**1. NAME AND TITLE**

MKENO-DAR: Direct Angular Representation Monte Carlo Code for Criticality Safety
Analysis

**AUXILIARY ROUTINES**

INIT: Data pool initialization

MTCOPY: Doubly differential data pooling operation

COPY: Data pool management

MAIL-D: Cross-section calculation

REMAIL-D: Cross-section condensation

DATACV: Doubly differential data format conversion

TREE: Data pool tree structure visualization

**DATA LIBRARY**

MKENO-DAR-LIB: Card-image form of the doubly differential data used in MKENO-DAR 2.

**2. CONTRIBUTOR**

Japan Atomic Energy Research Institute, Tokai Research Establishment, Tokai-mura, Naka-gun,
Ibaraki-ken, Japan.

**3. CODING LANGUAGE AND COMPUTER**

Fortran, Assembler; FACOM M-380/M200.

**4. NATURE OF PROBLEM SOLVED**

MKENO-DAR calculates the effective neutron multiplication factor and neutron flux distribution in a three dimensional media, solving multigroup neutron transport equation with a precise angular distribution function for neutron scattering.

MKENO-DAR was developed from CCC-492/MULTI-KENO which was developed from KENO-IV. MULTI-KENO divides the system into many subsystem SUPER BOXES where the size of BOX
TYPEs in each SUPER BOX can be selected independently. MKENO-DAR improves the
representation of scattering angle over that in MULTI-KENO.

**5. METHOD OF SOLUTION**

Solutions of the transport problem which use Legendre polynomials to represent scattering processes require very high expansion order to represent precisely scattering that behaves like a delta function. To overcome this problem, MKENO-DAR uses a scattering probability angular distribution function prepared with cross sections which are expressed directly with the method called "Direct Angular Representation" (DAR) without using Legendre polynomials. That is, the maximum numbers of expansion coefficients of Legendre polynomials stored in the ENDF/B-IV nuclear data file are taken into account by the FAIR CROSS program, which is a nuclear constants processing module of the radiation shielding code system RADHEAT-V4. With the above angular cross sections, scattering probability angular distribution functions are produced for MKENO-DAR, which uses the Monte Carlo method to calculate the neutron multiplication factor and neutron flux in a three dimensional media.

The number of scattering angles used to make the cumulative distribution function can be different
for each energy group. The cross section data in DLC-118/MGCLIB is compatible with MKENO-DAR.

**6. RESTRICTIONS OR LIMITATIONS**

MKENO-DAR is flexibly dimensioned so that the allowed size of a problem is limited only by the
total data storage available.

**7. TYPICAL RUNNING TIME**

Running time for MKENO-DAR is highly problem dependent. Typical problems run between 2
and 50 minutes on the FACOM-M380, depending on the number of histories requested, the statistical
weighting used, the presence or absence of reflectors, complexity of the geometry, the number of
energy groups and the type of materials in the problem. A finite cylinder of highly-enriched 235U-H2O was executed on a FACOM-M380 in 11.08 minutes using 30,000 neutron histories and 137
neutron energy groups.

**8. COMPUTER HARDWARE REQUIREMENTS**

FACOM M-380/M200.

**9. COMPUTER SOFTWARE REQUIREMENTS**

Fortran IV, Assembler, FACOM OS/F4 operating system.

**10. REFERENCES**

**a. Included in package:**

Y. Naito and H. Nakae, "User's Manual of the MKENO-DAR Code System," JAERI-M 86-107 (August 1986).

Y. Naito, Y. Komuro and M. Nakayama, "MKENO-DAR: A Direct Angular Representation
Monte Carlo Code for Criticality Safety Analysis," JAERI-M 84-061 (March 1984).

**b. Background information:**

Y. Naito, M. Yokota and K. Nakano "MULTI-KENO: A Monte Carlo Code for Criticality Safety Analysis," (March 1983).

L. M. Petrie and N. F. Cross "KENO-IV: An Improved Monte Carlo Criticality Program,"
(November 1975).

**11. CONTENTS OF CODE PACKAGE**

Included are the documents referenced in (10.a) and 1 tape cartridge in tar format, which contains
the source codes, sample problem input and output, as well as binary data libraries used in the sample
runs. The card image form of the doubly differential data (MKENO-DAR-LIB) is included.

**12. DATE OF ABSTRACT**

January 1988.

**KEYWORDS:** COMPLEX GEOMETRY; CRITICALITY CALCULATIONS; MONTE CARLO;
MULTIGROUP; NEUTRON; REACTOR PHYSICS