MeV neutron incidence energy, are compared with measured DDX data. Second, comparisons are performed for simple calculational benchmarks using different computational procedures. Third, comparisons are performed for available simple and clean benchmark experiments in spherical geometry, providing measured data for the neutron leakage spectra. This three-stage approach allows a qualified assessment of the analysed beryllium crosssection data for use in neutron fusion applications.

2. Beryllium data evaluations 2.1. L A N L evaluation

This evaluation was performed by Young and Stewart in 1979 [3] with the main purpose of providing suitable data in ENDF/B format that accurately represent the 9Be double-differential cross-sections measured by Drake et al. in 1977 [5]. To achieve this goal, the so-called pseudo-level technique was used to represent the DDX data: for a series of excitation energy bins the excitation functions and the associated angular distributions are given on the file. Thus the continuum-neutron emission is described by a sum of discrete pseudo-levels that can be handled like discrete inelastic scattering levels in the conventional way by the processing codes. Note that Young and Stewart did not perform a "physical evaluation" of the 9Be D D X data but instead performed numerical fits to Drake et al.'s experimental data using smooth inter- and extrapolations. The L A N L evaluation has been adopted in the EFF-1 data file. The angular distributions of both the elastic and inelastic (n, 2n) scattering are given in terms of Legendre polynomials on the data file.

Table 1 Comparison of 9Be reaction cross-sections (barn) at 14 MeV neutron incidence energy (averaged over the interval 13.914.2 MeV) Cross-section

EFF-1

EFF-2

ENDF/B-VI

O-tot %,zn ~r~j ano~lel

1.503 0.522 0.952 0.551

1.5124 0.4853 1.010 0.514

1.5124 0.4853 1.010 0.514

625

2.2. L L N L evaluation

This evaluation was performed by Perkins et al. in 1985 [1] for ENDF/B-VI using a Monte Carlo technique to construct the double-differential (n, 2n) crosssection. Use was made of experimental D D X data measured by Drake et al. [5], Baba et al. [6] and Takahashi et al. [7]. The evaluated DDX data were obtained in specified energy and angular bins and are represented as tabulated functions, i.e. pointwise in energy and angle in the laboratory system on file 6 of ENDF/B-VI. Elastically scattered neutrons are described by pointwise angular distributions in the centreof-mass system. Thus, the LLNL evaluation avoids any approximation of the angular distribution of the scattered neutrons in terms of Legendre polynomials. This data representation is appropriate for rigorous SN transport calculations in which D D X data are used directly in the segmented angular space without the need for Legendre polynomial approximations [8]. The 9Be (n, 2n) reaction cross-section obtained in the L L N L evaluation is very close to those used in ENDF/B-V and in the LANL evaluation. Based on more recent differential measurements, this cross-section has been reduced for ENDF/B-VI, although not documented. Therefore, the 14 MeV (n, 2n) cross-sections of E N D F / B-VI and EFF-1 differ by approximately 10% (see Table 1). 2.3. EFF-2 evaluation

This is the most recent 9Be evaluation, performed by Field et al. (University of Birmingham, UK) [2] for the European Fusion File. It can be regarded as an update of the ENDF/B-VI evaluation; it uses the same excitation functions (e.g. see Table 1) and angular distributions for elastic scattering, but a very different approach for the construction of the double-differential (n, 2n) cross-section. In this approach an exact analytical model is used for the kinematic description of the different many-particle break-up reactions contributing to the (n, 2n) process. Use is made of Drake et al.'s experimental DDX data and of the evaluated data of Perkins et al. The evaluated double-differential (n, 2n) cross-section data are stored in file 6 of EFF-2, adopting a tabular representation both for the continuum part and for a separated sharp peak which describes inelastic scattering at the 2.429 MeV level in 9Be. To facilitate the processing of this unusual representation with the NJOY code [9], a derived file was generated by Hogenbirk et al. [10] in which the sharp peak has been

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U. Fischer, E. Wiegner / Fusion Engineering and Design 28 (1995) 624-635

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3. Secondary energy distributions Graphical comparisons of the different beryllium SED are shown in Fig. 1 along with experimental neutron emission spectra measured by Drake et al. [5] and Takahashi et al. [11] at 14 MeV neutron incidence energy. The processed E N D F / B - V I and EFF-1 and -2 beryllium SED were obtained by angular integration of the total scattering matrices in the 14 MeV neutron source group of a slightly modified G A M - I I group structure (13.9-14.2MeV). Note the very different

shape of the neutron emission spectrum in its continu u m part around and below 1 MeV. The use of Drake et al.'s and Takahashi et al.'s data in the E N D F / B - V I and EFF-1 evaluation is clearly reflected in the evaluated emission spectrum. The recent EFF-2 evaluation, although based on Drake et al.'s data, underestimates the measured SED in the continuum part around 1 MeV. It overemphasizes, however, the 6.7 MeV level excitation resulting in an overestimation of the emission spectrum between 4 and 6 MeV. Comparisons of the SED at selected scattering angles with measured D D X data of Takahashi et al., Drake et al. and Baba et al. [12] are shown in Figs. 2 and 3. Again there are significant differences between the E F F 2 evaluation and the measured D D X data with strong

