Nuclear data uncertainty analysis for the Po-210 production in MYRRHA

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MYRRHA is a multi-purpose research reactor able to operate in sub-critical and critical modes and currently in the design phase at SCK•CEN. The choice of LBE was driven by its chemical stability, low melting temperature, high boiling point, low chemical reactivity with water and air and a good neutronic performance.

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Nội dung Text: Nuclear data uncertainty analysis for the Po-210 production in MYRRHA

EPJ Nuclear Sci. Technol. 4, 48 (2018) Nuclear Sciences © L. Fiorito et al., published by EDP Sciences, 2018 & Technologies https://doi.org/10.1051/epjn/2018044 Available online at: https://www.epj-n.org REGULAR ARTICLE Nuclear data uncertainty analysis for the Po-210 production in MYRRHA Luca Fiorito1,*, Alexey Stankovskiy2, Augusto Hernandez-Solis2, Gert Van den Eynde2, and Gasper Zerovnik3 1 Nuclear Energy Agency/Data Bank, 46 Quai Alphonse le Gallo, 92100 Boulogne-Billancourt, France 2 SCK•CEN Belgian Nuclear Research Center, Boeretang 200, 2400 Mol, Belgium 3 European Commission Joint Research Centre, Retieseweg 111, 2440 Geel, Belgium Received: 7 December 2017 / Received in ﬁnal form: 7 February 2018 / Accepted: 8 June 2018 Abstract. MYRRHA is a multi-purpose research reactor able to operate in sub-critical and critical modes and currently in the design phase at SCK•CEN. The choice of LBE was driven by its chemical stability, low melting temperature, high boiling point, low chemical reactivity with water and air and a good neutronic performance. As a drawback, the neutron capture in 209Bi results in the production of 210Po, a highly radiotoxic alpha emitter with relatively short half-life (≈138 days). The 210Po production represents a major safety concern that has to be addressed for the reactor licensing. In this work we used the ALEPH-2 burnup code to accurately calculate the 210 Po production in a MYRRHA operating cycle. The impact of using different nuclear data libraries was evaluated and the reliability of the results was determined by quantifying the uncertainty of the 210Po concentration. The uncertainty quantiﬁcation was carried out sampling the currently available nuclear data covariance matrices with the SANDY code. Also, estimates of the sensitivity proﬁles were obtained with a linear regression approach. The activation yield of the 209Bi neutron capture reaction was assessed as the largest nuclear data source of uncertainty, however the lack of covariances for such data represent a capital drawback for the 210Po content prediction. 1 Introduction the 209Bi capture cross section and the associated branching ratio (production yield) to 210gBi/210mBi a 210 Po is the last-but-one daughter product of the 238U decay point of interest. Experimental data are very scarce chain, which makes it the only polonium isotope existing in in the literature (EXFOR), especially in the resonance nature. However, because of its relatively short half-life regions. As a consequence, discrepancies are evident (≈138 days), it is present only in traces. A pure a in the evaluated nuclear data, which lead to diverging emitter, 210Po decays to the stable isotope 206Pb emitting predictions of the 210Po production in nuclear reactor. 5.407 MeV a particles with a speciﬁc activity of 166 TBq/g. The goals of this paper are to analyze the status of the The technological interest in 210Po is to be associated to its current evaluated nuclear data for 209Bi and to highlight huge radiotoxicity when ingested or inhaled, since this the differences between evaluations. Then, the effect of isotope is retained for weeks in the human body. Its lethal the different libraries is studied for the 210Po prediction dose from intake is estimated to be much smaller than 1 mg. at the end of a MYRRHA irradiation cycle. Also, a 210 Po is of great concern for the new generation of nuclear rough uncertainty value is assessed for this quantity reactors (GEN-IV) involving leadbismuth eutectic (LBE), by propagating the nuclear data covariances using the where polonium is artiﬁcially produced. The major produc- SANDY code, based on Monte Carlo sampling. tion process is reported in Figure 1 and it involves the 209Bi activation to the 210Bi ground state, which in turn b-decays 2 Polonium production in MYRRHA to 210Po with a half-life of 5.013 days. The use of LBE as coolant material in fast reactor An innovative