**1. NAME AND TITLE**

FOCUS: Adjoint Monte Carlo Neutron Transport Code System.

**2. CONTRIBUTOR**

Inter-University Reactor Institute, Delft, The Netherlands, through the OECD NEA Data Bank,
Gif-sur-Yvette, France.

**3. CODING LANGUAGE AND COMPUTER**

Fortran IV, Assembler language; IBM 370/3033.

**4. NATURE OF PROBLEM SOLVED**

FOCUS was designed to solve a form of the adjoint neutron transport equation by the Monte Carlo method, from which any quantity related to neutron transport may be calculated. It was developed particularly for the calculation of differential quantities, such as point values, at one or more of the space, energy, direction, and time variables of quantities such as neutron flux, detector response, reaction rate, etc., or averages of such quantities over a small volume of the phase space.

Different types of problems can be treated, such as: systems with a fixed neutron source which may be a mono-directional source located outside the system, and eigenfunction problems in which the neutron source distribution is given by the (unknown) fundamental mode eigenfunction distribution. An equivalent treatment of a one-velocity thermal group is introduced. Due to a strong control of the sequence of random numbers per particle history, differences in estimated quantities from two systems due to small differences in geometry or cross section can be calculated with relatively small standard deviation.

Complex three-dimensional geometries and detailed cross-section information can be treated using
Monte Carlo methods. Cross-section data are derived from ENDF/B, with anisotropic scattering and
discrete or continuous inelastic scattering taken into account. Energy is treated as a continuous variable
and time dependence may also be included.

**5. METHOD OF SOLUTION**

A transformed form of the adjoint Boltzmann equation in integral representation is solved for the space, energy, direction, and time variables using Monte Carlo methods. Adjoint particles are defined with properties which are, in some respects, contrary to those of neutrons. Adjoint particle histories are constructed from which estimates of the desired quantity are obtained. Adjoint cross-sections are defined with which the nuclide and reaction type are selected in a collision. The energy after a collision is selected from adjoint energy distributions calculated together with the adjoint cross-sections in advance of the actual Monte Carlo calculation. For multiplying systems, successive generations of adjoint particles are obtained which will die out for subcritical systems with a fixed neutron source and which will be kept approximately stationary for eigenfunction problems.

Completely arbitrary problems can be handled by defining a neutron source and/or neutron
detector in simple user-written subroutines. Importance sampling devices, such as splitting, Russian
roulette, and path length stretching depending on energy and space region, are available.

**6. RESTRICTIONS OR LIMITATIONS**

Due to array dimensions, the number of different cross-section media in a system is limited to 16.
Each medium can contain at most 10 different nuclides. The total number of different nuclides in the
system is limited to 100. At most, 9 fissionable nuclides are allowed in the system. No limits apply
to the cross-section data or geometry description; however, to save computer storage, cross-section
data may be stored for only a limited energy range at a time.

**7. TYPICAL RUNNING TIME**

Running time is strongly dependent upon the complexity of the problem, the particular quantity
to be calculated, and the statistical accuracy desired. These factors may cause running time to vary
from about 0.5 minutes to several hours.

**8. COMPUTER HARDWARE REQUIREMENTS**

The code is operable on the IBM 370/3033 computer. Core storage is dependent upon the
complexity of the problem. In general, 256 K to 320 K bytes will be sufficient. FOCUS requires
simultaneous access to up to 4 files on disk or tape, depending upon the options selected. A clock is
required.

**9. COMPUTER SOFTWARE REQUIREMENTS**

A Fortran H Extended compiler, OPT=2, is required.

**10. REFERENCES**

J. E. Hoogenboom, "FOCUS A Versatile Non-Multigroup Adjoint Monte Carlo Neutron Transport Code," IRI-131-77-06/THD-H-RF-144 (1979).

J. E. Hoogenboom, "ETOF A Program to Prepare a Cross-Section Data Tape from the ENDF/B File for the Adjoint Monte Carlo Code FOCUS," IRI-131-77-05/THD-H-RF-146 (1979).

J. E. Hoogenboom and P. F. A. de Leege, "ADX A Code to Calculate Adjoint Neutron Cross
Sections from the ENDF/B File," IRI-131-77-04/THD-H-RF-145 (1979).

**11. CONTENTS OF CODE PACKAGE**

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

**12. DATE OF ABSTRACT**

February 1982.

**KEYWORDS: ** MONTE CARLO; ENDF/B FORMAT; ADJOINT; NEUTRON; COMPLEX
GEOMETRY; TIME-DEPENDENT