Fig. 2. Secondary energy distribution of 9Be (n, xn) at a scattering angle of 60° in the laboratory system(14MeVneutron incidence energy). Fig. 3. Secondary energy distribution of 9Be (n, xn) at a scattering angle of 150° in the laboratory system (14MeV neutron incidence energy).

U. Fischer, E. Wiegner / Fusion Engineering and Design 28 (1995) 624-635

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overestimations at forward angles and strong underestimations at backward angles. The ENDF/B-VI data show a relatively good agreement at forward angles with a slight overestimation of the 6.7 MeV level excitation, but a strong underestimation of the continuum emission spectrum at backward angles. The L A N L evaluation shows an overestimation of the continuum part at small forward angles (with respect to Takahashi et al.'s data), but good agreement at scattering angles larger than 50 °, including the backward region. In addition, the 6.7 MeV level excitation seems not to be overestimated in this evaluation. The observed overand underestimations at different angles and secondary energies will lead to compensation effects in calculating neutron transport beryllium assemblies with different layer thicknesses.

4. Benchmark calculations

Benchmark calculations have been performed for beryllium spherical shell assemblies with a central 14 MeV neutron source and shell thicknesses of 5 and 30 cm. The transport calculations were performed with the O N E T R A N code [13] using the SN/PL approximation procedure in the conventional way and the ANTRA1 code [8] applying a direct numerical integration scheme for the scattering integral without the need to use Legendre polynomials. In the latter case a special type of scattering matrices, called angular segmented scattering (ASS) matrices, has to be provided. For the ENDF/B-VI and EFF-2 beryllium data the processing of appropiate ASS matrices is straightforward: the D D X data, given as tabulated functions on the files, are integrated over specified angular segments corresponding to those of the subsequent SN calculations. Thus, ENDF/B-VI- and EFF-2-based ANTRA1 calculations for beryllium do not rely on any kind of Legendre polynomial approximation, either in the underlying cross-section data or in solving the transport equation. In using the O N E T R A N code with ENDF/B-VI and EFF-2 beryllium data, scattering matrices of the conventional PL type have to be provided. In this case, the tabulated D D X data given on the file are numerically

fitted to a truncated Legendre polynomial series expansion by the NJOY processing code [9]. The impact on the calculated leakage spectra of the Legendre polynomial fit approximation is shown in Figs. 4 and 5 for EFF-2 data. In the case of a thin 5 cm thick beryllium spherical shell, rigorous ANTRA1 calculations agree well with approximate ONETRAN/PL calculations. In the case of a 30 cm thick spherical shell there is a slight disagreement, which means that the solution of the SN/P L calculation does not converge towards the exact one. A similar observation has been made previously for ENDF/B-VI data [14]. The impact on the calculated leakage spectra of the different beryllium evaluations is more severe. Figs. 6 and 7 show the spectra calculated by ANTRA1 for 5 and 30 cm thick spherical shells, respectively. Note the very different shapes of the calculated leakage spectra caused by the different SED/SAD of the beryllium data evaluations and the associated exicitation functions as discussed above. In particular, the strong differences between the ENDF/B-VI and EFF-2 spectra are only due to the different SED/SAD of the (n, 2n) reaction. The total number of neutron leakages from the beryllium spheres, however, is not very sensitive to the beryllium data evaluations used. This is due to the fact that the 9Be (n, 2n) reaction rate depends both on its excitation function and on the energy and angle distribution (SED/SAD) of the emitted neutrons. A harder SED, for instance, can in addition to the primary neutrons induce more (n, 2n) reactions than a softer SED. This effect becomes significant for shell thicknesses of several mean free paths, where multiple collisions are more probable. This is observed by comparing EFF-2- and ENDF/B-VI-based calculations (with identical (n, 2n) cross-sections but different SED/SAD) with E F F - l - b a s e d calculations for beryllium spherical shell assemblies of varying thickness (Table 2). Note that the difference in the 9Be (n, 2n) cross-section amounts to about 10% between EFF-1 data on the one hand and EFF-2 and ENDF/B-VI data on the other. This roughly corresponds to the maximum difference in the 9Be (n, 2n) reaction rate (given by M - 1 in Table 2) which is obtained for small shell thicknesses. For larger shell thicknesses this difference reduces to

Fig. 4. Neutron leakage spectra of a 5 cm thick beryllium spherical shell: comparison of EFF-2-based ANTRA1 and ONETRAN calculations. Fig. 5. Neutron leakage spectra of a 30 cm thick beryllium spherical shell: comparison of EFF-2-based ANTRA1 and ONETRAN calculations.

