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2.1 SRAC Free Format................................................................................................................28 2.2 General Control and Energy Structure Specification ............................................................ 31 2.3 User’s Library Specification.................................................................................................. 43 2.4 PIJ ; Collision Probability Method (CPM)............................................................................ 44 2.5 ANISN ; One-dimensional S N Transport Calculation ........................................................... 65 2.6 TWOTRAN ; Two-dimensional S N Transport Calculation ................................................... 75 2.7 TUD ; One-dimensional Diffusion Calculation..................................................................... 87 2.8 CITATION ; Multi-Dimensional Diffusion Calculation........................................................ 90 2.9 Material Specification ......................................................................................................... 121 2.10 Reaction Rate Calculation ................................................................................................... 129 2.11 Cell Burn-up Calculation..................................................................................................... 135 2.12 PEACO ; The hyperfine Group Resonance Absorption Calculation................................... 147 3. I/O FILES.................................................................................................................................... 149 3.1 Contents of PDS files .......................................................................................................... 149 3.1.1 Public Fast Library [PFAST] / User Fast Library [UFAST]............................................ 150 3.1.2 Public Thermal Library [PTHERMAL] / User Thermal Library [UTHERMAL] .......... 156 3.1.3 Public MCROSS Library [PMCROSS]/ User MCROSS Library [UMCROSS] ............ 158 3.1.4 Effective Microscopic Cross-Section File [MICREF] .................................................... 158 3.1.5 Fine Group Macroscopic Cross-Section File [MACROWRK]....................................... 163 3.1.6 Coarse Group Macroscopic Cross-section File [MACRO]............................................. 165 3.1.7 Flux File [FLUX] ............................................................................................................ 172 3.2 I/O Files in Sequential Organization ................................................................................... 174 3.2.1 Common PS Files............................................................................................................ 175 3.2.2 PS files for PIJ................................................................................................................. 175 3.2.3 PS files for ANISN.......................................................................................................... 176 3.2.4 PS files for TWOTRAN .................................................................................................. 176 3.2.5 PS files for TUD.............................................................................................................. 177 3.2.6 PS files for CITATION.................................................................................................... 177 3.3 Burn-up Chain Library ........................................................................................................ 178 4. Job Control Statements................................................................................................................ 191 5. Sample Input ............................................................................................................................... 195 5.1 Cell Burn-up Calculation (PIJ)............................................................................................ 195 5.2 Reaction Rate Calculation (PIJ) .......................................................................................... 198 5.3 S N Transport Calculation (PIJ, ANISN, TWOTRAN)......................................................... 201 5.4 Three-dimensional diffusion calculation (CITATION) ....................................................... 204 iv
5.5 BWR Fuel Assembly Calculation (PIJ)............................................................................... 208 6. Utility for PDS File Management ............................................................................................... 217 6.1 PDSTOTXT and TXTTOPDS............................................................................................. 217 6.2 PDSMDL............................................................................................................................. 217 6.3 Other utility programs ......................................................................................................... 220 7. Mathematical Formulations......................................................................................................... 221 7.1 Formulations of Collision Probabilities............................................................................... 221 7.1.1 General Theory................................................................................................................ 222 7.1.2 Collision Probabilities for Slab Lattice ........................................................................... 227 7.1.3 Collision Probabilities for One-dimensional Cylindrical Lattice .................................... 230 7.1.4 Collision Probabilities for Spherical System................................................................... 235 7.1.5 Collision Probabilities for Two-dimensional Cylindrical Lattice.................................... 238 7.1.6 Ray-Trace Method for Integration of Collision Probabilities.......................................... 240 7.2 Optional Processes for Microscopic Total and Macroscopic Transport Cross-sections...... 246 7.2.1 Microscopic Total Cross-section ..................................................................................... 246 7.2.2 Macroscopic Transport Cross-section ............................................................................. 246 7.3 Optional Processes for Resonance Absorption.................................................................... 249 7.3.1 Table-look-up Method of f-tables Based on NR Approximation in Homogeneous Systems............................................................................................................................ 249 7.3.2 Table-look-up Method of f-tables Based on IR Approximation ...................................... 251 7.3.3 Generalized Dancoff Correction Factor .......................................................................... 254 7.3.4 Direct Method for Calculating Neutron Flux Distribution (the Method in ‘PEACO’) ... 259 7.3.5 Resonance Absorption in Doubly Heterogeneous System .............................................. 264 7.4 Solution of Linear Equation ................................................................................................ 272 7.4.1 General Form of Linear Equation.................................................................................... 272 7.4.2 Iterative Procedure in Thermal Energy Range ................................................................ 274 7.4.3 Solution by Matrix Inversion in Fast Neutron Range...................................................... 276 7.4.4 Iterative Procedure for Eigenvalue Problem in Whole Energy Range ............................ 276 7.5 Smearing and Collapsing of Group Constants .................................................................... 278 7.5.1 Smearing.......................................................................................................................... 281 7.5.2 Spectrum for Collapsing.................................................................................................. 283 7.5.3 Collapsing of Group Constants ....................................................................................... 284 7.6 Reactivity Calculation by Perturbation Theory ................................................................... 286 7.6.1 First Order Perturbation................................................................................................... 286 7.6.2 Finite-difference Equation for Leakage Term ................................................................. 288 7.7 Cell Burn-up Calculation..................................................................................................... 288 v
Page 3 and 4: JAEA-Data/Code 2007-004 SRAC2006 :
Page 5: Contents 1. General Descriptions ..
