.. _sec-source-time:

Definition of time distribution
--------------------------------------------------

By specifying a time-distribution subsection starting with **t-type =**, the source can have a time distribution.
**t-type = 1, 2** correspond to rectangular and Gaussian distributions, respectively.
**t-type = 3, 4** define a time distribution by boundary points and intensity distribution.
**t-type = 5, 6** define a time-dependent intensity distribution by an arbitrary function.
In addition, **t-type = 100** can specify the type of time distribution as a function of energy.
Items with (D=***) are omissible.

t-type = 0, 1, 2
^^^^^^^^^^^^^^^^^

Time distribution, D = 0.
0: No time distribution. **t = 0.0**.
1: Rectangular distribution.
2: Gaussian distribution.

**t0 =**: Center time of the first time distribution [ns], D = 0.0.

**tw =**: Width of the time distribution [ns].
For the rectangular distribution, this is the full width.
For the Gaussian distribution, this is the full width at half maximum.

**tn =**: Number of time distributions.

**td =**: Interval between time distributions [ns].

**tc =**: Cutoff time [ns] for the Gaussian distribution, D = :math:`10 \times tw`.

t-type = 3
^^^^^^^^^^

An arbitrary time distribution is specified by giving time boundary points **t(i)** and the integrated values **w(i)** of the source particle generation probability in each bin.
The time distribution is represented by statistically adjusting the number of particles generated in each bin so that it is proportional to **w(i)**.

**ntt =**: Number of time groups.
Data are given in free format as follows.

(t(i), w(i), i = 1, ntt), t(ntt+1)

The integrated number of particles generated in each bin is proportional to **w(i)**.

t-type = 4
^^^^^^^^^^

The same time distribution as **t-type = 3** is generated.
However, whereas **t-type = 3** represents the time distribution by adjusting the number of generated particles, **t-type = 4** represents it by generating the same number of particles in all time bins and changing the integrated particle weight in proportion to **w(i)**.
In addition, by setting **o-type = 1** and giving the generation-number ratio **o(i)**, the number of generated particles in each bin can be changed to modify the statistics of a source at a specific time.

**ntt =**: Number of time groups.
Data are given in free format as follows.

(t(i), w(i), i = 1, ntt), t(ntt+1)

By default, **o-type = 0**, the same number of particles is generated in each bin.
When **o-type = 1** and **o(i)** is specified, the integrated number of generated particles in each bin is proportional to those values.

**o-type = 0, 1**: Generation-number option, D = 0.

- For 0, **o(i)=1** in all bins, and there is no following data.
- For 1, the generation-number ratio **o(i)** in each bin is given in the following line.

(o(i), i = 1, ntt)

t-type = 5
^^^^^^^^^^

A differential time spectrum, :math:`d\varphi/dt`, is given by an arbitrary function :math:`h(t)`.

**h(x)**: A function written in Fortran format.
Here, **x** represents time [ns].
Internal variables and constants can be used.

**ll**: Number of time groups.

**tg1**: Lower cutoff value of the time distribution [ns].

**tg2**: Upper cutoff value of the time distribution [ns].

t-type = 6
^^^^^^^^^^

The same time distribution as **t-type = 5** is generated.
However, whereas **t-type = 5** represents the time distribution by adjusting the number of generated particles, **t-type = 6** represents it by generating the same number of particles in all time bins and changing the integrated particle weight in proportion to **w(i)**.
In addition, by setting **o-type = 1** and giving the generation-number ratio **o(i)**, the number of generated particles in each bin can be changed to modify the statistics of a source at a specific time.

**h(x)**: A function written in Fortran format.
Here, **x** represents time [ns].
Internal variables and constants can be used.

**ll**: Number of time groups.
By default, **o-type = 0**, the same number of particles is generated in each bin.
When **o-type = 1** and **o(i)** is specified, the integrated number of generated particles in each bin is proportional to those values.

**tg1**: Lower cutoff value of the time distribution [ns].

**tg2**: Upper cutoff value of the time distribution [ns].

**o-type = 0, 1**: Generation-number option, D = 0.

- For 0, **o(i)=1** in all bins, and there is no following data.
- For 1, the generation-number ratio **o(i)** in each bin is given in the following line.

(o(i), i = 1, ll)


t-type = 100
^^^^^^^^^^^^

By specifying **t-type = 100** and modifying the PHITS source file, an arbitrary time distribution can be given as a function of energy.
To use this function, modify the subroutine **tdis01** in the source file ``sors.f``.

**tg1**: Lower cutoff value of the time distribution [ns].

**tg2**: Upper cutoff value of the time distribution [ns].