629

U. Fischer, E. Wiegner / Fusion Engineering and Design 28 (1995) 624-635

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about 3-4%. If the source neutron is accounted for in the balance, as is done for instance in an integral multiplication experiment, the difference in the calculated total neutron leakages is not more than 2% at the maximum.

5. Comparisons with integral experiments 5.1. Total absorption experiments In the past decade, several total absorption experiments on beryllium spherical shells have been performed to measure the total neutron leakages from the spheres (e.g. [15-17]). The most recent and consistent set of measurements was performed by Smith et al. at the INEL Laboratories [17]. In analysing the experiment with detailed 3d Monte Carlo calculations, perfect agreement was found with the L A N L Be evaluation. Likewise, a slightly worse agreement, being well within the experimental uncertainty of 3-4%, was obtained with the ENDF/B-VI beryllium data. Based on one-dimensional calculations with the ANTRA1 code, identical results with EFF-2 and ENDF/B-VI data were obtained for the INEL beryllium assemblies. From the discussion above it is clear, however, that total absorption experiments by themselves cannot be sufficient to decide if the beryllium data evaluations in question are satisfactory for neutron fusion applications [18]. 5.2. Measurements o f the neutron leakage spectrum Neutron leakage spectra from beryllium spherical shells have been measured in transmission experiments at IPPE Obninsk [19] and KfK [20,21]. Shell assemblies with thicknesses of 5 and 17cm were used in the experiments at IPPE Obninsk and KfK, respectively, the results of which are taken into account in this paper. For the Obninsk transmission experiment the calculated leakage spectra are compared with the measured spectrum in Fig. 8. In these calculations the experimental source neutron spectrum shown in Fig. 9 was used. No preference can be deduced from this comparison with regard to the quality of the beryllium data used. A

more detailed comparison obtained by integrating both the measured and the calculated leakage spectra arbitrarily over specified energy windows (Table 3) shows that for all beryllium data used C/E is near unity for the total neutron leakages due to compensating effects. Note, however, that the L A N L evaluation gives the best overall agreement and that for ENDF/B-VI and EFF-2 data there is a strong underestimation of the neutron leakages below 1.4 MeV neutron energy, which should be due to the lower (n, 2n) cross-section used in these evaluations. For the K A N T (Karlsruhe Neutron Transmission) experiment on the 17 cm thick beryllium spherical shell, the calculated leakage spectra are compared with the measured spectrum in Fig. 10. There is nearly perfect agreement with the measurement for the E F F - l - b a s e d calculation. For ENDF/B-VI data there is a severe underestimation in the evaporation part of the spectrum (around 1 MeV). This is due to the reduced cross-section of the (n, 2n) reaction which primarily populates this energy range. In the case of the EFF-2 data, this effect is compensated by a harder SED of the neutrons emitted in the (n, 2n) reaction. In the K A N T experiment, the neutron leakage spectrum was measured from 15 MeV down to thermal energies by applying different spectroscopic techniques [20,21]. In addition, the experiment was analysed by Monte Carlo calculations with the MCNP code and the L A N L Be data, applying a detailed three-dimensional model of the beryllium assembly, the target chamber and the neutron detection system. Good agreement was obtained between the three-dimensional EFF-l-based M C N P calculation and the measured spectrum down to thermal energies (see [21]). In the case of the one-dimensional E F F - l - b a s e d calculations there is agreement with both the three-dimensional MCNP calculation and the measured spectrum down to about 0.4 eV. There is a well established Maxwellian distribution below 0.4 eV which cannot be reproduced by the ANTRA1 calculation because of missing upward scattering data. In addition, neutron streaming through the openings in the spherical shell cannot be handled with a one-dimensional calculation. For these reasons, there is a discrepancy in the total neutron leakages calculated by ANTRA1 (one-dimensional) and MCNP (three-dimensional) for this beryllium assembly when using the same

Fig. 6. Neutron leakage spectra of a 5 cm thick beryllium spherical shell: comparison of EFF-1-, EFF-2- and ENDF/B-VI-based ANTRA1 calculations. Fig. 7. Neutron leakage spectra of a 30 cm thick beryllium spherical shell: comparison of EFF-1-, EFF-2- and ENDF/B-VI-based ANTRA1 calculations.

