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

.. only:: html

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

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

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

.. _sphx_glr_gen_examples_ionic_plot_HNC_electron_ion_potential.py:


HNC: Electron-Ion Potentials
============================

This example reproduces Figure 4.6 in :cite:`Wunsch.2011`, showing
the different potentials implemented to treat the electron-ion interaction.

This plot shows quite plainly, notable differences between various models.

.. warning::

    We are not able to reproduce Fig. 4.6 from :cite:`Wunsch.2011`. Even if
    :math:`\lambda_{ab}` is fixed to a forcing the Deutsch Potential to the
    correct value at :math:`r = 0`, would need to modify the temperature to
    match the Klimontvich-Kraeft potential.

.. GENERATED FROM PYTHON SOURCE LINES 18-86



.. image-sg:: /gen_examples/ionic/images/sphx_glr_plot_HNC_electron_ion_potential_001.svg
   :alt: plot HNC electron ion potential
   :srcset: /gen_examples/ionic/images/sphx_glr_plot_HNC_electron_ion_potential_001.svg
   :class: sphx-glr-single-img


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

 .. code-block:: none

    [[[-1.32294303]
      [ 0.52917721]]

     [[ 0.52917721]
      [-0.21167088]]] angstrom






|

.. code-block:: Python


    import jax.numpy as jnp
    import jpu.numpy as jnpu
    import matplotlib.pyplot as plt

    import jaxrts
    from jaxrts import hnc_potentials, ureg

    plt.style.use("science")

    fig, ax = plt.subplots()

    state = jaxrts.PlasmaState(
        ions=[jaxrts.Element("He")],
        Z_free=[2.5],
        mass_density=[
            1.23e23 / ureg.centimeter**3 * jaxrts.Element("He").atomic_mass
        ],
        T_e=1e5 * ureg.kelvin,
    )

    r = jnp.linspace(0, 10, 1000) * ureg.angstrom

    KK = hnc_potentials.KlimontovichKraeftPotential()
    Kelbg = hnc_potentials.KelbgPotential()
    Deutsch = hnc_potentials.DeutschPotential()

    KK.include_electrons = "SpinAveraged"
    Kelbg.include_electrons = "SpinAveraged"
    Deutsch.include_electrons = "SpinAveraged"

    # Get lambda_ab from the limit of Deutsch:
    # for r-> 0: V_Deutsch -> q1q2/(4 pi eps_0 lam_ab)
    # This will only be correct for the ei part!
    lambda_ab = -KK.q2(state) / (4 * jnp.pi * ureg.epsilon_0 * 5 * ureg.rydberg)


    n = jaxrts.units.to_array([state.n_i[0], state.n_e])
    d = jnpu.cbrt(3 / (4 * jnp.pi * (n[:, jnp.newaxis] + n[jnp.newaxis, :]) / 2))

    print(lambda_ab.to(ureg.angstrom))


    ax.plot(
        (r / d[0, 0]).m_as(ureg.dimensionless),
        -KK.full_r(state, r)[1, 0, :].m_as(ureg.rydberg),
        label="Klimontvich Kraeft",
    )
    ax.plot(
        (r / d[0, 0]).m_as(ureg.dimensionless),
        -Kelbg.full_r(state, r)[1, 0, :].m_as(ureg.rydberg),
        label="Kelbg",
    )

    ax.plot(
        (r / d[0, 0]).m_as(ureg.dimensionless),
        -Deutsch.full_r(state, r)[1, 0, :].m_as(ureg.rydberg),
        label="Deutsch",
    )

    ax.set_xlabel("$r\\; [d_i$]")
    ax.set_ylabel("$V_{ei}\\; [\\mathrm{Ryd}]$")

    ax.legend()
    ax.set_xlim(0, 5.0)
    # ax.set_ylim(0, 10)
    plt.tight_layout()
    plt.show()


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

   **Total running time of the script:** (0 minutes 2.351 seconds)


.. _sphx_glr_download_gen_examples_ionic_plot_HNC_electron_ion_potential.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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