J. Sanz, O. Cabellos, J. Juan, N. García-Herranz Universidad Nacional de Educación a Distancia (UNED) Universidad Politécnica de Madrid (UPM) Analysis of Available Cross-Section Uncertainty Data and Progress in Defining Uncertainty Methodologies for Inventory Calculations J. Sanz, O. Cabellos, J. Juan, N. García-Herranz Universidad Nacional de Educación a Distancia (UNED) Universidad Politécnica de Madrid (UPM) Second IP EUROTRANS Internal Training Course on Nuclear Data for Transmutation June 9, 2006

2 Outline INTRODUCTIONOBJECTIVES PART I: ANALYSIS OF AVAILABLE NEUTRON CROSS SECTION UNCERTAINTY DATA FOR INVENTORY CALCULATIONS PART II: PROGRESS IN UNCERTAINTY METHODOLOGIES CONCLUSIONS FUTURE WORK

3 Introduction One of the objectives in NUDATRA Domain is to evaluate the impact of nuclear data uncertainties on relevant fuel cycle and repository parameters

4 Introduction In order to reach these goals three main elements are required: I.Cross section uncertainties (  ) II.Computational techniques enable to assess the impact of  on the isotopic inventory and other inventory-related responses III.List of relevant parameters for the uncertainty evaluation and required target accuracies in those parameters Our group is mainly involved in steps I and II

5 Objectives I.Review, processing and analysis of the neutron cross-section uncertainty data available in the most recent internationally distributed nuclear data libraries Result: compilation of the best current available uncertainty data for use in inventory codes (covariance matrices: uncertainties –diagonal values– and their correlations – off-diagonal values –) II.Definition of appropriate methodologies to propagate nuclear data uncertainties to the isotopic inventory Capability to evaluate the impact of cross section uncertainties on the inventory predictions Applications to EUROTRANS : assess if further improvement of nuclear data is required

6 PART I Analysis of available neutron cross- section uncertainty data for inventory calculations I.1 Review and compilation of available cross-section uncertainty data I.2 Processing the uncertainty data for inventory prediction I.3 Analysis of uncertainties: comparison of the previous uncertainty data

7 Uncertainty data for all reactions included in the point-wise cross-section library (13,006 in FENDL-2.0, 12,617 in EAF-2003, 62,637 in EAF-2005) For non-threshold reactions  3-4 groups For threshold reactions  1-2 groups Activation-oriented nuclear data libraries FENDL UN/A-2.0, EAF2003/UN and the recently released EAF2005 Included information:  j,LIBRARY (relative error in the j energy group) Assumptions: xs within the same energy group are fully correlated; xs in different groups are assumed to be statistically independent  no covariances included, covariance matrix diagonal Reaction Energy (eV)  j,EXP (%) Covariance matrix (relative) Pu240 (n,  ) 1.0E E E E E E I.1 Review of available uncertainty cross-section data

8 General purpose evaluated nuclear data files BROND-2.2 (last updated 1993) CENDL-2.1 (last updated 1995) ENDF/B-VI.8 (october 2001); ENDF/B-VIIb (2005) JEF-2.2 (1993) JEFF-3.0/1 (may 2005) JENDL-3.3 (2002) IRDF (1993); IRDF2002 (2002) I.1 Review of the nuclear data uncertainties available (cont.) Library # of materials with covariance data (MF33 and MF40) # aprox. of xs with covariance data BROND-2.23  30 CENDL-2.19  65 ENDF/B-VI.844  400 ENDF/B-VIIb35> 200 IRDF > 100 IRDF200248> 100 JEF  120 JEFF  350 JENDL  160 Data of interest for inventory calculations: MF33, MF 39 (no data in the libraries), MF40 Stored values: absolute ( ) or relative covariances ( ) Uncertainty information in “covariance files” nu(bar)MF31 resonance parametersMF32 reaction cross sectionsMF33 angular distributionsMF34 energy distributionsMF35 radionuclide production yieldsMF39 radionuclide production xsMF40  covariance information is still scarce in all major data files Data covariances for:

