NEA-1846 FSKY4C.

1. NAME OR DESIGNATION OF PROGRAM:  FSKY4C

3. DESCRIPTION OF PROGRAM OR FUNCTION

FSKY4C computes skyshine dose of gamma ray for a system consisting of point sources, multi-layer shields simulating a reactor containment vessel and an infinite homogeneous medium of air. The output includes both the exposure dose and the effective dose of gamma ray at points of detection arranged on the horizontal plane in the medium of air. FSKY4C can be applied to shields with 3 types of geometry including upper spherical shell (spherical dome), upper slab, and side cylinder and their combination up to 3 layers. It is assumed that all shields are symmetric against rotation with respect to the Z axis perpendicular to the plane including points of detection for skyshine dose, and that all sources locate along the Z axis.
  
FSKY4C version 1.0 corrects problems in:
- calculation of radiations penetrating through multi-layer shields for the energy spectrum of a source specified by users,
- calculation of radiations penetrating through multi-layer shields for an angular limit specified by users,
- calculation of edge correction factor.

4. METHODS

Calculation of energy spectrum of gamma ray flux penetrated through the shields:
  
Energy spectrum of gamma ray flux penetrated through a single-layer shield with a path length X is computed approximately by multiplying the flux of uncollided gamma ray penetrated through the shield with a data for gamma Buildup Flux Energy Spectrum (BFE), defined as the gamma flux energy spectrum at the distance X from a point isotropic source in the infinite homogeneous medium with the same composition as the shield divided by the flux of uncollided gamma ray at the distance X in the same medium. Energy spectrum of gamma ray flux penetrated through multi-layer shield is computed with an approximation that angular distribution of flux penetrated through the first layer and incident on the second layer is concentrated into the direction of uncollided gamma ray. The data base including BFE with 18 energy groups as the function of the distance and the source energy for 7 materials is generated by the method of invariant embedding and used in FSKY4C.
  
Energy spectrum of gamma ray flux penetrated through the outer-most layer of shield is corrected with the edge correction factor, defined as the flux on the outer surface of a semi-infinite medium located at the distance X from the source divided by the flux at the same distance in the infinite medium. The data base for the edge correction factor is generated by the method of invariant embedding and used in FSKY4C.
  
Transport calculation of gamma ray in the infinite homogeneous medium of air :
Gamma ray skyshine dose is computed in FSKY4C by solving the transport equation for gamma ray in the infinite homogeneous medium of air with the point source emitting radiations with the energy-angle distribution same as the flux penetrated through the shields, according to Buildup Factor & Line Beam Response Function method (abbreviated by BF-LBRF method). The method combines 1) calculation of skyshine dose due to a point isotropic source by using the buildup factor of gamma ray for air, and 2) calculation of skyshine dose due to a conical beam from the source by using the Line Beam Response Function. The data base for the buildup factor for air as the function of the distance from the source and the source energy is generated by the method of invariant embedding. The data base for the anisotropy coefficient, defined as the skyshine dose due to a conical beam in a direction with energy E divided by the skyshine dose due to an isotropic source with the same energy E, is generated as the function of direction and energy of the source radiation, hight of the source from the horizontal plane, and the distance from the source based on the Line Beam Response Function calculated by using the Monte Carlo code EGS4.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The geometry of shields simulating a reactor containment vessel is restricted to 3 types including upper spherical shell (spherical dome) , upper slab, and side cylinder and their combination up to 3 layers. The material of shield is restricted at present to 7 materials, including water, iron, 4types of concrete, and lead. The composition of air is restricted at present to that given by the report NBS29. The source of gamma rays is assumed to point sources locating along the axis perpendicular to the horizontal plane including points of detection.

6. TYPICAL RUNNING TIME

About 1sec for a typical case (1 point source with 18 energy groups spectrum, 2 layers of shield, 28 points of detectors covering from 100m to 10km) by using PC (Dell dimension 8400).

7. UNUSUAL FEATURES

1. Very short running time applicable to time-dependent skyshine calculation
2. FSKY4C covers a thick shield (up to thickness of 100 mean free paths for energy of incident gamma ray) and a long distance in air (up to 300 mean free paths for source energy), where Monte Carlo Method is difficult to be applied.

10. REFERENCES

- Yasuhiro Sasaki, Yoshitaka Yoshida, Akinao Shimizu, et al.,:
Development of Quick Calculation Method for Gamma-Ray Skyshine Dose, INSS journal, 14, pp384-396
Background references:
- A. Shimizu, T. Onda, Y. Sakamoto:
'Calculation of Gamma-Ray Buildup Factor up to Depths of 100mfp by the Method of Invariant Embedding, - Generation of an Improved Data Set-', J. Nucl. Sci. Technol. 41,413 (2004)
- H. Hirayama, Y. Harima, Y. Sakamoto, N. Kurosawa, M. Nemoto:
'Data Library of the Line-and Conical-Beam Response Functions and Four-Parameter Empirical Formula in Approximating the Response Functions for Gamma-ray Skyshine Analyses', KEK Report. 2008-2 (2008)

- FSKY4C ver.1.0: Gamma Ray Skyshine Analysis Code, User's Guide (Dec. 2009)

11. HARDWARE REQUIREMENTS:  Windows OS machines.

13. SOFTWARE REQUIREMENTS:  Windows XP.

15. NAME AND ESTABLISHMENT OF AUTHORS

- Yoshitaka Yoshida, Institute of Nuclear Safety System, Sata 64, Mihama-cho, Mikata-gun, Fukui., Japan
- Akinao Shimizu, Radiation Dose Analysis Network, Kita-machi 4-13-14, Kokubunji-city, Tokyo, Japan

Source codes
Object files
Data libraries
Sample input and outpout files
User's Guide