research reactor MYRRHA [1] is being systems and/or spallation target in subcritical Accelera- developed at SCK•CEN, Mol, Belgium. Its major feature is tor Driven System (ADS) such as Multi-Purpose its sub-critical operation mode where the highly-enriched hYbrid Research Reactor for High-tech Applications MOX fueled core is coupled to a high-power linear proton (MYRRHA) [1] makes the nuclear data evaluation of accelerator. The accelerator delivers a 4 mA beam of 600 MeV protons to the LBE spallation target that generates * e-mail: lucaﬁorito.11@gmail.com neutrons, thus driving the sub-critical core. The pool reactor This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
2 L. Fiorito et al.: EPJ Nuclear Sci. Technol. 4, 48 (2018) Table 1. Different channels for the polonium production in the spallation target of MYRRHA. Isotope Channel % in total production rate ðp;2nÞ 209 Bi !208 Po 98.98 208 Po ða; 5nÞ208 1:63 h 209 Bi! At !208 Po 1.02 ðp;nÞ 209 209 Bi !209 Po 97.33 Po ða; 4nÞ 209 5:41 h 209 Bi ! At!209 Po 2.67 ðn;gÞ 5:013 d 209 Bi !210 Bi !210 Po 99.8 ða;3nÞ 8:1 h 209 Bi !210 At !210 Po 0.18 210 Po ðp;gÞ 209 Bi !210 Po 0.02 ðn;gÞ 209 ðn;gÞ 210 22:3 y 5:013 d 208 Pb ! Pb ! Pb !210 Bi !210 Po 9.8 104 thus determining the strategy of its handling after deﬁnitive shutdown of the reactor [8]. During normal reactor operation, most of the polonium (not only 210Po, but also 208,209Po, which are less radiotoxic due to their longer half-life but equally hazardous since they are a-emitters as well) is retained in LBE. This can cause problems during maintenance operations or if coolant leakage occurs. However, some polonium will migrate to Fig. 1. Scheme of Po production following bismuth activation. the cover gas in the reactor plenum and will diffuse outside the primary system when the reactor is opened for refueling or maintenance. Therefore, a continuous removal of polonium from LBE is foreseen [9]. concept implies that the LBE serves as coolant as well. The There are several ways to produce polonium installation is also assumed to be able to operate in a critical from LBE in MYRRHA. Since the MYRRHA central mode as a heavy liquid metal cooled fast reactor, when the sub-assembly is occupied by the spallation target, beam line is removed and extra MOX fuel assemblies are which is not separated from the main LBE pool, the added to the core periphery. This research facility will serve spallation reactions of primary protons and secondary as a demonstrator for minor actinide transmutation, testing high-energy neutrons with LBE circulating in this of GEN-IV and fusion reactor materials, producing medical assembly also produce polonium isotopes. The contri- radioisotopes, as well as for fundamental physics research [2]. butions of competing reaction channels in the spallation The use of heavy liquid metal coolants such as lead target are summarized in Table 1. The results show or LBE is advantageous from the safety and economic that the neutron activation of 209Bi is the main point of view. These materials are inert with respect to mechanism leading to the 210Po production even in the air and water, have low melting and operating temper- spallation target, needless to say about the whole core. atures, as well as low vapor pressure [3]. However, The other production channels can be neglected either these coolants face several technological challenges. because of the negligible associated cross section, the One of the most important issues is the radiological small particle ﬂux or the unlikely sequence of reactions. hazard associated with activation of LBE coolant Therefore, efforts should concentrate on assessing under neutron irradiation. The major concern is the the uncertainty of the neutron capture reaction rate formation of 210Po, which has an inhalation and leading to the formation of 210Bi in the ground state. ingestion radiotoxicity among the highest of all the known radionuclides [4,5]. In a typical neutron envi- ronment characteristic of fast reactors (neutron ﬂuxes at the level of 1015n/(cm2 s)) its activity can reach up to 3 Current status of the evaluated 209 Bi (h, g) 1011 Bq/kg [6]. In the MYRRHA reactor pool, assuming cross sections that all 210Po is retained in LBE, the estimated production of this radioisotope after one irradiation The 209Bi (h, g) cross section data were taken from cycle at nominal power would be at the level of 350 g, or the nuclear data libraries JEFF-3.2 [10], ENDF/B-VII.1 5.5 104 TBq [7]. In addition, this polonium isotope [11], JENDL-4.0 [12], TENDL-2015 [13] and BROND- contributes the most to the decay heat of LBE, 3.1 [14] and they were compared to estimate analogies
