**1. NAME AND TITLE**

NRN: Multigroup Removal-Diffusion Code System for Planes, Cylinders and Spheres.

**AUXILIARY ROUTINES**

NECO: Group Constant Data Generator.

REBOX: Multigroup Removal Code, Box Geometry.

REMC: Multigroup Removal Code, Spheres and Cylinders.

NEDI: Multigroup Diffusion and Slowing Down Code.

The NRN code system was originally designed for a Ferranti Mercury computer; was later
rewritten in FORTRAN IV for the IBM 7044, and has been converted to run on the CDC 6600.
NRN originated in Europe; has been distributed by RSIC nineteen times between 19661977.

**2. CONTRIBUTOR**

Aktiebolaget (AB) Atomenergi, Stockholm, Sweden through the NEA Computer Programme Library, Ispra (Varese), Italy

**3. CODING LANGUAGE AND COMPUTER**

FORTRAN IV; CDC-6600.

**4. NATURE OF PROBLEM SOLVED**

Given a distribution of fissions (e.g., power distribution) in certain allowed geometric regions, the program solves for neutron flux densities, neutron absorption rate (from which secondary gamma-ray source rates may be determined), various dose rates, energy deposit rate (by energy groups) in primary knock on atoms.

Provision is also made to adapt the routines REBOX and REMC to the computation of gamma-ray dose rates from gamma-ray sources in the central region (core).

**5. METHOD OF SOLUTION**

NRN is a system of codes built around the Spinney method of combining high energy exponential attenuation with lower energy diffusion. The high energy exponentially attenuating flux is broken into several energy groups, for each of which removal cross sections are required.

NECO computes all required macroscopic quantities from a specification of the microscopic quantities and the material compositions. It computes the required removal cross sections, a unique and very significant feature of NRN. (In this computation a simplified transport cross section model is used to assess the effect of elastic scattering. This simplification should limit the range of effective application of the method to some range of shield thicknesses. Very likely the range of interesting reactor shields will fall within that range.)

The exponential attenuation of the fast group fluxes (removal fluxes) is carried out in REBOX, if the source region is a sphere or a small cylinder. The integration over the source volume is carried out by a mesh-sum procedure in REBOX and by a Monte Carlo procedure in REMC.

The diffusion code, NEDI, is driven by the removal fluxes as sources in the shield region computed in REBOX or REMC and by some interior boundary conditions given as input. NEDI is limited to multiregion infinite slab, infinite cylinder, and spherical geometries. Hence, except in the spherical case, there is a geometric inconsistency between NEDI and REBOX or REMC. This is to be interpreted as an approximation, not an error. NEDI further provides for transverse buckling in the slab and cylindrical cases in order to estimate the effect of truncating the infinite systems.

In the spirit of this method it is held that diffusion theory is not appropriately used in the higher
energy ranges and over very large distances from the effective source. Hence, NEDI is applied
only in the ``shield region'' after the driving removal flux densities have been determined for that
region. The specification of reasonable external boundary conditions on this region is not difficult,
but the specification of reasonable internal boundary conditions is very difficult. If a significant
part of the final answer depends heavily upon the diffusion current or flux (rather than the removal
current or flux) at the interior shield boundary, this program should be used only with great
circumspection.

**6. RESTRICTIONS OR LIMITATIONS**

Number of energies < 19

Number of ID numbers for materials

(if REBOX and REMCO are used) < 4

(if only NEDI is used) < 10

Number of elements + 4 times the number of materials 100

Number of groups (if NEDI is used) < 35

Number of groups (without NEDI) < 50

Number of mesh intervals in a region < 200

Total number of mesh intervals in shield < 600

Number of regions (restricted by NEDI) < 30

Number of regions (REBOX only) < 50

Number of dose rates < 12

Number of dose rates (restricted by NEDI) < 10

Core divisions in the x, y, and z directions < 60 each

Number of different materials < 15

Dose rates printed out only for region boundaries (REMC-REBOX). If desired at interior
locations, artificial boundaries must be defined.

**7. TYPICAL RUNNING TIME**

RSIC has made no study of typical running time.

**8. COMPUTER HARDWARE REQUIREMENTS**

Originally designed for the Ferranti Mercury, NRN has been recoded for the IBM 7044 and
was made compatible with the IBM 7090, the CDC 3600 and currently CDC 6600. A maximum of
eight tape units is used.

**9. COMPUTER SOFTWARE REQUIREMENTS**

The packaged code can be compiled and run in the CDC 6000 series Operating Systems. A
maximum of eight tape assignments are made on two channels.

**10. REFERENCES**

Kj. Nyman, K. Lindblom, Kj. Olsson, K. Malen, E. Aalto, and G. Olsson, "A Preliminary User's Manual for the NRN Shield Design Method in FORTRAN IV Language," AE-FFA-673, AE-RFN-213 (October 1965).

E. Aalto, R. Fraki, and K. Malen, "The Fine Adjustment of the Neutron Penetration in the
NRN Method," *Nucl. Sci. Eng*., 22(4), 443-450 (1965).

L. Hjarne and M. Leimdorfer, "A Method for Predicting the Penetration and Slowing Down of
Neutrons in Reactor Shields," *Nucl. Sci. Eng.*, 24(2), 165-174 (1966).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced documents and one (1.2MB) DOS diskette which contains the
source codes and input and output for a sample problem.

**12. DATE OF ABSTRACT**

July 1967; updated July 1981.

**KEYWORDS: ** REMOVAL-DIFFUSION; SPINNEY METHOD; NETURON; SLAB; ONE-DIMENSION