1 / 30

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

summer
Download Presentation

JEFFDOC-1159

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related