NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROBLEM OR FUNCTION, METHOD OF SOLUTION, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHOR, MATERIAL, CATEGORIES

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Program name | Package id | Status | Status date |
---|---|---|---|

MINX | PSR-0105/01 | Tested | 01-MAR-1978 |

MINX-I.2 | PSR-0105/02 | Tested | 01-NOV-1977 |

Machines used:

Package ID | Orig. computer | Test computer |
---|---|---|

PSR-0105/01 | CDC 7600 | CDC 7600 |

PSR-0105/02 | IBM 370 series | IBM 370 series |

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3. DESCRIPTION OF PROBLEM OR FUNCTION

MINX calculates fine-group averaged infinitely diluted cross sections and self-shielding factors from ENDF/B-IV data. Its primary purpose is to generate a pseudo-composition-independent multigroup library which is input to the SPHINX space-energy collapse program (2) (PSR-0129) through standard CCCC-III (8) interfaces. MINX incorporates and improves upon the resonance capabilities of existing codes such as ETOX (5) (NESC0388) and ENDRUN (9) and the high-order group-to-group transfer matrices of SUPERTOG (10) (PSR-0013) and ETOG (11). Fine group energy boundaries, Legendre expansion order, gross spectral shape component (in the Bondarenko flux model), temperatures and dilutions can all be used specifically.

MINX calculates fine-group averaged infinitely diluted cross sections and self-shielding factors from ENDF/B-IV data. Its primary purpose is to generate a pseudo-composition-independent multigroup library which is input to the SPHINX space-energy collapse program (2) (PSR-0129) through standard CCCC-III (8) interfaces. MINX incorporates and improves upon the resonance capabilities of existing codes such as ETOX (5) (NESC0388) and ENDRUN (9) and the high-order group-to-group transfer matrices of SUPERTOG (10) (PSR-0013) and ETOG (11). Fine group energy boundaries, Legendre expansion order, gross spectral shape component (in the Bondarenko flux model), temperatures and dilutions can all be used specifically.

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4. METHOD OF SOLUTION

Infinitely dilute, unbroadened point cross sections are obtained from resolved resonance parameters using a modified version of the RESEND program (3) (NESC0465). The SIGMA1 (4) (IAEA0854) kernel-broadening method is used to Doppler broaden and thin the tabulated linearized pointwise cross sections at 0 K (outside of the unresolved energy region). Effective temperature- dependent self-shielded pointwise cross sections are derived from the formulation in the ETOX code. The primary modification to the ETOX algorithm is associated with the numerical quadrature scheme used to establish the mean values of the fluctuation intervals. The selection of energy mesh points, at which the effective cross sections are calculated, has been modified to include the energy points given in the ENDF/B file or, if the energy-independent formalism was employed, points at half-lethargy intervals. Infinitely dilute group cross sections and self-shielding factors are generated using the Bondarenko flux weighting model with the gross spectral shape under user control. The integral over energy for each group is divided into a set of panels defined by the union of the grid points describing the total cross section, the reaction cross section of interest and the gross spectral shape. The integration scheme actually employed in MINX is adaptive Simpson's procedure for which the initial estimate is based on the unionized grid described above. The computation of elastic and discrete group- to-group matrices is based upon a semi-analytic scheme which treats the rapidly fluctuating cross-section behaviour analytically. Where this laboratory-system-based scheme becomes difficult to implement (e.g., light nuclei, inelastic thresholds), an alternative numerical integration in the center-of mass system is employed. Multigroup transfer matrices for processes in which the outgoing neutron energy and angular distribution is uncoupled are computed by direct numerical integration.

Infinitely dilute, unbroadened point cross sections are obtained from resolved resonance parameters using a modified version of the RESEND program (3) (NESC0465). The SIGMA1 (4) (IAEA0854) kernel-broadening method is used to Doppler broaden and thin the tabulated linearized pointwise cross sections at 0 K (outside of the unresolved energy region). Effective temperature- dependent self-shielded pointwise cross sections are derived from the formulation in the ETOX code. The primary modification to the ETOX algorithm is associated with the numerical quadrature scheme used to establish the mean values of the fluctuation intervals. The selection of energy mesh points, at which the effective cross sections are calculated, has been modified to include the energy points given in the ENDF/B file or, if the energy-independent formalism was employed, points at half-lethargy intervals. Infinitely dilute group cross sections and self-shielding factors are generated using the Bondarenko flux weighting model with the gross spectral shape under user control. The integral over energy for each group is divided into a set of panels defined by the union of the grid points describing the total cross section, the reaction cross section of interest and the gross spectral shape. The integration scheme actually employed in MINX is adaptive Simpson's procedure for which the initial estimate is based on the unionized grid described above. The computation of elastic and discrete group- to-group matrices is based upon a semi-analytic scheme which treats the rapidly fluctuating cross-section behaviour analytically. Where this laboratory-system-based scheme becomes difficult to implement (e.g., light nuclei, inelastic thresholds), an alternative numerical integration in the center-of mass system is employed. Multigroup transfer matrices for processes in which the outgoing neutron energy and angular distribution is uncoupled are computed by direct numerical integration.

