.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gen_examples/ionic/plot_static_structure_factors_Gregori2006.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_static_structure_factors_Gregori2006.py>`
        to download the full example code

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

.. _sphx_glr_gen_examples_ionic_plot_static_structure_factors_Gregori2006.py:


Plot static structure factors in the Approximation by Gregori for T_i != T_e
============================================================================

This scripts plots :math:`S_{ee}`, :math:`S_{ei}`, :math:`S_{ii}` and :math:`q`
for Beryllium with an ionization of 2 at :math:`T_e = 20\text{eV}` and
:math:`n_e = 2.5\times 10^{23} 1 / \text{cm}^3`.
This script reproduces Fig.1 in :cite:`Gregori.2006`, showing the impact of
differences between the ion- and electron temperature on the static structure
factors as well as on the screening charge :math:`q`.

.. GENERATED FROM PYTHON SOURCE LINES 12-93



.. image-sg:: /gen_examples/ionic/images/sphx_glr_plot_static_structure_factors_Gregori2006_001.svg
   :alt: plot static structure factors Gregori2006
   :srcset: /gen_examples/ionic/images/sphx_glr_plot_static_structure_factors_Gregori2006_001.svg
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    from jax import numpy as jnp

    import jaxrts

    ureg = jaxrts.ureg

    m_i = jaxrts.Element("Be").atomic_mass
    n_e = ureg("2.5e23/cm³")
    T_e = ureg("20eV") / (1 * ureg.k_B)
    Z_f = 2

    T_e_prime = jaxrts.static_structure_factors.T_cf_Greg(T_e, n_e)
    T_D = jaxrts.static_structure_factors.T_Debye_Bohm_Staver(
        T_e_prime, n_e, m_i, Z_f
    )
    k_De = jaxrts.static_structure_factors._k_D_AD(T_e_prime, n_e)

    k_over_kDe = jnp.linspace(0, 10, 400)

    k = k_over_kDe * k_De


    plt.style.use("science")
    fig, ax = plt.subplots(2, 2, sharex=True, figsize=(5, 4))

    for i, T_i_over_T_e in enumerate([0.1, 0.5, 1.0]):
        T_i = T_e * T_i_over_T_e
        T_i_prime = jaxrts.static_structure_factors.T_i_eff_Greg(T_i, T_D)

        Sii = jaxrts.static_structure_factors.S_ii_AD(
            k, T_e_prime, T_i_prime, n_e, m_i, Z_f
        )
        Sei = jaxrts.static_structure_factors.S_ei_AD(
            k, T_e_prime, T_i_prime, n_e, m_i, Z_f
        )
        See = jaxrts.static_structure_factors.S_ee_AD(
            k, T_e_prime, T_i_prime, n_e, m_i, Z_f
        )
        # This is the q calculated by Gregori.2006
        simple_q = jnp.sqrt(Z_f) * Sei / Sii
        # For comparison, also calculate the full q using e.g. Gregri 2003 and
        # assert that these results are not too different.
        q = jaxrts.ion_feature.q_Gregori2004(k, m_i, n_e, T_e, T_i, Z_f)
        q = jnp.real(q.m_as(ureg.dimensionless))

        ax[0, 0].plot(k_over_kDe, Sii.m_as(ureg.dimensionless), label=T_i_over_T_e)
        ax[1, 0].plot(k_over_kDe, Sei.m_as(ureg.dimensionless), label=T_i_over_T_e)
        ax[0, 1].plot(k_over_kDe, See.m_as(ureg.dimensionless), label=T_i_over_T_e)
        ax[1, 1].plot(
            k_over_kDe,
            simple_q.m_as(ureg.dimensionless),
            color=f"C{i}",
            label="Simple q" if T_i_over_T_e == 0.1 else None,
        )
        ax[1, 1].plot(
            k_over_kDe[3:],
            q[3:],
            color=f"C{i}",
            label="Full q" if T_i_over_T_e == 0.1 else None,
            ls="dashed",
        )

    for a in ax[1, :]:
        a.set_xlabel("$k/k_{De}$")

    for a in [ax[0, 0], ax[1, 0], ax[0, 1]]:
        a.set_ylim(-0.05, 1.05)

    ax[0, 0].set_ylabel("$S_{ii}(k)$")
    ax[1, 0].set_ylabel("$S_{ei}(k)$")
    ax[0, 1].set_ylabel("$S_{ee}(k)$")
    ax[1, 1].set_ylabel("$q(k)$")

    ax[0, 1].legend(loc="lower right")
    ax[1, 1].legend(loc="upper right")

    plt.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 5.685 seconds)


.. _sphx_glr_download_gen_examples_ionic_plot_static_structure_factors_Gregori2006.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_static_structure_factors_Gregori2006.ipynb <plot_static_structure_factors_Gregori2006.ipynb>`

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

      :download:`Download Python source code: plot_static_structure_factors_Gregori2006.py <plot_static_structure_factors_Gregori2006.py>`


.. only:: html

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

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