**1. NAME AND TITLE**

MARC-PN: A Neutron Diffusion Code System with Spherical Harmonics Option.

**AUXILIARY ROUTINES:**

FD5: Routine to read card image data and write it out in variable length records.

DECIN: Free format data reading package.

**DATA LIBRARY:**

FD5: 37-group fast reactor cross section set.

The MARC diffusion theory code developed from CRAM.

**2. CONTRIBUTOR**

United Kingdom Atomic Energy Authority, Risley, Warrington, England, through the OECD
Nuclear Energy Agency Data Bank, Gif-sur-Yvette Cedex, France.

**3. CODING LANGUAGE AND COMPUTER**

FORTRAN IV and Assembler language; ICL 2982, IBM 3081 (A); FORTRAN 77, VAX 8810.

**4. NATURE OF PROBLEM SOLVED**

MARC-PN solves the multigroup diffusion or neutron transport equation in most geometries of
interest. The code has a finite element option so that irregular problems can be accommodated. Input
may be taken from various cross section libraries such as FD5 (developed by UKAEA for fast reactor
studies), those in the SCALE package or the shielding sets CASK and EURLIB. A comprehensive set
of post edits is available including perturbation calculations, reaction rate evaluations and burn-up
changes for fuel management.

**5. METHOD OF SOLUTION**

In MARC-PN, the flux is expanded as a series of unnormalized spherical harmonics terminated
at some odd order N and the approximation denoted by PN. A set of linked first order differential
equations results for the coefficients of the series and, by eliminating odd terms, this yields a second
order system, which may be solved by a mesh centered difference technique or a finite element
approach.

**6. RESTRICTIONS OR LIMITATIONS**

For the VAX 8810 version (B), using the CRAM method, the variable
(12+NDSCAT)*NG*JMAX must be less than 30000. For the PDQ method,
(6+NDSCAT)*JMAX*IMAX must be less than 30000. NG is the number of groups; NDSCAT is the
number of down scatters; IMAX and JMAX are the number of points in x and y directions.

**7. TYPICAL RUNNING TIME**

No study has been made by RSIC of typical running times for MARC-PN. The test case for the
VAX 8810 version took 113 seconds of CPU time at NEA Data Bank.

**8. COMPUTER HARDWARE REQUIREMENTS**

The code is operable on the ICL 2982 or the IBM 3081 computers and also the VAX 8810.

**9. COMPUTER SOFTWARE REQUIREMENTS**

Special library type routines are furnished in FORTRAN IV and Assembler languages (A). On
the VAX 8810, the FORTRAN 77 compiler was used under the VAX/VMS Version 5.1-1 operating
system.

**10. REFERENCES**

**a. Included in the documentation:**

J. K. Fletcher, "A User's Guide to the MARC and PN Computer Codes," TRG Report 2911(R), The Reactor Group, United Kingdom Atomic Energy Authority (September 1976).

J. K. Fletcher, "A Finite Element Option for the MARC Transport/Diffusion Theory Computer Code, Northern Division Report," United Kingdom Atomic Energy Authority, ND-R-560(R) (January 1981).

J. K. Fletcher, "CTD: A Computer Program to Solve the Three-Dimensional Multigroup Diffusion Equation to XYZ and Triangular-Z Geometries," TRG Report 2344(R) (1973). J. K. Fletcher, ``The Solution of the Multigroup Neutron Transport Equation Using Spherical Harmonics,'' TRG Report 2547(R) (1974).

J. K. Fletcher, "Further Work on the Solution of the Static Multi-Group Neutron Transport
Equation Using Spherical Harmonics," TRG Report 2849(R) (1976).

**b. Background information:**

J. K. Fletcher, "The Solution of the Multigroup Neutron Transport Equation Using Spherical
Harmonics," *Nucl. Sci. Eng.* 84, 33-46 (1983).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced document (10.a) and one (1.2MB) DOS diskette which contains the
source code, data library, and sample problem input and output.

**12. DATE OF ABSTRACT**

December 1981; revised February 1983; updated October 1983 and December 1990.

**KEYWORDS: ** DIFFUSION THEORY; MULTIGROUP; NEUTRON; SLAB; CYLINDRICAL
GEOMETRY; SPHERICAL GEOMETRY; SPHERICAL HARMONICS;
COMPLEX GEOMETRY