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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The principal restriction is the computing time available for a given desired accuracy, number of groups, and Legendre order. The paging technique and variable dimensioning make efficient use of available core storage; very large problems have been run with MINX (e.g. a complete 171-group P3 neutron library at ORNL and an extensive 240-group P4 library at LASL).

The principal restriction is the computing time available for a given desired accuracy, number of groups, and Legendre order. The paging technique and variable dimensioning make efficient use of available core storage; very large problems have been run with MINX (e.g. a complete 171-group P3 neutron library at ORNL and an extensive 240-group P4 library at LASL).

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6. TYPICAL RUNNING TIME

This is difficult to define because it is a sensitive function of the (a) accuracy required, (b) number of resonances, (c) number of groups, (d) Legendre expansion order, (e) number of temperature and dilutions, etc. Sample times for CDC 7600 are indicated below. For a problem with 50 groups, Legendre expansion P3, generally four temperatures involving 0 K, five dilution factors, tolerances: resonance reconstruction 0.5 % (1 % for U-238), linearization 0.2 %, Doppler thinning 0.2 %, adaptive integration 0.1 %, we find:

Isotope ENDF/B-IV MINX Timing

MAT No. (sec)

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Na-33 1156 667

Fe 1192 1075

O-16 1276 590

U-238 1262 6454

Pu-239 1264 3505

This is difficult to define because it is a sensitive function of the (a) accuracy required, (b) number of resonances, (c) number of groups, (d) Legendre expansion order, (e) number of temperature and dilutions, etc. Sample times for CDC 7600 are indicated below. For a problem with 50 groups, Legendre expansion P3, generally four temperatures involving 0 K, five dilution factors, tolerances: resonance reconstruction 0.5 % (1 % for U-238), linearization 0.2 %, Doppler thinning 0.2 %, adaptive integration 0.1 %, we find:

Isotope ENDF/B-IV MINX Timing

MAT No. (sec)

------- --------- -----------

Na-33 1156 667

Fe 1192 1075

O-16 1276 590

U-238 1262 6454

Pu-239 1264 3505

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7. UNUSUAL FEATURES OF THE PROGRAM

MINX generates and uses (in the resolved energy region) a linearly interpolable, infinitely dilute temperature-dependent pointwise cross-section library in ENDF/B-IV format. This feature permits efficient computation of group cross sections with accurate Doppler broadening of single-level and multi- level cross sections. The multigroup constants generated therefrom are thus known to be compatible with the pointwise cross sections retrieved by contuous-energy Monte Carlo codes. New, accurate algorithms for the computation of Legendre moments of group-to-group transfer matrices have been developed and implemented. These calculations are based on an expansion of the differential scattering cross section in the laboratory system and use a semi- analytic procedure which treats the rapidly fluctuating cross- section behaviour analytically. Where Legendre expansion in the lab system becomes difficult (e.g. for light nuclei or near inelastic thresholds) an alternative numerical integration in the centre-of- mass is employed. The procedures employed in MINX for constructing, interpolating and integrating cross sections are intended to provide and quantify user control of computational errors (assuming that the data base and weighting function are known explicitly). A paging technique which manipulates huge amounts of cross-section information one block at a time (block size variable), is used throughout MINX, in addition to variable dimensioning to reduce storage requirements and to use available storage efficiently. Finally, the code and the multigroup data sets derived therefrom are intended to satisfy nuclear design standards currently being implemented under auspicies of the American National Standards Institute.

