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7.8 One-Point Kinetics Parameters The following one-point kinetics parameters can be obtained by CITATION of SRAC. • Effective delayed neutron fraction ⎡ * d BVF ∫ ∑φ ⎤ ⎢ g ( r) χ g, i ( r) ∑ Σ i. g' ( r) φ g' ( r) dV ⎥ g g' β = ∑ = ∑ ⎢ ⎥ eff β eff , i (7.8-1) i i ⎢ * t ∫ ⎥ ⎢ ∑φ g ( r) χ g ( r) ∑νΣ f . g' ( r) φ g' ( r) dV ⎥ ⎣ g g' ⎦ • Effective decay constant for the i-th family of delayed neutron precursor. ∫ ∑ ∫ ∑ * ∑ φg ( r) χ g, i ( r) Σi. g' ( r) φ g' ( r) dV 1 g g' = λeff , i * d BVF φ ( r) χ ( r) Σ ( r) φ ( r) dV g g d g, i ∑ g' BVL i. g' g' (7.8-2) • Effective delayed neutron life time l = ∫ ∑ g ∫ ∑ k g * 1 φ g ( r) φ( r) dV υ ( r) t g χ ( r) * φ g ( r) k eff ∑ g' g νΣ f . g' ( r) φ ( r) dV g' = k eff Λ (7.8-3) BVF i where, Σ ( ν N ) ≡ ∑ β m g, m f , g, m m (7.8-4) i, g σ m BVL i i ≡ ∑ ( β ν σ / ) Σi, g m g, m f , g, m N m λm (7.8-5) m 1 1 Σ υ , g ≡ ≈ (7.8-6) E ( eV ) ( E + E ) / 2 g g, Lower g, Upper The averaged neutron velocity for the g-th group is given by υ (m / sec) = g 2 × 1.60219E −19 m ( kg) n 1 Σ υ, g 1 = 13831.68 × Σ υ, g The macroscopic cross-sections defined by Eqs.(7.8-4), (7.8-5) and (7.8-6) are stored in the MACRO file for the calculation of the one-point kinetics parameters. Theses cross-sections are collapsed and/or homogenized in the same manner (cf. Sec.7.5) as other usual macroscopic cross-sections ( Σ , , etc.). a,g Σ f , g 290
8. Tables on Cross-Section Library 8.1 Symbols to denote nuclide Table 8.1-1 Chemical symbols (zz-Tag) Z Element Name zz-Tag Z Element Name zz-Tag Z Element Name zz-Tag 1 Hydrogen H0 35 Bromine BR 71 Lutetium LU 1 Deuterium D0 36 Krypton KR 72 Hafnium HF 1 Tritium T0 37 Rubidium RB 73 Tantalum TA 2 Helium HE 38 Strontium SR 74 Tungsten W0 3 Lithium LI 39 Yttrium Y0 75 Rhenium RE 4 Beryllium BE 40 Zirconium ZR 76 Osmium OS 5 Boron B0 41 Nioblium NB 77 Iridium IR 6 Carbon C0 42 Molybdenum MO 78 Platinium PT 7 Nitrogen N0 43 Technetium TC 79 Gold AU 8 Oxygen O0 44 Ruthenium RU 80 Mercury HG 9 Fluorine F0 45 Rhodium RH 81 Thallium TL 10 Neon NE 46 Palladium PD 82 Lead PB 11 Sodium NA 47 Silver AG 83 Bismuth BI 12 Magnesium MG 48 Cadmium CD 84 Polonium PO 13 Aluminium AL 49 Indium IN 85 Astatine AT 14 Silicon SI 50 Tin SN 86 Radon RN 15 Phosphorus P0 51 Antimony SB 87 Francium FR 16 Sulfur S0 52 Tellurium TE 88 Radium RA 17 Chlorine CL 53 Iodine I0 89 Actinium AC 18 Argon AR 54 Xenon XE 90 Thorium TH 19 Potassium K0 55 Cesium CS 91 Protactinium PA 20 Calcium CA 56 Barium BA 92 Uranium U0 21 Scandium SC 57 Lanthane LA 93 Neptunium NP 22 Titanium TI 58 Cerium CE 94 Plutonium PU 23 Vanadium V0 59 Praseodymium PR 95 Americium AM 24 Chromium CR 60 Neodymium ND 96 Curium CM 25 Manganese MN 61 Promethium PM 97 Berkelium BK 26 Iron FE 62 Samarium SM 98 Californium CF 27 Cobalt CO 63 Europium EU 99 Einsteinium ES 28 Nickel NI 64 Gadolinium GD 100 Fermium FM 29 Copper CU 65 Terbium TB 101 Mendelevium MD 30 Zinc ZN 66 Dysprosium DY 102 Nobelium NO 31 Gallium GA 67 Holmium HO 103 Lawrencium LR 32 Germanium GE 68 Erbium ER 104 Kurchatovium KU 33 Arsenic AS 69 Thulium TM 34 Selenium SE 70 Ytterbium YB 291
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JAEA-Data/Code 2007-004 SRAC2006 :
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Contents 1. General Descriptions ..