L. Fiorito et al.: EPJ Nuclear Sci. Technol. 4, 48 (2018) 3 Fig. 2. 209 Bi (n, g) cross section data: absolute values. Fig. 3. 209 Bi (n, g) cross section data: ratios to JENDL-4.0. and differences in the evaluations. Figure 2 shows provided by Mutti. No unresolved resonance formalism the cross sections these libraries. Also, a ratio of each was used. The total cross section below 6.5 MeV was adopted cross section to the JENDL-4.0 evaluation is shown in from the ENDF/B-VI.8 library. All other data were Figure 3 to enhance the contrast. produced with the TALYS code [18] with model parameters adjusted to reproduce the existing experimental data. The 3.1 JEFF-3.2 background contribution to the elastic cross section in the resolved resonance region (RRR) present in JEFF-3.1 was The JEFF-3.2 ﬁle inherits most of its data from the JEFF-3.1 set to zero. evaluation. JEFF-3.1 adopts the resolved resonance param- eters below 200 keV from JENDL-3.3, based on [15]. 3.2 ENDF/B-VII.1 Modiﬁcations of JEFF-3.2 from JEFF-3.1 include an update of the resonance parameters using Mutti values [16] (based The ENDF/B-VII.1 ﬁle adopts the cross section data and on the capture measurements at GELINA) and the values resolved resonance parameters from the ENDF/B-VI from the Atlas of neutron resonances [17] for parameters not evaluation. The resolved resonance region extends up to
4 L. Fiorito et al.: EPJ Nuclear Sci. Technol. 4, 48 (2018) 100 keV. Its resonance parameters were taken from Mughabghab [15] with modiﬁed scattering radius to ﬁt experimental data. Above 100 keV, the energy dependent cross section is given, evaluated on numerous experimental data. Despite signiﬁcant ﬂuctuations in the cross section the unresolved resonance formalism was not used, which might lead to biased results close to 100 keV in combination with strong self-shielding. A background contribution to the cross section above 99.46 keV is present in the RRR. 3.3 JENDL-4.0 The JENDL-4.0 evaluation was adopted from JENDL-3.0 with some modiﬁcations. The resonance parameters (RRR below 200 keV) from Mughabghab [15] were updated taking Fig. 4. 209 Bi ratio sg/sm. into account the Domingo-Pardo et al. data [19] measured at n_TOF. A bound state was introduced to reproduce the constant value that is only few percents smaller than thermal capture cross section from Mughabghab [17]. In the the Borella et al. [21] experimental values (feeding g rays) RRR a background cross section was added. Above the RRR, at thermal energy. Above 1 MeV the existing trend is no unresolved resonance formalism was used and the capture reversed, with the branching ratio to the meta state mostly cross section was normalized at 500 keV to the measurements being slightly more enhanced. by Saito et al. [20] based on TOF measurements at the Pelletron accelerator in Tokyo. 4.2 ENDF/B-VII.1 3.4 TENDL-2015 ENDF/B-VII.1, as well as the previous ENDF/B releases, does not provide any information on the branching ratios. The parameters for the resolved resonance region (limited Such a lack of data might lead to a critical overestimation of to 100 keV) were taken directly from ENDF/B-VII.1. No the 210Po production by those evolution codes that interpret unresolved resonance formalism was used. The TENDL- the missing data as the absence of the 210Bi meta state. 2015 cross sections were re-evaluated using the TALYS [18] software and possibly renormalized to experimental data. 4.3 JENDL-4.0 Between 100 and 200 keV, the energy dependence of the total cross section seems nonphysical. JENDL-4.0 introduced the isomeric ratio in the thermal region from the table of Mughabghab [17]. The calculated 3.5 BROND-3.1 data at 30 keV are consistent with the experimental measurement by Saito et al. [22]. BROND-3.1 adopted the JENDL-3.3 data for the resolved resonance region, with the exception of the bound state that 4.4 BROND-3.1 was not included. Hence, the thermal capture cross section was slightly modiﬁed compared to the Mughabghab [17] BROND-3.1 reproduces the strong energy-dependence of evaluation. A smooth background was added to the capture the isomeric ratio in all energy ranges by taking into cross section in the resolved resonance range between 30 and account the latest experimental data including both 200 keV to compensate the loss of the resonances. The Borella et al. [23] results for the 801.6 eV resonance and continuous-energy cross section was also taken from JENDL. the Saito et al. [20] measurements. 