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

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

.. _sphx_glr_gen_examples_free_free_plot_BornCollision_Frequency.py:


Born Collision Frequency
========================

Calculate the Born Collision Frequency and compare it to the published data
shown in :cite:`Fortmann.2010`. While the shape seems to be similar, overall,
there is a difference that we currently don't understand.

.. GENERATED FROM PYTHON SOURCE LINES 9-90



.. image-sg:: /gen_examples/free_free/images/sphx_glr_plot_BornCollision_Frequency_001.svg
   :alt: plot BornCollision Frequency
   :srcset: /gen_examples/free_free/images/sphx_glr_plot_BornCollision_Frequency_001.svg
   :class: sphx-glr-single-img





.. code-block:: Python


    from pathlib import Path

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

    import jaxrts

    ureg = jaxrts.ureg

    try:
        current_folder = Path(__file__).parent
    except NameError:
        current_folder = Path.cwd()
    data_dir = current_folder / "../../../tests/data/Fortmann2010/Fig1"

    # :cite:`Fortmann.2010` calculated these values at zero kelvin. This is
    # currently not implemented, in our code. We therefore use a finite
    # temperature, instead, accepting that we might deviate slightly from the
    # published result
    T = 0.1 * ureg.electron_volt / ureg.k_B
    Zf = 1.0
    fig, ax = plt.subplots(2)


    @jax.tree_util.Partial
    def S_ii(q):
        return jnpu.ones_like(q)


    for r_s in [1.0, 2.0, 5.0]:
        n_e = 3 / (4 * jnp.pi * (r_s * ureg.a0) ** 3)
        w_f = jaxrts.plasma_physics.fermi_energy(n_e) / (1 * ureg.hbar)

        @jax.tree_util.Partial
        def V_eiS(q):
            return jaxrts.plasma_physics.coulomb_potential_fourier(
                Zf, -1, q
            ) / jaxrts.free_free.dielectric_function_RPA_0K(
                q, 0 * ureg.electron_volt, n_e
            )

        E_f = jaxrts.plasma_physics.fermi_energy(n_e)
        E = jnp.linspace(-200, 200, 2000) * E_f
        nu = jaxrts.free_free.collision_frequency_BA_fullFit(
            E, T, S_ii, V_eiS, n_e, Zf
        )
        dimless_nu = (nu / w_f).m_as(ureg.dimensionless)
        E_over_Ef_real, nu_real = onp.genfromtxt(
            data_dir / f"Re_rs{r_s:.0f}.csv", unpack=True, delimiter=","
        )
        E_over_Ef_imag, nu_imag = onp.genfromtxt(
            data_dir / f"Im_rs{r_s:.0f}.csv", unpack=True, delimiter=","
        )
        ax[0].plot(E_over_Ef_real, nu_real)
        ax[1].plot(E_over_Ef_imag, nu_imag)
        ax[0].plot(
            (E / E_f).m_as(ureg.dimensionless), jnp.real(dimless_nu), ls="dashed"
        )
        ax[1].plot(
            (E / E_f).m_as(ureg.dimensionless), jnp.imag(dimless_nu), ls="dashed"
        )
        nu = jaxrts.free_free.collision_frequency_BA_0K(E, S_ii, V_eiS, n_e, Zf)
        dimless_nu = (nu / w_f).m_as(ureg.dimensionless)
        ax[0].plot(
            (E / E_f).m_as(ureg.dimensionless), jnp.real(dimless_nu), ls="dotted"
        )
        ax[1].plot(
            (E / E_f).m_as(ureg.dimensionless), jnp.imag(dimless_nu), ls="dotted"
        )
        ax[0].plot(
            0.1,
            0.11523
            * r_s**2
            * (jnp.log(1 + 6.02921 / r_s) - 1 / (1 + r_s / 6.02921)),
            marker="x",
        )
    plt.show()


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

   **Total running time of the script:** (0 minutes 10.549 seconds)


.. _sphx_glr_download_gen_examples_free_free_plot_BornCollision_Frequency.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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