U. Fischer, E. Wiegner / Fusion Engineering and Design 28 (1995) 624 635

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632 Table 2

Neutron balance for beryllium spherical shells with a central 14 MeV neutron source, results of one-dimensional ANTRA1 calculations using the given data Shell thickness

EFF-1

(cm)

L

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M

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1.36 1.68 2.01 2.18

0.03 0.07 0.15 0.38

1.40 1.75 2.15 2.56

1.34 1.65 1.97 2.14

0.03 0.07 0.15 0.41

1.38 1.72 2.12 2.55

1.34 1.65 1.96 2.14

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ENDF/B-VI

L = Neutron leakages per source neutron; A = total neutron absorptions per source neutron; M = A + L = total neutron multiplication factor.

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underlying EFF-1 beryllium data. Note, however, that this discrepancy is due only to the insufficient description of the experiment by the one-dimensional transport code. From the K A N T transmission experiment, a preference for the L A N L beryllium data evaluation can be deduced.

6. Conclusion

The beryllium data evaluations of the ENDF/B-VI, EFF-1 and EFF-2 data files have been analysed with regard to their use in neutron fusion applications. Very different secondary energy and angle distributions, in

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U. Fischer, E. Wiegner / Fusion Engineering and Design 28 (1995) 624-635

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EFF-2

ENDF/B-VI

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0.83 0.88 1.14 1.29 1.12 0.86 0.98 0.98

0.88 0.81 0.96 1.09 1.05 0.89 0.98 0.96

addition to different excitation functions in particular for the (n, 2n) reaction, have been found to be responsible for the observed under- and overestimations in comparing calculated and measured neutron leakage spectra from spherical beryllium shells. Based on the analysis of these experiments, a preference for the

L A N L beryllium data evaluation, contained in the EFF-1 file, can be deduced, and the observed deficiencies call for improvements in the E F F - 2 and the E N D F / B - V I data evaluation. Owing to compensating effects, the calculated total number of neutron leakages and, consequently, the neutron multiplication of beryl-

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U. Fischer, E. Wiegner / Fusion Engineering and Design 28 (1995) 624-635

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lium are insensitive to the beryllium data evaluations used. Therefore, total neutron absorption experiments are not sufficient to arrive at a qualified assessment of the beryllium data evaluations for use in neutron transport calculations.

Acknowledgement This work was performed in the framework of the Nuclear Fusion Project of the Kernforschungszentrum Karlsruhe and is supported by the European Communities within the European Fusion Technology Programme.

[3]

[4] [5]

[6]

[7]

References [1] S.T. Perkins, E.F. Plechaty and R.J. Howerton, A reevaluation of the 9Be (n, 2n) reaction and its effect on neutron multiplication in fusion blanket applications, Nucl. Sci. Eng. 90 (1985) 83. [2] G.M. Field, T.D. Beynon and H. Gruppelaar, Modelling inelastic emission cross-sections for 9Be (n, 2n), presented

[8]

[9]

at the Int. Conf. on Nuclear Data for Science and Technology, Jiilich, Germany, 13-17 May, 1991. P.G. Young and L. Stewart, Evaluated data for n + 9Be reactions, Report LA-7932-MS, Los Alamos National Laboratory, 1979. K. Shibata, Evaluation of neutron nuclear data of 9Be for JENDL-3, Report JAERI-M 84-226, 1984. M. Drake, et al., Double-differential beryllium neutron cross-sections at incident neutron energies of 5.9, 10.1 and 14.2 MeV, Nucl. Sci. Eng. 63 (1977) 401. M. Baba, et al. The interaction of fast neutron with 9Be, in Proc. Conf. Nuclear Physics/Reactor Data, United Kingdom Atomic Energy Authority, Harwell, 1978, p. 198. A. Takahashi, et al., Measurement of double differential neutron emission cross sections with 14 MeV source for D, Li, Be, C, O, AI, Cr, Fe, Ni, Mo, Cu, Nb, and Pb, in Proc. Int. Conf. Nuclear Data for Science and Technology, Antwerp, Belgium, 6-10 September, 1982, CONF820906, Reidel, Dordrecht, 1982, p. 360. A. Schwenk-Ferrero, Verfahren zur numerischen L6sung der Neutronentransportgleichung mit strenger Behandlung der anisotropen Streuung, Berickt KfK-4788, Kernforschungszentrum Karlsruhe, 1990. R.E. McFarlane, D.W. Muir and R.M. Boicourt, The NJOY nuclear data processing system, Vols. I, II, III,

U. Fischer, E. Wiegner / Fusion Engineering and Design 28 (1995) 624-635

[ 10]

[11]

[12]

[13]

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