1ACE file perturbation tool
Japan Atomic Energy Agency (JAEA)
Kenichi TADA

Ref: K. Tada, R. Kondo, T. Endo, A. Yamamoto, "Development of ACE file
perturbation tool using FRENDY," J. Nucl. Sci. Technol., 60, pp.624-631(2023).
https://www.tandfonline.com/doi/full/10.1080/00223131.2022.2130463

2Perturbation of ACE file
• Perturbation tool decreases or increases cross section (XS) or

number of neutron per fission (ν) or fission spectrum (χ).

• XS or χ is multiplied by perturbation factor 𝑓 within arbitrary energy range.

• This tools can be adopted to two analyses.
• Sensitivity analysis with direct perturbation method• Uncertainty analysis with random sampling method
XS [barn] [barn]
微視的断面積100000

Energy range of
perturbation

10000

𝜎′ = 𝑓 × 𝜎

1000

XS is discontinuity
at boundaries ofenergy region.

100
106.0

6.2

6.4 6.6 6.8 7.0 7.2
Incident neutron
E [eV] energy [eV]

7.4

3

Relations of each reaction type
MT = 1MT = 2Total

MT = 3MT = 5, 11, 17, 22 - 26, 28 - 37,
41 - 42, 44 - 45, 152 - 154, 156 Fission
181, 183 - 190, 194 - 196,198 - 200
Elastic

MT = 18
MT = 19 - 21, 38

MT = 102, 108 - 117,155, 182, 191 - 193, 197

MT = 103 (n, γ)
MT = 600 - 649

MT = 4

MT = 16

MT = 50 - 91

MT = 875 - 891

MT = 27(n, n’)
MT = 101(n, 2n)MT = 104

MT = 106

MT = 650 - 699

MT = 750 - 799

MT = 105

MT = 107

MT = 700 - 749

MT = 800 - 849

4Example of fission XS perturbation
Perturbed fission XS (MT=18): 𝜎18 ′ = 𝒇 × 𝜎18 (Perturabtion factor: 𝑓)
MT18 contains MT=19-21 and 38.
MT=19-21 and 38 are also perturbed.
𝜎19 ′ = 𝒇 × 𝜎19 , 𝜎20 ′ = 𝒇 × 𝜎20 ,𝜎21 ′ = 𝒇 × 𝜎21 , 𝜎38 ′ = 𝒇 × 𝜎38

MT = 1MT = 3MT = 27

MT=1, 3, and 27 contain MT=18.
XS of MT=1, 3, and 27 are modified.
∆𝜎18 = 𝜎18 ′ − 𝜎18
𝜎1 ′ = 𝜎1 + ∆𝜎18 , 𝜎3 ′ = 𝜎3 + ∆𝜎18
𝜎27 ′ = 𝜎27 + ∆𝜎18

MT = 18
MT=19, 20,21, and 38

5How to use perturbation tool
• Compile of perturbation tool
• Run “make” command on“frendy_20YYMMDD/tools/perturbation_ace_file”.
• Executable file (perturbation_ace_file.exe) is generated.
• Manual of perturbation tool is“frendy_20YYMMDD/tools/README_tools”.
./perturbation_ace_file.exe ace_file.ace perturbation_list.inp

Perturbation
ACE file name

Input file ofperturbation tool6

Input of perturbation tool
• Following four parameters must be set in one line.
• 1) Reaction type (MT number)• 2) Lower energy of perturbed energy range [MeV]• 3) Upper energy of perturbed energy range [MeV]• 4) Perturbation factor 𝑓 (𝜎′ = 𝑓 × 𝜎)
ACE file uses MeV
for unit of energy.

[Example of input of perturbation tool]218

1.0e-111.0e-6

1.0e-101.0e-51.1
0.9

7Random sampling
Covariance matrix of nuclear data

inp/Nddd_000x
102 2.00E+01 6.43E+00 8.78E-01
102 6.43E+00 4.30E+00 8.67E-01
102 4.30E+00 3.00E+00 8.62E-01．．．

• User has to prepare covariance matrix.
• We are now developing converter from GENDF file of
NJOY/ERROR to input of random sampling tool.

• Generation of perturbation factors using random

sampling method• See “/frendy_20yymmdd/tools/make_perturbation_factor/sample”

8

Uncertainty quantification using random
sampling method
Godiva (HMF-001)
GeometrySphere
Radius: 8.7 cm

Composition

U-235: 93.71 wt.%
U-238: 5.27 wt.%
U-234: 1.02 wt.%𝑘eff

1.000 ± 0.001

◆
◆
◆

◆

MCNP6.2
Number of perturbed ACE file: 100
Covariance data: 56groupcov7.1(from SCALE6.2.3)
MT=2,4,16,18,102,452, and 1018
(MT=452: ν, MT=1018: χ)

Godiva [1][1] ICSBEP NEA/NSC/DOC(95)03, Organization for
Economic Co-operation and Development-Nuclear
Energy Agency (OECD-NEA) (September 2016).

9

Calculation results (k-effective uncertainty)𝑘eff -uncertainty due to all nuclides and reactions ∆𝑘/𝑘 [%]Sensitivity analysis (SA) Random sampling method usingof MCNP6.2
perturbation tool
1.11
1.12 [0.98 – 1.24]
Comparison of 𝑘eff -uncertainty due to individual nuclide andreaction ∆𝑘/𝑘 [%]