.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gen_examples/free_free/plot_See0_RPA.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_See0_RPA.py>`
        to download the full example code

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

.. _sphx_glr_gen_examples_free_free_plot_See0_RPA.py:


Plot See0 using the RPA approximation
=====================================

This script reprocudes :cite:`Gregori.2003`, Fig. 1c. showing the calculation
of :math:`S_\text{ee}^{0, \text{RPA}}`.

.. GENERATED FROM PYTHON SOURCE LINES 8-63



.. image-sg:: /gen_examples/free_free/images/sphx_glr_plot_See0_RPA_001.svg
   :alt: plot See0 RPA
   :srcset: /gen_examples/free_free/images/sphx_glr_plot_See0_RPA_001.svg
   :class: sphx-glr-single-img





.. code-block:: Python


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

    import jaxrts
    import jaxrts.free_free as free_free

    ureg = jaxrts.units.ureg

    plt.style.use("science")

    lambda_0 = 0.26 * ureg.nanometer
    theta = 60
    n_e = 1e23 / ureg.centimeter**3

    E = jnp.linspace(-100, 100, 500) * ureg.electron_volts

    k = (4 * jnp.pi / lambda_0) * jnp.sin(jnp.deg2rad(theta) / 2.0)

    for count, T in enumerate(
        [
            0.8 * ureg.electron_volts,
            3.0 * ureg.electron_volts,
            13.0 * ureg.electron_volts,
        ]
    ):
        mu = jaxrts.plasma_physics.chem_pot_interpolationIchimaru(
            T / (1 * ureg.boltzmann_constant), n_e
        )

        vals = free_free.S0_ee_RPA_no_damping(
            k,
            T_e=T / (1 * ureg.boltzmann_constant),
            n_e=n_e,
            E=E,
            chem_pot=mu,
        ).m_as(ureg.second)

        if count == 0:
            norm = onp.max(vals)

        plt.plot(
            E.m_as(ureg.electron_volt),
            (vals / norm),
            label="T = " + str(T.m_as(ureg.electron_volt)) + " eV",
            color=f"C{count}",
        )

    plt.xlabel(r"$\omega$ [eV]")
    plt.ylabel(r"$S^0_{\text{ee}}$ [arb. units]")

    plt.legend()
    plt.tight_layout()
    plt.show()


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

   **Total running time of the script:** (0 minutes 2.706 seconds)


.. _sphx_glr_download_gen_examples_free_free_plot_See0_RPA.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_See0_RPA.ipynb <plot_See0_RPA.ipynb>`

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

      :download:`Download Python source code: plot_See0_RPA.py <plot_See0_RPA.py>`


.. only:: html

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

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