9 JENDL-3.3 MF33 : Reaction Cross Section Covariance Data Sub-library No. 10 Material (MAT) Reaction (MT) Covariance with (MAT, MT) Reaction (MT) Covariance with (MAT, MT) U (n,Total) (n,2n) (n,3n) (n,g) SELF U 233 (n,fission) 18(n,fission)SELF U 235 (n,fission) U 238 (n,fission) Pu 239 (n,fission) Pu 240 (n,fission) Pu 241 (n,fission) U (n,Total) (n,2n) (n,3n) (n,4n) (n,g) SELF U 235 (n,fission) 18(n,fission)SELF U 233 (n,fission) U 238 (n,fission) Pu 239 (n,fission) Pu 240 (n,fission) Pu 241 (n,fission) U (n,Total) (n,2n) (n,3n) (n,4n) (n,g) SELF 18(n,fission)SELF U 233 (n,fission) U 235 (n,fission) Pu 239 (n,fission) Pu 240 (n,fission) Pu 241 (n,fission) Pu (n,Total) (n,2n) (n,3n) (n,4n) (n,g) SELF 18(n,fission)SELF U 233 (n,fission) U 235 (n,fission) U 238 (n,fission) Pu 240 (n,fission) Pu 241 (n,fission) Pu (n,Total) (n,2n) (n,3n) (n,4n) (n,g) SELF 18(n,fission)SELF U 233 (n,fission) U 235 (n,fission) U 238 (n,fission) Pu 239 (n,fission) Pu 241 (n,fission) Pu (n,Total) (n,2n) (n,3n) (n,4n) (n,g) SELF 18(n,fission)SELF U 233 (n,fission) U 235 (n,fission) U 238 (n,fission) Pu 239 (n,fission) Pu 240 (n,fission) Most covariance matrices correlate only energy intervals of the same reaction and material (SELF) Covariance matrices correlating cross sections for two different reactions of the same material Covariance matrices correlating cross sections for the same reaction of different materials The total covariance matrix for a particular energy-dependent xs is made up of the contribution of single covariance matrices, each one defining a type of correlation

10 I.1 Review of the nuclear data uncertainties available (cont.) Since actinides play an important role in ADS studies, we have carried out a more detailed analysis on them. From the 50 neutron-induced cross-sections (on 10 targets) with covariance data: Most xs (38) have covariance matrices only correlating energy intervals (of the same reaction and material) (SELF) There are 8 xs correlated with xs of the same reaction type of different materials (for example, in JENDL-3.3, the Pu 241 (n,fission) is correlated with the U 235 (n,fission)) There are 3 xs with covariance matrices correlating different reaction types of different materials (that is the case of U 235 (n,fission), correlated with U 238 (n,  ) in IRDF ) Finally, there are 3 xs with data correlating two different reaction types of the same material (in JENDL-3.3, the U 235 (n,  ) is correlated with U 235 (n,fission)) Uncertainty information for a few reactions, more detailed uncertainties (energy correlations and correlations among different reactions or different isotopes)

11 “Home-made” ANL Covariance Matrix I.1 Review of the nuclear data uncertainties available (cont.)  G. Aliberti, G. Palmiotti, M. Salvatores, C. G. Stenberg Transmutation Dedicated Systems: An assessment of Nuclear Data Uncertainty Impact, Nucl. Sci. Eng. 146, (2004)  G. Palmiotti, M. Salvatores Proposal for Nuclear Data Covariance Matrix, JEFDOC 1063 Rev.1, January 20 (2005) ANL N. of MAT=42 H (bonded) B 10 Li 6-7 C O N 15 Cr 52 Fe 56 – 57 Er Bi He 4 Be 9 F 19 Al Na Si Ni 58 Gd Zr Pb Th 232 U 233 – 234 – 235 – 236 – 238 Np 237 Pu 238 – 239 – 240 – 241 – 242 Am 241 – 242m – 243 Cm 242 – 243 – – 246

12 Energy Group MeV E E E E E E E E E E E E E E E-7 1)the region above the threshold of fertile isotope fission cross-sections, and of many inelastic cross-sections, up to 20 MeV 2)the region of the continuum down to the upper unresolved resonance energy limit 3)the unresolved resonance energy region 4)the resolved resonance region 5)the thermal range 15 energy groups between 19.6 MeV and E(thermal) Diagonal values given in Aliberti et al.(2004) Energy correlations given in Palmiotti et al.(2005) (no correlations among isotopes or reaction types) The same correlations for all isotopes and reactions, under the form of full energy correlation in 5 energy bands:

