Physics explanation

The purpose of this distributed effort is to simulate the flux of gamma radiation outside a nuclear fuel assembly which is placed inside a steel box. To simulate this, a model of the geometry has been set up and the gamma flux is approximated using the so called 'line of sight point attenuation kernel method'. See figure 1.

Figure 1. The geometry used in the simulations, illustrating the steel box and the coordinate system.

Equation (1) shows how the flux of gamma radiation of a particular energy at the point P is simulated.

(1)

Where,

• V is the source volume.
• S is the source density.
• T is the transfer kernel.
• P is the point where the flux is to be simulated.

The transfer kernel T shows how gamma particles with a energy of E born at r' contribute to the flux at P. If this kernel takes into account all geometrical details and all physics processes, then the flux F is rigorously determined. However, it is difficult to find a transfer kernel that satisfies a full transport theory and the following simplifying approximations are used in the 'line of sight point attenuation kernel method'.

1. T depends only on a straight line from r' to P.
2. T does not depend on the geometry or material outside the line in 1.
3. T depends on the gamma particle energy.

Using these approximations, the transfer kernel is written as:

(2)

Where,

• R is the distance between r' and P.
• b is the relaxation number from r' to P.
• B is the build up factor taking into account scattering at small angles along the line between r' and P.

b is written according to equation (3).

(3)

Where,

• l is the line between r' and P.
• my is the attenuation coefficient.

In this distributed java simulation, the build up factor is further approximated to unity. I.e. the effect of scattering at small angles is neglected. So, as a summary, the flux is simulated using equation (4).

(4)

Furthermore, in the model used in this simulation, everything is assumed not to depend on the z coordinate. Using this assumption and equation (5), equation (4) can be rewritten to equation (6).

	(5)
	(6)

Here, the subscript xy means the projection in the xy plane. In the distributed simulation, equation (6) is approximated by the Riemann sum in equation (7).

(7)

delta-V_i is also further approximated by V/N.