4 Current status of the branching ratio of 5 Parametric study of the library the 209Bi (h, g) 210gBi/210mBi performances To correctly predict the production of 210Po the accurate A parametric study was carried out to assess whether the 210 knowledge of the branching ratio for the reactions 209Bi Po content prediction after a MYRRHA irradiation (h, g) 210gBi/210mBi is essential. Unfortunately, branching cycle in sub-critical mode was affected by the choice of the ratios are difﬁcult to be accurately measured by the TOF nuclear data library used for the calculation. The method. Therefore, the availability of accurate and reliable irradiation cycle of 90 days, with a constant core power data is very limited. A comparison of some evaluations of 70 MWth, was simulated with the ALEPH-2 burnup code with experimental measurements is shown in Figure 4. [24] developed at SCK•CEN. Capture cross sections ﬁrst and branching ratios later were sequentially replaced from 4.1 JEFF-3.2 different evaluations into the base library ENDF/B-VII.1. The analysis of the results is reported in Table 2. The JEFF-3.2 branching ratios were updated from the The largest difference in the 210Po concentration previous JEFF-3.1 evaluation. The branching ratio does obtained by replacing nuclear data from different not show any energy dependence up to 1 MeV, with a libraries is 46% for cross sections and 63% for branching
L. Fiorito et al.: EPJ Nuclear Sci. Technol. 4, 48 (2018) 5 Table 2. Relative difference between the 210Po concentrations. The value obtained with each library by replacing either (h, g) cross sections or branching ratios is compared to the 210Po concentration obtained when averaging the results of all the libraries. MAXMIN is the largest difference in 210Po obtained with two libraries. Eval. Cross section Branching ratio effect (%) effect (%) JEFF-3.2 12 25 ENDF/B-VII.1 21 45 JENDL-4.0 19 16 TENDL-2015 27 7 BROND-3.1 16 12 MAXMIN 46 70 STDEV 22 28 Fig. 5. Relative uncertainty of the 209Bi cross section from different nuclear data libraries as a function of incident neutron energy. ratios. Such deviations suggest inconsistencies between grid by the ERRORR module of NJOY [26]. From the the existing data evaluations, which lead to major uncertainty proﬁles it is evident that BROND and uncertainties when predicting the polonium content in ENDF/B provide a larger cross section uncertainty (about MYRRHA. 20%) compared to JEFF and TENDL up to about 100 keV. At 100 keV and beyond the trend is inverted, with JEFF reaching a relative uncertainty peak of almost 80%. 6 Nuclear data uncertainty propagation Concerning the correlation matrices, JEFF, ENDF and TENDL show zero correlation between the resonance The covariance matrices found in the nuclear data and fast regions as the two blocks were evaluated libraries were propagated to quantify the uncertainty of independently using different models. On the other hand, the 210Po content in the MYRRHA subcritical core. The BROND includes long-range correlations based on the uncertainty propagation was performed using ALEPH-2 assimilation of systematic uncertainties. in combination with the Monte Carlo sampling code For the JEFF and TENDL libraries, both resonance SANDY [25]. SANDY was used to sample random cross parameters and cross sections were sampled since both sections from each 209Bi nuclear data ﬁle. Together, the data types contained covariances (respectively sections samples reproduced the information contained in the MF32 and MF33 of a ENDF-6 ﬁle [27]). BROND and covariance sections of the corresponding ﬁle. ENDF/B only contained covariance matrices for the cross Figures 5 and 7 present the cross section covariances sections. It is relevant to mention that the ENDF/B available in the nuclear data ﬁles used for this study. The covariance matrix for 209Bi neutron capture cross section is plots were produced by the JANIS tool and display the far from being positive-deﬁnite, which means that not only correlation matrices collapsed on a 238-group energy it does not conform to the condition for Monte Carlo
6 L. Fiorito et al.: EPJ Nuclear Sci. Technol. 4, 48 (2018) Fig. 6. Relative uncertainty of the 209 Bi (n,n) cross section from different nuclear data libraries as a function of incident neutron energy. Fig. 7. Correlation matrices of the 209 Bi (n, g) cross section.
