Status of CALENDF-2005 J-Ch. Sublet and P. Ribon CEA Cadarache, DEN/DER/SPRC, 13108 Saint Paul Lez Durance, France

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Status of CALENDF-2005J-Ch. Sublet and P.
Ribon CEA Cadarache, DEN/DER/SPRC,13108 Saint
Paul Lez Durance, France

JEFFDOC-1159
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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

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Gauss Quadrature and PT-Mt
pi, st,i sx,i , x elastic, inelastic,
fission, absorption, n,xn with i1 to N
(steps)

• A probability distribution is exactly defined by
  its infinite moment sequence
• A PT-Mt is formed of N doublets (pi,si, i1,N)
  exactly describing a sever sequence of 2N moments
  of the st(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

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

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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

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Formalism interpretation- approximation
Coded MLBW leads to the worst results
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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 i1
  taking into account x i-1 and x i2.
• 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
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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
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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

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ECCO group library scheme
CALENDF PTs 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,
Fission matrix mt 5, mf 6 Thermal
scattering (inel, coh.-incoh. el.)
NJOY-99 I/O
CALENDF (2005 Build 69)
Cross-sections Probability Tables
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ECCOLIB-JEFF-3.1
1968 groups with Probability Table

• 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

• Reactions
• Total mt1
• Five partial bundles
• Elastic 2 mt2
• Inelastic 4 mt4 (22,23,28,29,32-36)
• (n, n-n?-n3?-np-n2?)
• 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)

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CALENDF-2005

• 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
• 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

-Resonance energies sampling (600 ? 1100)
? -Improved resonance grid ? -Improved Gaussian
quadrature table computation? -Total partials
sum MT1 ? -Probability tables order reduction
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CALENDF-2005 input data
CALENDF ENERgies 1.0E-5 20.0E6 MAILlage
READ XMAS172 SPECtre (borne inferieure,
ALPHA) 1 zones 0. -1. TEFF 293.6
NDIL 1 1.0E10 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
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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
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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
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Pointwise cross section comparison capture
Reconstruction Criteria CALENDF 0.02 NJOY 0.1
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Groupwise cross section total
ECCO 1968 Gprs
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Groupwise cross section total
ECCO 1968 Gprs in the URR 2.5 to 300 KeV
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Groupwise cross section fission
ECCO 1968 Gprs
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Groupwise cross section fission
ECCO 1968 Gprs in the URR 2.5 to 30 KeV
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CALENDF-2005 TPR
NOR table order
NPAR partials
ZA 94239. MAT9490 TEFF 293.6 1968 groupes de
1.0000E-5 A 1.9640E7 IPRECI4 IG 1
ENG1.947734E7 1.964033E7 NOR 1 I 0 NPAR5
KP 2 101 18 4 15 1.0000000 6.1156240
3.1681160 1.724428-3 2.2393880 2.630841-1
4.402475-1 ------ ------ IG 1000 ENG4.962983E3
5.004514E3 NOR 6 I -5 NPAR4 KP 2 101 18
4 0 3.531336-2 1.0019961 8.6737750
4.299923-1 8.187744-1 4.878567-2 3.248083-1
1.2990161 1.1169991 5.483423-1 1.1741220
4.879677-2 4.085168-1 1.6866171 1.2786191
1.5938320 2.3887190 4.880138-2 1.616318-1
2.3497941 1.6354571 3.5903290 3.4549100
4.884996-2 4.310538-2 3.4455461 2.4384861
4.3031440 5.6709050 4.876728-2 2.662435-2
4.2544421 2.9656441 7.1962560 5.5936690
4.874651-2
15 N,xN
I first negatif moment
2 Elastic
101 Absorption
18 Fission
4 Inelastic
1 Total
Probability
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CALENDF-2005 SFR
ZA 94239 MAT9490 TEFF293.6 1968 gr de
1.0000E-5 a 1.9640E7 IP4 NDIL 1 SDIL
1.00000E10 IG 1 ENG1.947734E7 1.964033E7
NK1 NOR 1 NPAR5 KP 2 101 18 4 15 SMOY
6.1156240 3.1681160 1.724428-3 2.2393880
2.630841-1 4.402475-1 SEF(0) 6.1156240
SEF(1) 3.1681160 SEF(2) 1.724428-3 SEF(3)
2.2393880 SEF(4) 2.630841-1 SEF(5)
4.402475-1 - - - - - - IG 1000 ENG4.962983E3
5.004514E3 NK1 NOR 6 NPAR4 KP 2 101 18 4
0 SMOY 1.7879211 1.3641901 1.8017940
2.3379080 4.880425-2 SEF(0) 1.7879211
SEF(1) 1.3641901 SEF(2) 1.8017940 SEF(3)
2.3379080 SEF(4) 4.880425-2
Total
Elastic
Absorption
Fission
Inelastic
N,xN

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Neutronic Applications

• The PT are the basis for the sub-group method,
  proposed in the 70s, 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

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PTs impact on the ICSBEP benchmarks
Excellent way to test the influence of the URR
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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 gt 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

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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,?f), (n,n), .
• ..

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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