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5.5 BWR Fuel Assembly Calculation (
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目次 1. 概要 ................
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5.4 三次元拡散計算 (CI
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1. General Descriptions 1.1 Functio
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essential programs of the integrate
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Sphere (Pebble, HTGR) 1D-Plate (JRR
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ecause the scattering cross-section
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As shown in Fig.1.4-1, one PDS file
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1.5.1 Fast Fission Energy Range (10
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i n m≠n i n i n i n i 1 i i g( C
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mixture(s) having resonant nuclides
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thermal energy range. In the fixed
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1.10 Calculation Scheme In Fig.1.10
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3 2 1 CALL MICREF [20] CALL REACT C
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homogenized P 1 spectrum obtained a
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Consequently next step ’CALL MACR
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1.11 Output Information Major calcu
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(4) A floating number may be entere
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2.2 General Control and Energy Stru
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cell. = 2 The PEACO routine (hyperf
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should be avoided for the core wher
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Note: Usually IC15=1 is used in FBR
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Behrens’ term of the Benoist mode
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Only the first character (capital l
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NET ∑ i= 1 NEGT( i ) =(Total numb
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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
Page 251 and 252: In Fig.7.1-5, the line PQ’ define
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Page 255 and 256: the arrays T and II, respectively.
Page 257 and 258: Note that among four terms appearin
Page 259 and 260: If a group-dependent form of Fick
Page 261 and 262: 7.3 Optional Processes for Resonanc
Page 263 and 264: 7.3.2 Table-look-up Method of f-tab
Page 265 and 266: has been introduced for the correct
Page 267 and 268: ϕ i ( 0 u ) = ∑ Pij ( u) W j ( u
Page 269 and 270: Geometry b i m f b f −( γ + γ )
Page 271 and 272: will be seen in the reference 65) .
Page 273 and 274: The lattice cell under study may co
Page 275 and 276: (2) Two resonance-absorbing composi
Page 277 and 278: One of the physical problems associ
Page 279 and 280: and V = V + V , F f m where Σ m ,
Page 281 and 282: We shall discuss the following two
Page 283 and 284: where X = 2R p ( Σ C = 2R πρ R p
Page 285 and 286: • the reduced collision probabili
Page 287 and 288: The root mean square (RMS) residual
Page 289 and 290: group flux and for the fast group f
Page 291 and 292: Table 7.5-1 (1/2) Nomenclature Symb
Page 293 and 294: 7.5.1 Smearing Smearing or spatial
Page 295 and 296: 7.5.2 Spectrum for Collapsing The f
Page 297 and 298: Here, an equivalent relation holds
Page 299 and 300: 1 F = K ∑∫ g * χ g ( r) ϕ g (
Page 301: M dN i ( t) M = ∑ f j→iλ j N i
Page 305 and 306: Table 8.1-2 (2/2) Element index (zz
Page 307 and 308: JEFF-3.0 are based on other nuclear
Page 309 and 310: Table 8.2-1 (1/8) List of SRAC publ
Page 317 and 318: 8.3 Energy Group Structure The ener
Page 319 and 320: (4) Upper Boundary of PEACO Routine
Page 321 and 322: References 1) K. Tsuchihashi, H. Ta
Page 323 and 324: Experiment,” J. Nucl. Sci. Techno
Page 325: 75) K. Tasaka : “DCHAIN: Code for
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