Energy Spectrum of Prompt Fission Neutrons
=======================

The energy spectrum of the prompt fission neutrons, which we'll call as the
prompt fission spectrum for simplicity, represents the probability of neutrons
of different energies to be born in a fission event &mdash; a very important
parameter.

This quantity, usually denoted by $\chi_p$, is a probability distribution.
So let's check some simple approaches to it.


```python
import matplotlib as mpl
import matplotlib.pyplot as plt
from matplotlib.ticker import MaxNLocator
import sympy as sym
from sympy.plotting import plot

mpl.style.use('seaborn')
```


```python
def neutron_pop(k):
    """
    Gived the ratio of neutron pupulation in generation i, N_i, by the initial neutron population N_0 given the number of generations.
    """
    ni_by_n0 = k**i
    return ni_by_n0

```


```python
i = sym.symbols('i')
crit_pop = neutron_pop(1.0)
super_pop = neutron_pop(1.18)
sub_pop = neutron_pop(0.9)

gen = 10

population = plot(sub_pop, crit_pop, super_pop, (i, 0, gen),
                  adaptive = False,
                  nb_of_points = 500,
                  size=(5,3),
                  xlabel='generation (-)',
                  ylabel='$N_i/N_0$ (-)',
                  axis_center=(-0.1,0.7),
                  show=False)
```


```python
x0, y0 = population._series[0].get_points()
x1, y1 = population._series[1].get_points()
x2, y2 = population._series[2].get_points()

fig, ax = plt.subplots(figsize=(5,3))
ax.plot(x0, y0, label='k=0.90')
ax.plot(x1, y1, label='k=1.00')
ax.plot(x2, y2, label='k=1.18')
ax.set_xlabel('generation')
ax.set_ylabel('$N_i/N_0$')
ax.xaxis.set_major_locator(MaxNLocator(integer=True))

ax.legend()

plt.savefig(f'k_pop_i{gen}.pdf', bbox_inches='tight')
```


```python

```

ipynb
e311565481c7d1c2beaa951579a5f43b9bcd4185
Jupyter Notebook
2022-01-13T10:39:12.000Z
2022-01-13T10:39:12.000Z
6c9ad03029dcd0c7bbc3dfc5f38918ca401189a5
MIT
deOliveira-R/course_reactor_physics
criticality/criticality.ipynb
6c9ad03029dcd0c7bbc3dfc5f38918ca401189a5
MIT
deOliveira-R/course_reactor_physics
criticality/criticality.ipynb
6c9ad03029dcd0c7bbc3dfc5f38918ca401189a5
MIT
deOliveira-R/course_reactor_physics
criticality/criticality.ipynb