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JEFFDOC-1159

JEFFDOC-1159. Status of CALENDF-2005 J-Ch. Sublet and P. Ribon CEA Cadarache, DEN/DER/SPRC , 13108 Saint Paul Lez Durance, France. CALENDF-2005. Probability tables means a natural discretisation of the cross section data to describe an entire energy range

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JEFFDOC-1159

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  1. JEFFDOC-1159 Status of CALENDF-2005J-Ch. Sublet and P. RibonCEA Cadarache, DEN/DER/SPRC,13108 Saint Paul Lez Durance, France

  2. CALENDF-2005 • Probability tables means a natural discretisation of the cross section data to describe an entire energy range Circa 1970, Nikolaev described a sub-group method and Levitt a probability table method for Monte Carlo • The probability table (PT) approach has been introduced, exploited in both resolved (RRR) and unresolved (URR) resonance ranges • The Ribon CALENDF approach is based on Gauss quadrature as a probability table definition • This approach introduces mathematical rigorousness, procuring a better accuracy and some treatments that would be prohibited under other table definition such as group condensation and interpolation, isotopic smearing

  3. Gauss Quadrature and PT-Mt • A probability distribution is exactly defined by its infinite moment sequence • A PT-Mt is formed of N doublets (pi,σi, i=1,N) exactly describing a sever sequence of 2N moments of the σt(E) distribution • Such a probability table is a Gauss quadrature and as such will benefit from their entire mathematical settings • The only degree of freedom is in the choice of moments for which a standard is proposed in CALENDF, dependant on the table order, and associated to the required accuracy pi, σt,i [σx,i , x = elastic, inelastic, fission, absorption, n,xn] with i=1 to N (steps)

  4. Gauss Quadrature and PT-Mt XS distribution in a group G Cross section over energy PT discretisation G= [Einf, Esup]

  5. Padé Approximant and Gauss Quadrature Moments, othogonal polynomials, Padé approximants and Gauss quadrature are closely related and allow to establish a quadrature table The second line is the Padé approximant that introduces an approximate description of higher order momenta

  6. Partials cross sections • Partials cross sections steps follow this equation • The consistency between total and partials is obtained, ascertained by a suitable choice of the indices n • In the absence of mathematical background there is no reason why partial cross section steps cannot be slightly negative, and sometimes this is the case. • However, the effective cross section reconstructed from the sum of the steps values is always positive.

  7. PT-Moments • The moments taken into account are not only from 0 to 2N-1 for the total, but negative moments are also introduced in order to obtain a better numerical description of the excitation function deeps (opposed to peaks) of the cross-section • CALENDF standard choice ranges from 1-N to N for total cross section, and -N/2 to (N-1)/2 for the partials • It is also possible to bias the PT by a different choice of moment (reduortp code word), this feature allows a better accuracy to be reached according to the specific use of a table of reduced order • For examples for deep penetration simulation or small dilution positive moments are not of great importance

  8. Unresolved Resonance Range • Generation of random ladders of resonance: the “statistical Hypothesis” • For each group, or several in case of fine structure, an energy range is defined taking into account both the nuclei properties and the neutronic requirement (accuracy and grid) • A stratified algorithm, improved by an antithetic method creates the partials widths • The treatment of these ladders is then the same as for the RRR (except, in case of external, far-off resonance) • Formalism: Breit Wigner Multi Niveau (# MLBW) or R-Matrix if necessary

  9. Formalism interpretation- approximation Coded MLBW leads to the worst results

  10. Interpolation law • The basic interpolation law is cubic, based over 4 points • y = Pn(x) • y = a + bx +cx2 + dx3 • applicable to interpolate between xi and x i+1 taking into account x i-1 and x i+2. • In this example cubic interpolation always gives an accuracy bellow 10-3 for an energy grid spacing up to 40% Ratio of subsequent energies points

  11. Reconstruction accuracy 0.1% 1.6Kev – 0.99eV points IP= 1 32256 IP =2 44848 IP =3 63054 IP =4 90231 IP =5 130920 IP =6 186678 ref. x1.4 steps

  12. CALENDF 2005 • CALENDF-2005 is composed of modules, each performing a set of specific tasks • Each module is call specifically by a code word followed by a set of options and/or instructions particular to the task in hand • Input and output streams are module specific • Dimensional options have been made available to the user • Sometimes complex input variables are exemplified in the User Manual, around 30 cases • As always, QA test cases are a good starting point for new user

