Examples of multi-source
--------------------------------------------------

Examples of multi-source are shown below.
These examples also include energy distributions using functions and an angular-distribution example.
First, the list of source sections is shown.

.. _ex-source-ex1:

.. code-block:: text
  :caption: Example of multi-source

     1:   [ Source ]
     2:    totfact = 3
     3:   <source> = 9.72
     4:     s-type = 1
     5:       proj = proton
     6:         z0 = 2
     7:         z1 = 29
     8:         r0 = 5
     9:         r1 = 4
    10:        dir = 0.0
    11:     e-type = 6
    12:        eg1 = 1.e-6
    13:        eg2 = 1.e-3
    14:        nm  = -200
    15:       set: c10[1.e-4]
    16:       f(x) = x**(1.5)*exp(-x/c10)
    17:   <source> = 1
    18:     s-type = 1
    19:       proj = photon
    20:         z0 = 1
    21:         z1 = 2
    22:         r0 = 5
    23:        dir = -1
    24:     e-type = 5
    25:        eg1 = 1.e-3
    26:        eg2 = 5.e-1
    27:        nm  = 200
    28:        set: c10[1.e-1]
    29:        set: c20[1.e-1/2.35482]
    30:       f(x) = exp(-(x-c10)**2/2/c20**2)
    31:   <source> = 1
    32:     s-type = 1
    33:       proj = neutron
    34:         z0 = 29
    35:         z1 = 30
    36:         r0 = 5
    37:     e-type = 6
    38:        eg1 = 1.e-2
    39:        eg2 = 1.e+3
    40:        nm  = -200
    41:        set: c10[92.469]
    42:        set: c20[5.644e+10]
    43:       f(x) = c10/c20*exp(-sqrt(x*(x+1876))/c10)*(x+938)/sqrt(x*(x+1876))
    44:        dir = data
    45:     a-type = 5
    46:        ag1 = 0
    47:        ag2 = 1
    48:        nn  = 200
    49:       g(x) = exp(-(x-1)**2/0.3**2)

This example contains three sources starting with **<source>**.
The first source is a cylinder with :math:`z` from 2 cm to 29 cm and radius 5 cm.
However, because **r1 = 4** is defined, the inner region of radius 4 cm is excluded.
Thus, it is a hollow cylindrical source.
The next source is also a cylinder of radius 5 cm, with a thickness of 1 cm from :math:`z=1` cm to 2 cm.
The last source is the same thin cylinder as the previous one, but with :math:`z` from 29 cm to 30 cm.
The values defined by **<source>** for each source are the relative ratios of the sources.
Here, they are set to the volume ratios of each source.
Therefore, in this multi-source setting, particles are generated uniformly in the defined source regions.
The coordinate distribution calculated by **[t-product]** with **output = source** and **icntl = 6** is shown below.
This source defines a 1-cm-thick surface region of a cylinder.

.. figure:: ./source2.png
  :alt: multi-source1
  :name: fig-multi-source1
  :width: 30em

  Multi-source, spatial distribution

.. figure:: ./source4a.png
  :alt: multi-source2
  :name: fig-multi-source2
  :width: 30em

.. figure:: ./source3.png
  :alt: multi-sourcee
  :name: fig-multi-source3
  :width: 30em

Next, the three source particles are proton, photon, and neutron.
Their energy distributions are defined by functions.
The first is a Maxwell distribution, the second is a Gaussian distribution, and the last is an arbitrary function.
The first Maxwell distribution is equivalent to **e-type=7** with

.. code-block:: text

  e-type = 7
    et0 = 1.e-4
    et1 = 1.e-6
    et2 = 1.e-3

The second Gaussian distribution is equivalent to **e-type=2** with

.. code-block:: text

  e-type = 2
    eg0 = 1.e-1
    eg1 = 1.e-1
    eg2 = 1.e-4
    eg3 = 5.e-1

These energy distributions calculated by **[t-product]** with **output=source, icntl=6** are shown below.
The results are plotted for each particle, so the energy distribution of each source is shown in a different color.

.. figure:: ./source1.png
  :alt: multi-source4
  :name: fig-multi-source4
  :width: 30em

  Multi-source, energy distribution

The first source has **dir=0**, that is, 90 degrees.
The second has **dir=-1**, that is, 180 degrees.
The third has **dir=data** and therefore has an angular distribution.
Here, a Gaussian distribution centered at 0 degrees is defined by a function.
This result is shown below using **[t-cross]**.

.. figure:: ./cross01.png
  :alt: multi-source5
  :name: fig-multi-source5
  :width: 30em

  Multi-source, angular distribution