MINX generates and uses (in the resolved energy region) a linearly interpolable, infinitely dilute temperature-dependent pointwise cross-section library in ENDF/B-IV format. This feature permits efficient computation of group cross sections with accurate Doppler broadening of single-level and multi- level cross sections. The multigroup constants generated therefrom are thus known to be compatible with the pointwise cross sections retrieved by contuous-energy Monte Carlo codes. New, accurate algorithms for the computation of Legendre moments of group-to-group transfer matrices have been developed and implemented. These calculations are based on an expansion of the differential scattering cross section in the laboratory system and use a semi- analytic procedure which treats the rapidly fluctuating cross- section behaviour analytically. Where Legendre expansion in the lab system becomes difficult (e.g. for light nuclei or near inelastic thresholds) an alternative numerical integration in the centre-of- mass is employed. The procedures employed in MINX for constructing, interpolating and integrating cross sections are intended to provide and quantify user control of computational errors (assuming that the data base and weighting function are known explicitly). A paging technique which manipulates huge amounts of cross-section information one block at a time (block size variable), is used throughout MINX, in addition to variable dimensioning to reduce storage requirements and to use available storage efficiently. Finally, the code and the multigroup data sets derived therefrom are intended to satisfy nuclear design standards currently being implemented under auspicies of the American National Standards Institute.

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8. RELATED AND AUXILIARY PROGRAMS

Three utility codes are provided to manipulate the CCCC data files:

LINX: will combine two multi-isotope CCCC files (ISOTXS or BRKOXS

only) (6) (PSR-0129)

BINX: will convert CCCC data (ISOTXS, BRKOXS, or DLAYXS) from binary to BCD mode or vice-versa and selectively print the contents

of the files (6) (PSR-0129).

CINX: will exactly collapse fine group data (ISOTXS, BRKOXS, or

DLAYXS) to a subset coarse group structure, and will also

change the format of the data to 1DX/PERT-V form, if desired

(7) (PSR-0117).

These codes were written to be as IBM-compatible as possible. The changes required are identified on the listings with "C IBM comment" cards.

Three utility codes are provided to manipulate the CCCC data files:

LINX: will combine two multi-isotope CCCC files (ISOTXS or BRKOXS

only) (6) (PSR-0129)

BINX: will convert CCCC data (ISOTXS, BRKOXS, or DLAYXS) from binary to BCD mode or vice-versa and selectively print the contents

of the files (6) (PSR-0129).

CINX: will exactly collapse fine group data (ISOTXS, BRKOXS, or

DLAYXS) to a subset coarse group structure, and will also

change the format of the data to 1DX/PERT-V form, if desired

(7) (PSR-0117).

These codes were written to be as IBM-compatible as possible. The changes required are identified on the listings with "C IBM comment" cards.

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Package ID | Status date | Status |
---|---|---|

PSR-0105/01 | 01-MAR-1978 | Tested at NEADB |

PSR-0105/02 | 01-NOV-1977 | Tested at NEADB |

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10. REFERENCES

(1) C.R. Weisbin, P.D. Soran, R.E. MacFarlane, D.R. Harris,

R.J. LaBauve, J.S. Hendricks, J.E. White, R.B. Kidman:

MINX: A Multigroup Interpretation of Nuclear X-sections from

ENDF/B.

LA-6486-MS (September 1976)

(2) W.J. Davis, M.B. Yarbrough, A.B. Bortz:

SPHINX: A One Dimensional Diffusion and Transport Nuclear Cross

Section Processing Code.

WARD-XS-3045-17 (August 1977)

(3) O. Ozer:

RESEND: A Program to Preprocess ENDF/B Materials with Resonance

Files into a Pointwise Form.

BNL-17134 (1972)

(4) D.E. Cullen:

SIGMA (Version 74-1): A Program to Exactly Doppler Broaden

Tabulated Cross Sections in the ENDF/B Format.

UCID-16426 (1974)

(5) R.E. Schenter, J.L. Baker, R.B. Kidman:

ETOX: A Code to Calculate Group Constants for Nuclear Reactor

Calculations.

BNWL-1002 (1969)

(6) R.E. MacFarlane, R.B. Kidman:

LINX and BINX: CCCC Utility Codes for the MINX Multigroup Pro-

cessing Code.

LA-6219-MS (February 1976)

(7) R.B. Kidman, R.E. MacFarlane:

CINX: Collapsed Interpretation of Nuclear X-Sections.

LA-6287-MX (April 1976)

(8) B.M. Carmichael:

Standard Interface Files and Procedures for Reactor Physics

Codes, Version III.

LA-5486-MS (February 1974)

(9) B.A. Hutchins, C.L. Cowan, M.D. Kelley, J.E. Turner:

ENDRUN II - A Computer Code to Generate a Generalized Multigroup Data File for ENDF/B.