  13. ECCO group library scheme CALENDF PT’s are used by the neutronic codes ERANOS, APOLLO and TRIPOLI Codes Cross-sections Angular distributions Emitted spectra Interfaces NJOY (99-125) Data GENDF GENDF* ENDF-6 MERGE (3.8) GECCO (1.5) + updates: Dimensions, … NJOY-99 I/O Fission matrix mt = 5, mf = 6 Thermal scattering (inel, coh.-incoh. el.) CALENDF (2005 Build 69) Cross-sections Probability Tables

  14. Temperatures 293.2 573.2 973.2 1473.2 2973.2 5673.2 GENDF* MF 1 Header MF 3 Cross sections MF 5 Fission spectra MF 6 Scatter matrices MF 50 Sub group data ECCOLIB-JEFF-3.1 1968 groups with Probability Table • Reactions Total: mt1 • Five partial bundles Elastic 2: mt2 Inelastic 4: mt4 (22,23,28,29,32-36) (n, n’-n’-n’3-n’p-n’2…) N,xN 15: mt16,17 (24,25,30) 37 (41,42) (n, 2n-3n-2n-3n,n,2n2-n,4n-2np-3np) Fission 18: mt18 (n, f-nf-2nf) Absorption 101: mt102-109, 111 (116) (n, -p-d-t-He--2-3-2p…)

  15. CALENDF-2005 Fortran 90/95 SUN, IBM, Linux and Window XP (both with Lahey) Apple OsX with g95 and ifort User manual  QA  Many changes in format, usage  and some in physics: Test cases, ~ 30 Group boundaries hard coded (Ecco33, Ecco1968, Xmas172, Trip315, Vitj175) Probability table and effective cross sections comparison Pointwise cross sections Increased accuracy and robustness CALENDF-2005 -Resonance energies sampling (600  1100) -Improved resonance grid -Improved Gaussian quadrature table computation -Total = partials sum # MT=1 -Probability tables order reduction

  16. CALENDF-2005 input data CALENDF ENERgies 1.0E-5 20.0E+6 MAILlage READ XMAS172 SPECtre (borne inferieure, ALPHA) 1 zones 0. -1. TEFF 293.6 NDIL 1 1.0E+10 NFEV 9 9437 './jeff31n9437_1.asc' SORTies NFSFRL 0 './pu239.sfr' NFSF 12 './pu239.sf' NFSFTP 11 './pu239.sft' NFTP 10 './pu239.tp' IPRECI 4 NIMP 0 80 Energy range Group structure Weighting spectrum Temperature Dilution Mat. and ENDF file Output stream name - unit Calculational accuracy indice Output dumps or prints on unit 6 indices

  17. CALENDF-2005 input data REGROUTP NFTP 10 './pu239.tp' NFTPR 17 './pu239.tpr' NIMP 0 80 REGROUSF NFSF 12 './pu239.sf' NFSFR 13 './pu239.sfdr' NIMP 0 80 REGROUSF NFSF 11 './pu239.sft' NFSFR 14 './pu239.sftr' NIMP 0 80 COMPSF NFSF1 13 './pu239.sfdr' NFSF2 14 './pu239.sftr' NFSFDR 20 './pu239.err' NFSFDA 21 './pu239.era' NIMP 0 80 END Regroup probability tables computed on several zones of a singular energy group, used also for several isotopes Regroup effective cross section computed on several zones of a singular energy group Idem but for the cross section computed from the probability tables Compare the effective cross section files -Relative difference as the Log of the ratio -Absolute difference as the ratio

  18. Pointwise cross section comparison: total A Cubic interpolation requires less points than a linear one But many more points exists in the CALENDF pointwise file in the URR, tenths of thousand … CALENDF 115156 pts NJOY 72194 pts