13 I.2 Processing the uncertainty data for inventory prediction Covariance data have to be processed into multigroup to be used by an inventory code Uncertainties in the activation-oriented nuclear data libraries are in a group structure  diagonal covariance matrices are ready for use by the inventory code (cross- sections need to be processed in the same group structure to assure the consistency) Files MF33 of the general-purpose evaluated data files need to be processed to yield the multigroup covariance matrices. Computational processing tools: NJOY (ERRORR/COVR modules) ERRORRJ  Multigroup covariance matrices with energy correlations  Multigroup covariance matrices correlating different isotopes or reaction types We are able to process covariance data to yield multigroup covariance matrices ready for use by inventory codes (such as ACAB) In preparation at the NEA Data Bank: they are extracting relevant covariance data from current evaluations in major data files and processing them in the ANL 15-multigroup structure. The derived covariance matrix in called NEA-K Covariance Matrix

14 material mat-mt=(9440,102) grp energy x-sec. rel.s.d. std.dev E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+00 >> column material mat-mt=(9440,102) vs row material mat-mt=(9440,102) row column Example: 240 Pu (n,gamma) from JENDL-3.3 processed by ERRORRJ in the ANL 15-group structure

15 Example: Covariance 239 Pu (n,fission)/ 235 U (n,fission) from JENDL-3.3 processed by ERRORRJ in the ANL 15-group structure 1st material mat-mt=(9437, 18) vs 2nd material mat-mt=(9228, 18) grp energy 1st x-sec. 2nd x-sec. 1st r.s.d. 2nd r.s.d E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+00 column material mat-mt=(9437, 18) vs row material mat-mt=(9222, 18) row … column … … … … … … … … … … 11 …

16 I.3 Analysis of uncertainties (ADS concept consists of an 800 MWth fast core cooled by lead-bismuth eutectic in forced convection, E. González et. al., CIEMAT) Goal: generate an extended ADS uncertainty library made of a compilation of the best current available data to inventory calculations: EAF-2005/UN (uncertainties for all reactions, variances in a 2/4 groups, no off-diagonal elements) ENDF covariance files (MF33) (few reactions, more detailed uncertainties, correlations between energy groups, isotopes and reaction types)  to take them if exist; if not To be consistent  standard cross-sections from the corresponding evaluation Test: comparison of the multigroup uncertainties obtained after processing data from different sources with a typical ADS neutron flux

17 I.3 Analysis of uncertainties (cont.) Comparison of effective uncertainties (1-group) IsotopeFENDL/UNEAF2003/UNENDF/B-VI 237 Np Pu Pu Pu Pu Pu Am m Am Am Uncertainties (  %) in actinide (n,  ) cross sections Comparison of uncertainties in a 3-group structure (that used in EAF-2003) Energy range (eV)Cross sections in 3 groupsCovariance matrices in 3 groups (absolute) EiEi E i+1 EAF-2003ENDF/B-VIEAF-2003ENDF/B – VI.R8 4.0E+3-2.0E+74.05E-14.02E-14.56E-30.00E E-35.28E-40.00E+0 1.0E-1-4.0E+32.79E E+09.88E-50.00E+05.28E-42.35E-30.00E+0 1.0E-5-1.0E-11.09E-51.08E-50.00E E E E-15 Uncertainties in the Pu240(n,  ) with the EAF-2003 group structure Good agreement of the processed uncertainties from the 2 types of uncertainty data sources  Recommendation = ENDF covariance files + EAF/UN + Palmiotti?

18 PART II Progress in defining uncertainty methodologies II.1 Main features of the two proposed methodologies to estimate propagation of cross section uncertainties to the isotopic inventory and associated parameters II.2 Application to the actinide inventory of typical ADS irradiated fuel II.3 Effect of the correlation structure on the results

19 1)Sensitivity / Uncertainty Analysis Method based on the first order Taylor series to estimate uncertainty indices for each reaction cross section in a continuous irradiation scenario 2) Monte Carlo Uncertainty Analysis To treat the global effect of all cross sections uncertainties in activation calculations, we have proposed an uncertainty analysis methodology based on Monte Carlo random sampling of the cross sections Assignment of a Probability Density Function (PDF) to each cross section II.1 Methodologies Goal: to analyse how xs uncertainty is transmitted to X

20 Sensitivity Analysis We solve at the same time the nuclide concentration X i and the partial derivative Sensitivity coefficient Relative error in X i due to changes in cross-sections Relative error in cross-sections

21 Sensitivity Analysis (cont.)

22 Monte Carlo Method Based on a random sampling  a PDF is assigned to each  j Probability distribution of  j ?

23 We use simultaneous random sampling of all the XS PDFs involved in the problem From the sample of the random vector , the matrix A is computed and the vector of nuclide quantities X is obtained Repeating the sequence, we obtain a sample of isotopic concentration vectors. The statistic estimators of the sample can be estimated Enables to investigate the global effect of the complete set of  on X... Monte Carlo Method (cont.)

