**1. NAME AND TITLE**

MADONNA: Two-dimensional Neutron Streaming Coupled Removal-Diffusion-Albedo-Transport Code System.

**AUXILIARY ROUTINES**

MACRO: Macroscopic Multigroup Neutron Data Generator.

REMOVAL: Calculation of Removal Neutron Fluxes (by Point Kernel Method) and Removal Scattering Sources.

DIFUSION: Calculation of Diffusion Neutron Fluxes Using Removal Scattering Sources.

PROBABILITY: Calculation of Transmission Probabilities Between Wall Surfaces Using Kernel-Albedo and Line-of-Sight Techniques.

CURRENT: Calculation of Reflected Currents at Duct Wall Surfaces by Albedo-Transport Methods.

**DATA LIBRARY**

MACRO-Mi: Microscopic Data Library Based on DLC-2D (Binary).

**2. CONTRIBUTOR**

Mitsubishi Atomic Power Industries, Inc., Tokyo, Japan, through the Japan Atomic Energy
Research Institute Code Center.

**3. CODING LANGUAGE AND COMPUTER**

Fortran IV; IBM 370/169.

**4. NATURE OF PROBLEM SOLVED**

MADONNA is a modular code system for two-dimensional neutron streaming calculations in
reactor shielding with various shapes of void, such as cylindrical duct, annular duct, and stepped or
offset annuli.

**5. METHOD OF SOLUTION**

MADONNA is based upon a removal-diffusion method coupled with an albedo-transport equation.
The albedo-transport equations are solved in void regions with initial leakage currents obtained from
the diffusion equation solution for an imaginary system where the original voids are filled. The
removal-diffusion equation is then solved in the whole system where the voids are replaced with the
boundary conditions expressed in terms of the net neutron currents to facilitate the solution of the
albedo-transport equation.

**6. RESTRICTIONS OR LIMITATIONS**

The principal restriction on the complexity of the problem is the availability of core storage. All
large modules are variably dimensioned. The array sizes are set for the particular problem being run
at execution.

**7. TYPICAL RUNNING TIME**

Running times for this system are a function of the number of removal neutron groups, diffusion
neutron groups, spatial nodes in a calculational geometry and subdivisions at duct wall surfaces.

**8. COMPUTER HARDWARE REQUIREMENTS**

MADONNA is operable on the IBM 370/169 computer. The amount of core storage required
depends upon the problem. All large modules are variably dimensioned.

**9. COMPUTER SOFTWARE REQUIREMENTS.**

A Fortran IV G-level compiler is required.

**10. REFERENCE**

**a. Included in the documenation:**

T. Nishimura, Y. Baba and H. Kinjo, "MADONNA Two-Dimensional Streaming Calculation
Code," Mitsubishi Atomic Power Industries, Inc. (August 1981).

**b. Background information:**

T. Nishimura and H. Kinjo, "Development of a Computer Code for Neutron Streaming Calculation
in LMFBR," pp 680-687 in *Proceedings of Fifth International Conference on Reactor Shielding,
Knoxville, Tennessee, April 17-23, 1977*, Conf. 770401.

DLC-2D 100 Group Neutron Cross-Section Data Based on ENDF/B. RSIC Data Library Collection.

P. C. Miller and A. Packwood, "The Exploitation of a Simplified Albedo Theory for Neutron and
Gamma-Ray Streaming in Practical Design Situation," pp. 1098-1130 in *Proceedings of Fourth
International Conference on Reactor Shielding, Paris, France, Oct. 9-13, 1972*, CONF 721018.

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced document (10.a) and one (1.2MB) DOS diskette which contains the
source code and sample problem input and output, a microscopic library based on DLC-2D in
hexadecimal.

**12. DATE OF ABSTRACT**

August 1982; revised September 1983.

**KEYWORDS: ** ALBEDO; KERNEL; REMOVAL-DIFFUSION; STREAMING; TWO-DIMENSIONS; NEUTRON; DUCT GEOMETRY; MULTIGROUP