CCC-0233 CRYSTAL-BALL.

1. NAME OR DESIGNATION OF PROGRAM:  CRYSTAL-BALL.

3. DESCRIPTION OF PROBLEM OR FUNCTION

CRYSTAL-BALL is a program for determining neutron spectra from activation measurements and their associated errors.

A subsidiary program, XSTAPE, converts activation cross sections from the SAND-II data library into pointwise cross sections in a format that can be read by the main program. An energy grid consistent with the SAND-II grid (2) is used, however the subroutine specifying the energy spacings can be easily changed.

CRYSTAL-BALL itself uses the cross section data, together with an initial guess of the neutron spectrum to calculate the integral and differential spectrum and the corresponding reaction rates and monitor responses. An option to plot spectrum data using CALCOMP plotter routines is included.

4. METHOD OF SOLUTION

Measured activities are related to the neutron  flux and cross section by an integral equation of the first kind. CRYSTAL-BALL uses the method of F.W. Stallman (1) to solve a set of  these equations.

The method is based on a direct approximation of the Dirac delta operator by a linear combination of integral operators. It involves  minimizing an integral expression involving both the true spectrum and a user-supplied estimate, subject to a tolerance limit.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM:

6. TYPICAL RUNNING TIME:

7. UNUSUAL FEATURES OF THE PROGRAM

Techniques solving these integral  equations by expanding the neutron spectrum in terms of some set of  functions frequently result in numerical oscillations and instabilities, and they tend to calculate spectrum shapes which are  characteristic of the expansion function. The CRYSTAL-BALL technique, using experimental data, has been found to be highly stable unless very low convergence criteria are requested.

8. RELATED AND AUXILIARY PROGRAMS

The subsidiary program, XSTAPE, which generates an appropriate activation cross section data set, is a modification of the SAND-II CSTAPE program.

10. REFERENCES

- F.W. Stallman:
  Numerical Solution of Integral Equations
  Numerische Mathematik vol. 15 pp. 297-305 (1970).
- W.N. McElroy, S. Bert, T. Crockett, R.G. Hawkins:
  SAND-II - A Computer Automated Iterative Method for Neutron Flux
  Determination by Foil Activation
  AFWL-TR-67-41 vol. 1-4.

- F.B.K. Kam and F.W. Stallmann:
  CRYSTAL BALL - A Computer Program for Determining Neutron Spectra
  from Activation Measurements
  ORNL-TM-4601 (June 1974).

11. MACHINE REQUIREMENTS:

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

The plotting option utilises the plot package INTRIGUE-II, and the CALCOMP plotter routines. Three subprograms of INTRIGUE-II, namely GRID, XTENS and TENS, have been modified slightly.

15. NAME AND ESTABLISHMENT OF AUTHOR

   F.B.K. Kam
   Operations Division
   Oak Ridge National Laboratory
   Oak Ridge, Tennessee 37830, U.S.A.

   F.W. Stallman
   University of Tennessee
   Knoxville, Tennessee, U.S.A.

File name	File description	Records
CCC0233_01.001	CROSS SECTION LIBRARY	2599
CCC0233_01.002	XSTAPE SOURCE F4 EBCDIC	504
CCC0233_01.003	XSTAPE DD CARDS	2
CCC0233_01.004	CRYSTAL-BALL SOURCE F4 EBCDIC	816
CCC0233_01.005	CRYSTAL-BALL DD CARDS	2
CCC0233_01.006	CRYSTAL-BALL INPUT DATA	34
CCC0233_01.007	XSTAPE OUTPUT	5925
CCC0233_01.008	CRYSTAL-BALL OUTPUT	334