General Electric Co report GEAP-13703 (March 1971)

(10) R.Q. Wright, N.M. Greene, J.L. Lucius, C.W. Craven:

SUPERTOG: A Program to Generate fine Group Constants and PN

Scattering Matrices from ENDF/B.

ORNL-TM-2679 (1969).

(11) D.E. Kusner, R.A. Daniels:

ETOG-1, A FORTRAN IV Program to Process Data from the ENDF/B

File to MUFT GAM and ANISN Formats.

Westinghouse Corporation Report WCAP-3845-1 (December 1969)

(1) C.R. Weisbin, P.D. Soran, R.E. MacFarlane, D.R. Harris,

R.J. LaBauve, J.S. Hendricks, J.E. White, R.B. Kidman:

MINX: A Multigroup Interpretation of Nuclear X-sections from

ENDF/B.

LA-6486-MS (September 1976)

(2) W.J. Davis, M.B. Yarbrough, A.B. Bortz:

SPHINX: A One Dimensional Diffusion and Transport Nuclear Cross

Section Processing Code.

WARD-XS-3045-17 (August 1977)

(3) O. Ozer:

RESEND: A Program to Preprocess ENDF/B Materials with Resonance

Files into a Pointwise Form.

BNL-17134 (1972)

(4) D.E. Cullen:

SIGMA (Version 74-1): A Program to Exactly Doppler Broaden

Tabulated Cross Sections in the ENDF/B Format.

UCID-16426 (1974)

(5) R.E. Schenter, J.L. Baker, R.B. Kidman:

ETOX: A Code to Calculate Group Constants for Nuclear Reactor

Calculations.

BNWL-1002 (1969)

(6) R.E. MacFarlane, R.B. Kidman:

LINX and BINX: CCCC Utility Codes for the MINX Multigroup Pro-

cessing Code.

LA-6219-MS (February 1976)

(7) R.B. Kidman, R.E. MacFarlane:

CINX: Collapsed Interpretation of Nuclear X-Sections.

LA-6287-MX (April 1976)

(8) B.M. Carmichael:

Standard Interface Files and Procedures for Reactor Physics

Codes, Version III.

LA-5486-MS (February 1974)

(9) B.A. Hutchins, C.L. Cowan, M.D. Kelley, J.E. Turner:

ENDRUN II - A Computer Code to Generate a Generalized Multigroup Data File for ENDF/B.

General Electric Co report GEAP-13703 (March 1971)

(10) R.Q. Wright, N.M. Greene, J.L. Lucius, C.W. Craven:

SUPERTOG: A Program to Generate fine Group Constants and PN

Scattering Matrices from ENDF/B.

ORNL-TM-2679 (1969).

(11) D.E. Kusner, R.A. Daniels:

ETOG-1, A FORTRAN IV Program to Process Data from the ENDF/B

File to MUFT GAM and ANISN Formats.

Westinghouse Corporation Report WCAP-3845-1 (December 1969)

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Package ID | Computer language |
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PSR-0105/01 | FORTRAN-IV |

PSR-0105/02 | FORTRAN+ASSEMBLER |

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PSR-0105/01

File name | File description | Records |
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PSR0105_01.001 | INFORMATION | 10 |

PSR0105_01.002 | ENDF/B LIBRARY DATA (BCD , TAPE 408) | 18381 |

PSR0105_01.003 | SOURCE PROGRAM (F4,EBCDIC) | 14751 |

PSR0105_01.004 | SAMPLE PROBLEM INPUT DATA | 9 |

PSR0105_01.005 | SAMPLE PROBLEM PRINTED OUTPUT | 3723 |

PSR-0105/02

File name | File description | Records |
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PSR0105_02.002 | INFORMATION | 6 |

PSR0105_02.003 | SOURCE PROGRAM - FORTRAN-4 EBCDIC | 14675 |

PSR0105_02.004 | SOURCE PROGRAM - BAL EBCDIC | 183 |

PSR0105_02.005 | ENDF/B-4 LIBRARY TAPE 408 (REV.2) | 18381 |

PSR0105_02.006 | JCL CARDS | 24 |

PSR0105_02.007 | OVERLAY CARDS | 50 |

PSR0105_02.008 | SAMPLE PROBLEM INPUT DATA | 9 |

PSR0105_02.009 | SAMPLE PROBLEM PRINTOUT | 3721 |

Keywords: ENDF/B, group constants, multigroup, self-shielding.