.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "generated/gallery/user_guide/plot_ioneq.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_generated_gallery_user_guide_plot_ioneq.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_generated_gallery_user_guide_plot_ioneq.py:


Ionization fractions in equilibrium
===============================================

This example shows how to compute the ionization fraction as a function of
temperature, assuming equilibrium, for both a single ion as well as a whole
element.

.. GENERATED FROM PYTHON SOURCE LINES 9-19

.. code-block:: Python

    import astropy.units as u
    import matplotlib.pyplot as plt
    import numpy as np

    from astropy.visualization import quantity_support

    from fiasco import Element

    quantity_support()





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <astropy.visualization.units.quantity_support.<locals>.MplQuantityConverter object at 0x7fc3a21ca190>



.. GENERATED FROM PYTHON SOURCE LINES 20-21

First, create the `~fiasco.Element` object for carbon.

.. GENERATED FROM PYTHON SOURCE LINES 21-24

.. code-block:: Python

    temperature = 10**np.arange(3.9, 6.5, 0.01) * u.K
    el = Element('C', temperature)








.. GENERATED FROM PYTHON SOURCE LINES 25-32

The ionization fractions in equilibrium can be determined by calculating the
ionization and recombination rates as a function of temperature for every
ion of the element and then solving the associated system of equations.
This can be done by creating a `~fiasco.Element` object and then accessing
the `~fiasco.Element.equilibrium_ionization` property.
We can use this to plot the population fraction of each ion as a
function of temperature.

.. GENERATED FROM PYTHON SOURCE LINES 32-42

.. code-block:: Python

    for ion in el:
        ioneq = el.equilibrium_ionization[:, ion.charge_state]
        imax = np.argmax(ioneq)
        plt.plot(el.temperature, ioneq)
        plt.text(el.temperature[imax], ioneq[imax], ion.ionization_stage_roman,
                 horizontalalignment='center')
    plt.xscale('log')
    plt.title(f'{el.atomic_symbol} Equilibrium Ionization')
    plt.show()




.. image-sg:: /generated/gallery/user_guide/images/sphx_glr_plot_ioneq_001.png
   :alt: C Equilibrium Ionization
   :srcset: /generated/gallery/user_guide/images/sphx_glr_plot_ioneq_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 43-50

The CHIANTI database also includes tabulated ionization equilibria for
all ions in the database. The `ioneq` attribute on each
`~fiasco.Ion` object returns the tabulated population
fractions interpolated onto the `temperature` array.
Note that these population fractions returned by `~fiasco.Ion.ioneq` are
stored in the CHIANTI database and therefore are set to NaN
for temperatures outside of the tabulated temperature data given in CHIANTI.

.. GENERATED FROM PYTHON SOURCE LINES 50-55

.. code-block:: Python

    plt.plot(el.temperature, el[3].ioneq)
    plt.xscale('log')
    plt.title(f'{el[3].ion_name_roman} Equilibrium Ionization')
    plt.show()




.. image-sg:: /generated/gallery/user_guide/images/sphx_glr_plot_ioneq_002.png
   :alt: C IV Equilibrium Ionization
   :srcset: /generated/gallery/user_guide/images/sphx_glr_plot_ioneq_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 56-60

We can then compare tabulated and calculated results for a single ion.
Note that the two may not be equal due to differences in the rates when
the tabulated results were calculated or due to artifacts from the
interpolation.

.. GENERATED FROM PYTHON SOURCE LINES 60-67

.. code-block:: Python

    plt.plot(el.temperature, el.equilibrium_ionization[:, el[3].charge_state], label='calculated')
    plt.plot(el.temperature, el[3].ioneq, label='interpolated')
    plt.xlim(4e4, 3e5)
    plt.xscale('log')
    plt.legend()
    plt.title(f'{el[3].ion_name_roman} Equilibrium Ionization')
    plt.show()



.. image-sg:: /generated/gallery/user_guide/images/sphx_glr_plot_ioneq_003.png
   :alt: C IV Equilibrium Ionization
   :srcset: /generated/gallery/user_guide/images/sphx_glr_plot_ioneq_003.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.805 seconds)


.. _sphx_glr_download_generated_gallery_user_guide_plot_ioneq.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_ioneq.ipynb <plot_ioneq.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_ioneq.py <plot_ioneq.py>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_