**1. NAME AND TITLE**

TASK: Generalized One-Dimensional Radiation Transport and Diffusion Kinetics Code System.

**AUXILIARY ROUTINES**

ACPSD: Detector Response, and Cross-Power (CPSD) and Auto-Power (APSD), Spectral Density Data Generator.

FITSPEC: Spectral Fitting Routine.

**2. CONTRIBUTOR**

Oak Ridge National Laboratory, Oak Ridge, Tennessee.

**3. CODING LANGUAGE AND COMPUTER**

FORTRAN IV; IBM 360/370.

**4. NATURE OF PROBLEM SOLVED**

TASK solves the one-dimensional multigroup form of the reactor kinetics equations using either transport or diffusion theory allowing an arbitrary number of delayed neutron groups. TASK can also be used to efficiently solve standard static problems such as eigenvalue problems, distributed source problems, and boundary source problems.

**5. METHOD OF SOLUTION**

TASK employs a combination scattering and transfer matrix method in order to eliminate certain difficulties which arise in classical finite difference approximations. Within-group (inner) iterations are eliminated and solution convergence is independent of spatial mesh size. Convergence problems associated with sources in highly multiplicative media are circumvented and such problems are readily calculable. The time variable is removed by Laplace transformation. The code can be run either in an outer iteration mode or in closed (non-iterative) form. The running mode is dictated by the number of groups times the number of angles consistent with available storage.

ACPSD reads a TASK flux tape and computes an arbitrary number of detector responses at selected points in the system and produces both the cross and auto power spectra for any combination of detector pairs or single detectors. FITSPEC fits the point reactor model to the real part of the CPSD and to the APSD spectra generated by ACPSD.

**6. RESTRICTIONS OR LIMITATIONS**

Principal restrictions are available storage and computation time. The code is flexibly dimensioned and has an outer iteration option which means that there are no internal restrictions on group structure, quadrature, and number of ordinates. The generalized cylindrical geometry option is not complete in this version of the code. The feedback options and omega-mode search options are not included in this version of the code.

**7. TYPICAL RUNNING TIME**

A typical 13-region, 5-group, S_{4} fast reactor static distributed source problem required
approximately 1/2 minute on the IBM 360/91, whereas the entire kinetic response can be computed
in 8 to 10 minutes. A 16-group, S_{16} static 125-cm iron slab shielding problem with a boundary
source required about 4 minutes computation time.

**8. COMPUTER HARDWARE REQUIREMENTS**

TASK is operable on the IBM 360/370 computers. It requires 154K of storage plus data block storage to execute on the IBM 360/91. One tape is required if fluxes are needed for later analysis.

**9. COMPUTER SOFTWARE REQUIREMENTS**

A FORTRAN IV compiler and standard IBM 360 Operating System are required.

**10. REFERENCES**

**a. Included in the documentation:**

E. Tomlinson, "TASK," memo (September 1973).

A. R. Buhl, H. L. Dodds, Jr., J. C. Robinson, R. A. Lillie, O. W. Hermann, and R. J. Hinton, "A User's Manual for TASKA Generalized One-Dimensional Transport and Diffusion Kinetics Code," ORNL-TM-3811 (December 1972).

** b. Background information:**

H. L. Dodds, Jr., J. C. Robinson, and A. R. Buhl, "The Formulation and Application of the
Transfer-Scattering Matrix Method to Space-, Energy-, and Angular-Dependent Fast Reactor
Kinetics," *Nucl. Sci. Eng.*, 47, 262 (1972).

H. L. Dodds, Jr., "A New Calculational Method for Space-Energy-Angular-Dependent Reactor Kinetics," ORNL-TM-3136 (1971).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced document (10.a) and one (1.2MB) DOS diskette which contains source program and sample problem input and output, plus an ORNL Systems Subroutine.

**12. DATE OF ABSTRACT**

May 1975.

**KEYWORDS:** NEUTRON; DISCRETE ORDINATES; ONE-DIMENSION; TIME-DEPENDENT; DIFFUSION THEORY