5.3.14. xyz-mesh distribution source

By specifying s-type = 22, a complex spatial distribution of sources can be set. The spatial distribution can be defined by x-type, y-type, and z-type subsections and the data of relative intensities \(I_{ijk}, (i=1,\cdots,n_x; j=1,\cdots,n_y; k=1,\cdots,n_z)\). The data should be written below the subsections. The direction of the sources can be specified by dir, phi, and dom. Note that the direction in each xyz-bin cannot be changed. The parameters for the xyz-mesh distribution source are shown below. The order of parameters is free except for the data of the relative intensities. Parameters with (D=***) are optional.

Table 5.3.152 mesh

value	explanation
	Only xyz can be specified.

Table 5.3.153 dir

value	explanation
(D=1.0)	Direction cosine of the projectile relative to the z-axis.
all	Isotropic source.
data	An a-type subsection is required.

Table 5.3.154 phi

value	explanation
(D=all)	Azimuthal angle [degree].
all	Randomly selected in the range from 0 to 360 degrees.

Table 5.3.155 dom

value	explanation
(D=0.0)	Solid angle spread [degree].
-1	\(\cos^2\) bias distribution.

Table 5.3.156 e0

value	explanation
	For mono-energy source, specify the projectile energy [MeV/n]. For an energy spectrum, use e-type = instead.

Table 5.3.157 isbias

value	explanation
(D=0)	Option for representing the source distribution.
0	Represent the distribution by changing the number of generated particles from each mesh.
1	Represent the distribution by changing the source weight of each mesh. The source location is determined randomly from all meshes.
2	Represent the distribution by changing the source weight of each mesh while generating equal numbers of sources from each mesh.

Table 5.3.158 e-type

value	explanation
mono-energy source	Give the source energy [MeV/n] directly by e0.
energy spectrum	Specify the source energy distribution by e-type.

For the data of relative intensities \(I_{ijk}\), when nx, ny, and nz are all positive, the data should be written as follows:

\[I_{111}, I_{211}, \cdots, I_{n_x11}, I_{121}, I_{221}, \cdots, I_{n_xn_y1}, I_{112}, I_{212}, \cdots, I_{n_xn_yn_z}\]

where \(n_x = |nx|\), \(n_y = |ny|\), and \(n_z = |nz|\). For example, when ny and nz are negative, the data should be written as

\[I_{11n_z}, I_{21n_z}, \cdots, I_{n_x1n_z}, I_{12n_z}, I_{22n_z}, \cdots, I_{n_xn_yn_z}, I_{11(n_z-1)}, I_{21(n_z-1)}, \cdots, I_{n_xn_y1}\]

that is, in descending order with respect to \(k = n_z = |nz|\).

 1:   [ Source ]
 2:    s-type = 22
 3:      proj = neutron
 4:        e0 = 1.0
 5:       dir = all
 6:      mesh = xyz
 7:    x-type = 2
 8:        nx = 3
 9:      xmin = -10
10:      xmax =  10
11:    y-type = 2
12:        ny = -3
13:      ymin = -10
14:      ymax =  10
15:    z-type = 2
16:        nz = -2
17:      zmin = -10
18:      zmax =  10
19:        1 2 3
20:        4 5 6
21:        7 8 9
22:
23:        1 0 3
24:        0 5 0
25:        7 0 9

In this case, the source region is [\(-10\) cm \(\le x,y,z \le\) 10 cm], and the ranges in the \(x\), \(y\), and \(z\) axes are divided into 3, 3, and 2 bins, respectively. Because ny and nz are negative, the relative intensities \(I_{ijk}\) should be written in descending order for \(j\) and \(k\). Therefore, in lines 19-21 of the example, \(I_{ijk}\) with \(k = 2\), that is, in the region of [0 cm \(\le z \le\) 10 cm], are given as

\[\begin{split}\begin{pmatrix} I_{132} & I_{232} & I_{332} \\ I_{122} & I_{222} & I_{322} \\ I_{112} & I_{212} & I_{312} \end{pmatrix} = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix},\end{split}\]

and \(I_{ijk}\) with \(k = 1\), that is, in the region of [\(-10\) cm \(\le z \le\) 0 cm], are given in lines 23-25 as

(5.3.1)\[\begin{split}\begin{pmatrix} I_{131} & I_{231} & I_{331} \\ I_{121} & I_{221} & I_{321} \\ I_{111} & I_{211} & I_{311} \end{pmatrix} = \begin{pmatrix} 1 & 0 & 3 \\ 0 & 5 & 0 \\ 7 & 0 & 9 \end{pmatrix}.\end{split}\]

Fig. 5.3.5 and Fig. 5.3.6 show the source distribution of the example, obtained by [t-product] with output = source. The left and right panels are results in the regions of [0 cm \(\le z \le\) 10 cm] and [\(-10\) cm \(\le z \le\) 0 cm], respectively. In the left panel, the regions of 1, 2, 3, 4, 5, 6, … correspond to \(I_{132}, I_{232}, I_{332}, I_{122}, I_{222}, I_{322}, \cdots\), respectively. As the region number increases, the intensity in each region gradually increases. In the right panel, the sources do not generate in the regions of 2, 4, 6, and 8, which correspond to the elements of 0 on the right-hand side of Eq. (5.3.1).

Fig. 5.3.5 Results of the example above in the region of [0 cm \(\le z \le\) 10 cm].

Fig. 5.3.6 Results of the example above in the region of [\(-10\) cm \(\le z \le\) 0 cm].