L. Fiorito et al.: EPJ Nuclear Sci. Technol. 4, 48 (2018) 7 Table 3. Nuclear data uncertainty contribution to the 210 Po production and the integrated ﬂux. 210 Eval. Data Po (%) Flux (%) JEFF-3.2 xs 5.2 1.4 JEFF-3.2 res + xs 5.9 2.1 ENDF/B-VII.1 xs 10.9 2.6 TENDL-2015 res + xs 21.6 29.7 BROND-3.1 xs 11.8 1.7 such an approach does not require programming adjoint function constructs into the code, as it would be done for a derivative-based approach. ALEPH-2, not having derivative-based sensitivity capabilities, can only take advantage from this global approach, since its application is straightforward. Let us take a set of sampled input data in the form of perturbation coefﬁcients P, such as the perturbations generated by SANDY for the cross sections: 2 ð1Þ ð1Þ 3 p1 ⋯ pm 6 . . 7 6 . ⋱ .. 7 P ¼6 . 7 ð1Þ 4 pðnÞ ⋯ pðnÞ 5 1 m Fig. 8. 210Po production sensitivity to the 209Bi capture cross where m is the number of groups found in the cross section section and neutron ﬂux as a function of incident neutron energy. h covariance matrixi and n is the number of samples. ðiÞ ðiÞ pi• ¼ p1 ; . . . ; pm is the i th line of the above matrix. sampling but it is also mathematically inconsistent. The These perturbation coefﬁcients are used by SANDY to bias introduced in the samples to work around this issue generate a perturbed cross section ﬁle that, when included could impact signiﬁcantly on the results. in the ALEPH-2 calculation, it generates a response r(i). The calculated uncertainties on the 210Po concentra- After running ALEPH-2 for the n sample cases, a vector R tions are summarized in Table 3 together with the of responses is produced: corresponding calculated uncertainty on the integrated neutron ﬂux. The inﬂuence of the capture cross section 2 3 covariances on the polonium production ranges between rð1Þ 6 . 7 5.2% for JEFF and 21.6% from TENDL. Since only the R ¼ 4 .. 5: ð2Þ (h, g) cross section data were perturbed for BROND and ðnÞ r ENDF/B and because of the magnitude of such a reaction in the region of intense ﬂux, the effect on the integrated As a part of the global sensitivity approach used ﬂux is small. The energy self-shielding strongly anticorre- in this work, we introduced a linear regression model lates (up to 90%) the integrated ﬂux and the reaction of the type rate of 210Bi, which is proportional to the 210Po production. For TENDL and JEFF, the resonance parameters are R ¼ PSþe: ð3Þ also perturbed including correlations between capture and neutron widths. Consequently, the large uncertainty One thousand samples were used to determine the given in TENDL (Fig. 6) for the elastic scattering cross sensitivity coefﬁcients S = [s1, … ,sm]T of the response with section, which is the dominant reaction with 209Bi, has a respect to the cross sections in m energy groups, by direct bearing on the energy-shift of the neutron ﬂux minimizing the residues e with an ordinary least-square and generates considerable uncertainties both on the technique, as integrated ﬂux and on the 210Po production. Contrary to 1 the previous case, the two responses are now almost fully S ¼ PT P PT R: ð4Þ correlated. The sensitivity proﬁle is presented in Figure 8, 7 Sensitivity analysis via linear regression overlaid on the spatial-averaged MYRRHA ﬂux. The 210 Po production in MYRRHA exhibits a signiﬁcant A global approach to the sensitivity analysis of 210Po was sensitivity to the 209Bi capture cross section in correspon- performed based on Monte Carlo sampling and linear dence of the peak of the ﬂux (at about 100 keV) and of regression. Despite being less efﬁcient in computer time, the ﬁrst 209Bi resonances.
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