24 Reference system Fuel composition from the transmuter core used in Aliberti et al. (2004) [1] Neutron flux: x n / cm 2 s, ADS typical spectrum = MeV Irradiation period of 1 year as in [1] Analysis performed at 15 energy groups, with the structure adopted in [1] Uncertainty data only for major actinides: 238 Pu and 240 Pu, 239 Pu, 241 Pu, 242 Pu and minor actinides: 237 Np, 241 Am and 243 Am, 242m Am, 242 Cm, 243 Cm, 245 Cm, 246 Cm, 244 Cm and reaction types: (fission, capture and n,2n reactions) Covariance information taken from Aliberti et al.(2004) and Palmiotti et al. (2005): ANL covariance matrices (reference) Cross section data processed to the required multigroup structure from EAF-2003 II.2 Application Goal: to show the capabilities of ACAB to evaluate uncertainties in the actinide inventory

25 Results from Monte Carlo Inventory of actinides at the end of 1-year irradiation period computed by ACAB Results for a 1000 history-sampling II.2 Application (cont.) Initial, X i ×10 20 Final, X f ×10 20 (X f -X i )/X i Coefficient of variation of X f (in %) No Correlation Palmiotti’s Correlation Pu 238 0,423001, ,913,65,6 Am 241 8,080006, ,141,32,0 Am 242 0,109000, ,461,32,0 Am 243 5,830005, ,110,20,3 Cm 242 0,000400, ,498,713,5 Cm 244 2,370002, ,140,60,9 Cm 245 0,316000, ,222,43,6

26 Histogram of the 1000 values obtained by Monte Carlo Method

27 Results from Sensitivity/Uncertainty technique: comparison with Monte Carlo method Goal of the comparison of both approaches: checking the implementation Very different (bad implemented) Similar (well implemented) Some differences (no linearity for the irradiation time of the example) Results very similar II.2 Application (cont.) Coefficients of variation (in %) Taylor Aprox.Monte Carlo Pu 2385,365,63 Am 2411,892,01 Am 2421,952,04 Am 2430,240,25 Cm 24212,913,11 Cm 2440,780,85 Cm 2453,283,62

28 where  is a positive parameter between 0 and  (correlation range parameter)  small  high correlations  big  low correlations II.3 Effect of correlations We propose an exercise to assess the effect of the covariance structure on the results Energy range divided in G groups and E 1, E 2, … E G mean values of each group We define the correlation r ij between the groups with energies E i and E j as : Significant impact of the covariances in the inventory prediction? How much the xs uncertainty correlations can affect the actinide inventory?

29 II.3 Effect of correlations (cont.)

30 Initial ×10 20 Final ×10 20 Coefficient of variation of X f ( in %)  No Correlation10,50,250,100,05 Palmiotti ´s Correlation Pu 2380,423001,230003,64,85,97,28,68,95,6 Am 2418,080006,930001,31,72,12,83,23,32,0 Am 2420,109000,159001,31,82,22,73,33,52,0 Am 2435,830005,170000,2 0,3 Cm 2420,000400,398008,711,314,018,021,121,613,5 Cm 2442,370002,710000,60,80,9 1,1 0,9 Cm 2450,316000,385002,43,33,84,75,55,63,6 Uncertainty values obtained assuming a simple correlation model with a correlation range parameter  = 0.5 very similar to those obtained assuming Palmiotti’s correlation

31 We are able to process any uncertainty information to inventory calculations and the corresponding cross sections. Interest in using the best set of uncertainties currently available: ENDF + EAF/UN + Palmiotti ?? Two methodologies implemented in the inventory code ACAB to estimate nuclear data uncertainty propagation to the isotopic inventory of actinides  appropiated for ADS problems Potential of the Monte Carlo method highlighted Covariance matrices in any arbitrary multigroup structure can be handled by ACAB (at present, only energy correlations taken into account) The effect of the xs correlations are relevant on the actinides Conclusions

32 Generation of an extended ADS/UN library for all the isotopes of interest (not only actinides) to predict the inventory with the best set of uncertainties Deal with correlations among different isotopes and different reactions Definition of the reference system in order to perform appropriate tests (potential of Monte Carlo method) Fuel composition, neutron flux Follow-up EUROTRANS schedule Future Work at UNED / UPM