  19. Pointwise cross section comparison : capture Reconstruction Criteria: CALENDF 0.02% NJOY 0.1%

  20. Groupwise cross section: total ECCO 1968 Gprs

  21. Groupwise cross section: total ECCO 1968 Gprs in the URR 2.5 to 300 KeV

  22. Groupwise cross section: fission ECCO 1968 Gprs

  23. Groupwise cross section: fission ECCO 1968 Gprs in the URR 2.5 to 30 KeV

  24. CALENDF-2005 TPR NOR = table order NPAR = partials ZA= 94239. MAT=9490 TEFF= 293.6 1968 groupes de 1.0000E-5 A 1.9640E+7 IPRECI=4 IG 1 ENG=1.947734E+7 1.964033E+7 NOR= 1 I= 0 NPAR=5 KP= 2 101 18 4 15 1.000000+0 6.115624+0 3.168116+0 1.724428-3 2.239388+0 2.630841-1 4.402475-1 ------ ------ IG 1000 ENG=4.962983E+3 5.004514E+3 NOR= 6 I= -5 NPAR=4 KP= 2 101 18 4 0 3.531336-2 1.001996+1 8.673775+0 4.299923-1 8.187744-1 4.878567-2 3.248083-1 1.299016+1 1.116999+1 5.483423-1 1.174122+0 4.879677-2 4.085168-1 1.686617+1 1.278619+1 1.593832+0 2.388719+0 4.880138-2 1.616318-1 2.349794+1 1.635457+1 3.590329+0 3.454910+0 4.884996-2 4.310538-2 3.445546+1 2.438486+1 4.303144+0 5.670905+0 4.876728-2 2.662435-2 4.254442+1 2.965644+1 7.196256+0 5.593669+0 4.874651-2 15 N,xN I = first negatif moment 1 Total 2 Elastic 101 Absorption 18 Fission 4 Inelastic Probability

  25. CALENDF-2005 SFR ZA= 94239 MAT=9490 TEFF=293.6 1968 gr de 1.0000E-5 a 1.9640E+7 IP=4 NDIL= 1 SDIL= 1.00000E+10 IG 1 ENG=1.947734E+7 1.964033E+7 NK=1 NOR= 1 NPAR=5 KP= 2 101 18 4 15 SMOY= 6.115624+0 3.168116+0 1.724428-3 2.239388+0 2.630841-1 4.402475-1 SEF(0)= 6.115624+0 SEF(1)= 3.168116+0 SEF(2)= 1.724428-3 SEF(3)= 2.239388+0 SEF(4)= 2.630841-1 SEF(5)= 4.402475-1 - - - - - - IG 1000 ENG=4.962983E+3 5.004514E+3 NK=1 NOR= 6 NPAR=4 KP= 2 101 18 4 0 SMOY= 1.787921+1 1.364190+1 1.801794+0 2.337908+0 4.880425-2 SEF(0)= 1.787921+1 SEF(1)= 1.364190+1 SEF(2)= 1.801794+0 SEF(3)= 2.337908+0 SEF(4)= 4.880425-2 Total Elastic Absorption Fission Inelastic N,xN

  26. Neutronic Applications • The PT are the basis for the sub-group method, proposed in the 70’s, a method that allow to avoid the use of “effective cross section” to account for the surrounding environment. Method largely used in the “fast” ERANOS2 code system • The PT are also the basis behind a the sub-group method implemented in the LWR cell code APOLLO2: • In the URR, with large multigroup (Xmas 172) • In all energy range, with fine multigroup (Universal 11276) • It allows to account for mixture self-shielding effects (mixture = isotopes of the same element or of different nature) • The PT are also used to replace advantageously the “averaged, smoothed, monotonic, …” pointwise cross section in the URR; method used by the Monte Carlo code TRIPOLI-4.4

  27. PT’s impact on the ICSBEP benchmarks Excellent way to test the influence of the URR

  28. Neutronic Applications • Data manipulation processes are efficient and strict : isotopic smearing, condensation, interpolation and table order reduction • “Statistical Hypothesis”, exact at “high energy”, it means for 239 Pu > few hundred eV • In APOLLO2 the PT are used in the reactions rates equivalence in homogeneous media • The level of information in PT are greater than in effective cross section • Integral calculation: speed and accuracy

  29. Future work • Introduction of probability table based on half integer moments, as suggested by Go Chiba & Hironobu Unesaki • Fluctuation factors computation using an extrapolation method based on Padé approximant • Increases of the number of partial widths, to account for improvement in evaluation format; i.e. (n,γf), (n,n’), …. • ……..

  30. Conclusions • CALENDF-2002 http://www.nea.fr/abs/html/nea-1278.html • Improved version !! • CALENDF-2005; now • Full release through the OECD/NEA and RSICC, this time … Agenda

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