Page 9 and 10: 目次 1. 概要 ................
Page 11 and 12: 5.4 三次元拡散計算 (CI
Page 13 and 14: 1. General Descriptions 1.1 Functio
Page 15 and 16: essential programs of the integrate
Page 17 and 18: Sphere (Pebble, HTGR) 1D-Plate (JRR
Page 19 and 20: ecause the scattering cross-section
Page 21 and 22: As shown in Fig.1.4-1, one PDS file
Page 23 and 24: 1.5.1 Fast Fission Energy Range (10
Page 25 and 26: i n m≠n i n i n i n i 1 i i g( C
Page 27 and 28: mixture(s) having resonant nuclides
Page 29 and 30: thermal energy range. In the fixed
Page 31 and 32: 1.10 Calculation Scheme In Fig.1.10
Page 33 and 34: 3 2 1 CALL MICREF [20] CALL REACT C
Page 35 and 36: homogenized P 1 spectrum obtained a
Page 37 and 38: Consequently next step ’CALL MACR
Page 39 and 40: 1.11 Output Information Major calcu
Page 41 and 42: (4) A floating number may be entere
Page 43 and 44: 2.2 General Control and Energy Stru
Page 45 and 46: cell. = 2 The PEACO routine (hyperf
Page 47 and 48: should be avoided for the core wher
Page 49 and 50: Note: Usually IC15=1 is used in FBR
Page 51 and 52: Behrens’ term of the Benoist mode
Page 53 and 54: Only the first character (capital l
Page 55 and 56: NET ∑ i= 1 NEGT( i ) =(Total numb
Page 57 and 58:
Block-1 Control integers /18/ 1 IGT
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asymmetric cell is surrounded by en
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= 0 Isotropic (white) reflection =
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degree for the numerical angular in
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3 EPSG Extrapolation criterion 4 R
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Block-10’ Required if IGT=11, or
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= 2 Neutron from moderator = 3 Neut
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Unit Cell Periodic B.C. 4 2 3 1 RX(
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NX=4 NTPIN=6 NAPIN=1 NPIN(1)=6 6 ID
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RDP(1)=0.0 RDP(2) RDP(3) 14 13 12 R
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2.5 ANISN ; One-dimensional S N Tra
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7 IBR Right boundary condition, sam
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22 IPM Angular dependent incident s
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EV = best guess for α or 0.0 when
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Block-04* Positions of interval bou
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2.6 TWOTRAN ; Two-dimensional S N T
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Note: The original TWOTRAN uses two
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= 0 (internally set) 19 IHM Total n
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= 3 R-θ 31 IEDOPT Edit options. =
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= 1 Yes Block-4 Control floating po
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Repeat Block-20 through Block-21, N
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2.7 TUD ; One-dimensional Diffusion
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= 1 Monitor print at each inner ite
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equation is applied to meshes, the
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Pin Plate D2 D2 D1 D1 In cylindrica
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XYZ(1,2) Y-abscissa of the top side
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READ(9) (WORK(J+I),I=1,NDATA) END D
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absorption cross-section, each of w
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ITMX19 The upper limit of CPU time
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corner and there are the same numbe
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NUAC19 Override use of Chebychev po
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NUAC17 > 0 The constant for all gro
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ottom starting with a new card. For
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Card-006-3 Specification of meshes
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4 SIG3 Absorption cross-section (
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2 NFX2 Optional print control = 0 N
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Region 1 Region 2 Left Right X/R/R
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X T 22*11 Meshes 1 Mesh = 1 Region
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2.9 Material Specification ’Mater
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fuel pin: MU08F0U2 and those in MOX
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hydrogen, add character ‘0’ to
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Usually, enter IRES=2 for the heavy
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2.10 Reaction Rate Calculation The
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Block-1 Control integers for reacti
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3 U238 The position of the second n
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2.11 Cell Burn-up Calculation The i
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= 2 Information for debugging = 3 D
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chains under consideration is enlar
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MACROWRK file. 2 INTSTP Step number
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Block-8-1 Required if IBC6=1 /1/ NM
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e avoided. Because U08W and U080 ar
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2.12 PEACO ; The hyperfine Group Re
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3. I/O FILES We shall describe the
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(E(g),g=1,NGF+1) structure. Boundar
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LTH(1) = (LD(1)+1)*LA(1), ordered a
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Background cross-sections Member Yz
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INT(2) = 0 K-member only without sc
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Member name Contents **************
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(WEIGHT(g),g=1,NGF) Lethargy widths
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3.1.5 Fine Group Macroscopic Cross-
