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

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

.. _sphx_glr_gen_examples_ee_lfc_plot_ee_lfc_comparison.py:


LFC comparison
==============

This example compares different static (and quasi-static) local field
corrections that are available in jaxrts.

The model by Hubbard :cite:`Hubbard.1957` is a simple formula, and the first
attempt to formulate a LFC, but does not obey the correct limiting cases.

The dotted curves showing the models by :cite:`UtsumiIchimaru.1982` and
:cite:`Farid.1993` show no temperature dependence as they are only implemented
for zero-temperature, whey they are the respective limits for the interpolation
formulas.

Dornheim et al. :cite:`Dornheim.2020` argue, that while the :math:`k^2` scaling
for large :math:`k` as presented by Farid is correct for the static LFC, in
practice, rather an effective static LFC should be used that obeys the correct
limiting case for a full, :math:`\omega` dependent LCF. An analytical function
fitting their datapoints is provided in :cite:`Dornheim.2021`.

.. GENERATED FROM PYTHON SOURCE LINES 22-122



.. image-sg:: /gen_examples/ee_lfc/images/sphx_glr_plot_ee_lfc_comparison_001.svg
   :alt: $k_BT=$1e-01 eV, $k_BT=$5e+01 eV, $k_BT=$1e+03 eV
   :srcset: /gen_examples/ee_lfc/images/sphx_glr_plot_ee_lfc_comparison_001.svg
   :class: sphx-glr-single-img


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

 .. code-block:: none

    theta = 0.0069
    theta = 3.5
    theta = 6.9e+01






|

.. code-block:: Python


    import jax.numpy as jnp
    import jpu.numpy as jnpu
    import matplotlib.pyplot as plt
    import scienceplots  # noqa: F401

    import jaxrts

    ureg = jaxrts.ureg

    plt.style.use("science")


    temp = (
        jnp.array([0.1, 50, 1000]) * ureg.electron_volt / ureg.boltzmann_constant
    )

    n_e = 2.5e23 / ureg.centimeter**3
    kf = jaxrts.plasma_physics.fermi_wavenumber(n_e)
    k = jnpu.linspace(0 * kf, 7 * kf, 5000)

    fig, ax = plt.subplots(len(temp), sharex=True, figsize=(6, 9))


    for T, axis in zip(temp, ax):
        theta = (T / jaxrts.plasma_physics.fermi_temperature(n_e)).m_as(
            ureg.dimensionless
        )
        print(f"theta = {theta:.2}")
        if theta < 4:
            G_dornheim = [
                jaxrts.ee_localfieldcorrections.eelfc_dornheim2021(
                    _k, T, n_e
                ).m_as(ureg.dimensionless)
                for _k in k
            ]
            axis.plot(
                (k / kf).m_as(ureg.dimensionless),
                G_dornheim,
                label="Dornheim.2021 (QSA)",
                color="C3",
            )
        else:
            axis.text(0, 2, "outside Dornheim.2021 validity", color="C3")
        G_hubbard = jaxrts.ee_localfieldcorrections.eelfc_hubbard(k, T, n_e)
        G_geldart = jaxrts.ee_localfieldcorrections.eelfc_geldartvosko(k, T, n_e)
        G_gregori = jaxrts.ee_localfieldcorrections.eelfc_interp_gregori2007(
            k, T, n_e
        )
        G_farid = jaxrts.ee_localfieldcorrections.eelfc_farid(k, T, n_e)
        G_utsumi = jaxrts.ee_localfieldcorrections.eelfc_utsumiichimaru(k, T, n_e)
        G_fortmann = jaxrts.ee_localfieldcorrections.eelfc_interp_fortmann2010(
            k, T, n_e
        )
        axis.plot(
            (k / kf).m_as(ureg.dimensionless),
            G_gregori.m_as(ureg.dimensionless),
            label="Interp. Gregori.2007",
        )
        axis.plot(
            (k / kf).m_as(ureg.dimensionless),
            G_fortmann.m_as(ureg.dimensionless),
            label="Interp. Fortmann.2010",
        )
        axis.plot(
            (k / kf).m_as(ureg.dimensionless),
            G_hubbard.m_as(ureg.dimensionless),
            label="Hubbard.1957",
        )
        axis.plot(
            (k / kf).m_as(ureg.dimensionless),
            G_utsumi.m_as(ureg.dimensionless),
            label="Utsumi \\& Ichimaru (zero T)",
            ls="dotted",
            color="gray",
        )
        axis.plot(
            (k / kf).m_as(ureg.dimensionless),
            G_farid.m_as(ureg.dimensionless),
            label="Farid (zero T)",
            ls="dotted",
            color="black",
        )
        axis.plot(
            (k / kf).m_as(ureg.dimensionless),
            G_geldart.m_as(ureg.dimensionless),
            label="Geldart \\& Vosko (high T)",
            ls="dashed",
            color="black",
        )
        axis.set_title(
            f"$k_BT=${(T * ureg.boltzmann_constant).m_as(ureg.electron_volt):.0e} eV"  # noqa:E501
        )
        axis.set_ylabel("$G$")

    ax[0].legend(ncols=2)
    ax[-1].set_xlabel("$k / k_f$")

    plt.tight_layout()
    plt.show()


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

   **Total running time of the script:** (0 minutes 11.867 seconds)


.. _sphx_glr_download_gen_examples_ee_lfc_plot_ee_lfc_comparison.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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