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Member mmmmebfM or caseebxM /10*ng+
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Member caseBNUP Material-wise burn-
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Initial inventory in the restart ca
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(YDIOX(j),j=1,NOWSTP) Fission yield
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(n/cm 2 /sec*cm 3 ), NRR is number
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3.2.1 Common PS Files The following
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3.2.5 PS files for TUD The PS files
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at the first column. Block-1-1 Numb
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= ‘DAYS’ days = ‘YEARS’ yea
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GD156 XGD60001 641560 154.660 0 0 0
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: ZZ050 1.50080E+00 *FP-Yield-Data
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Kr83 Zr95 fission β + decay, EC (n
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Ge73 Ge74 As75 Ge76 fission β + de
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4. Job Control Statements In this c
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~SRAC/tool/lmmake/lmmk/lmmk.sh, whi
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5. Sample Input Several typical exa
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613.0 650.0 760.0 769.0 & cooling 7
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5 5 5 5 5 5 & 5 5 5 5 5 5 & 1 2 3 4
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5.3 S N Transport Calculation (PIJ,
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XFEN0001 2 0 5.78720E-02 XNIN0001 2
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Water reflector Extrapolated B.C. B
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1 1 1 1 1 1 1 2 3 008 -2 1 1 999 /
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Note: This sample is time consuming
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XCRN0008 0 0 1.55546E-02 XNIN0008 0
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****** Input for material specifica
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T-Region R-Region X-Region Reflecti
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6. Utility for PDS File Management
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To read in the microscopic cross-se
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7. Mathematical Formulations 7.1 Fo
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scattering kernel at point r’ fro
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The integration by R between R j- a
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G j Pij ( lattice) = Pij ( isolated
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We, however, should take care of th
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2 = ρ 2 + x r sin β = ρ R = x
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1 i ∑ − 1 k = j+ 1 λ ij = λ k
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where λ λ 1 is 2 is = = N ∑ k k
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2π ri −1 Pij = − Σ ∫ ρdρ
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In Fig.7.1-5, the line PQ’ define
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pin rod are divided into four regio
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the arrays T and II, respectively.
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Note that among four terms appearin
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If a group-dependent form of Fick
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7.3 Optional Processes for Resonanc
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7.3.2 Table-look-up Method of f-tab
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has been introduced for the correct
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ϕ i ( 0 u ) = ∑ Pij ( u) W j ( u
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Geometry b i m f b f −( γ + γ )
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will be seen in the reference 65) .
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The lattice cell under study may co
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(2) Two resonance-absorbing composi
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One of the physical problems associ
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and V = V + V , F f m where Σ m ,
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We shall discuss the following two
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where X = 2R p ( Σ C = 2R πρ R p
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• the reduced collision probabili
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The root mean square (RMS) residual
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group flux and for the fast group f
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Table 7.5-1 (1/2) Nomenclature Symb
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7.5.1 Smearing Smearing or spatial
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7.5.2 Spectrum for Collapsing The f
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Here, an equivalent relation holds
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1 F = K ∑∫ g * χ g ( r) ϕ g (
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M dN i ( t) M = ∑ f j→iλ j N i
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8. Tables on Cross-Section Library
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Table 8.1-2 (2/2) Element index (zz
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JEFF-3.0 are based on other nuclear
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Table 8.2-1 (1/8) List of SRAC publ
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Page 313 and 314:
Page 315 and 316:
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8.3 Energy Group Structure The ener
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(4) Upper Boundary of PEACO Routine
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References 1) K. Tsuchihashi, H. Ta
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Experiment,” J. Nucl. Sci. Techno
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75) K. Tasaka : “DCHAIN: Code for
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