.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/plasma/waves/plot_02_cma_diagram.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_api_gallery_plasma_waves_plot_02_cma_diagram.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_plasma_waves_plot_02_cma_diagram.py:


Stix's cold-plasma dielectric tensor and the CMA diagram
=============================================================

Thomas Stix's 1962 *The Theory of Plasma Waves* organized the zoo of
magnetized cold-plasma wave modes -- Alfven waves, whistlers, cyclotron
waves, the ordinary and extraordinary radio-propagation modes -- into a
single 3x3 dielectric tensor built from each species' plasma and
cyclotron frequencies,

.. math::

   \mathbf{K} = \begin{pmatrix} S & -iD & 0 \\ iD & S & 0 \\ 0 & 0 & P \end{pmatrix},

from which every cold-plasma dispersion relation follows as one
quartic equation in the refractive index. The Clemmow-Mullaly-Allis
(CMA) diagram maps the entire parameter space of that quartic onto one
two-dimensional plot.

:func:`~physicskit.plasma.waves.stix_parameters` builds :math:`S`,
:math:`D`, :math:`P` for an arbitrary multi-species plasma;
:func:`~physicskit.plasma.waves.cold_plasma_dispersion` solves the
resulting quartic at any propagation angle, and
:func:`~physicskit.plasma.waves.cma_coordinates` supplies the CMA
diagram's axes.

.. GENERATED FROM PYTHON SOURCE LINES 29-34

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    import physicskit as pk








.. GENERATED FROM PYTHON SOURCE LINES 35-39

Tracing a CMA trajectory
----------------------------
A magnetized electron-proton plasma, swept in wave frequency across
the electron cyclotron resonance, traces one path on the CMA map.

.. GENERATED FROM PYTHON SOURCE LINES 39-46

.. code-block:: Python


    n0, B0 = 1e19, 1.0
    wpe = pk.plasma.plasma_frequency(n0)
    wce = pk.plasma.cyclotron_frequency(pk.plasma.QE, pk.plasma.ME, B0)
    omega_scan = np.linspace(0.05 * wce, 5 * wce, 300)
    X, Y = pk.plasma.cma_coordinates(omega_scan, wpe, wce)








.. GENERATED FROM PYTHON SOURCE LINES 47-50

At a fixed frequency, the same species build S, D, P, and solving the
quartic gives the two cold-plasma wave branches at every propagation
angle to B0.

.. GENERATED FROM PYTHON SOURCE LINES 50-70

.. code-block:: Python


    species = [(n0, -pk.plasma.QE, pk.plasma.ME), (n0, pk.plasma.QE, pk.plasma.MP)]
    S, D, P = pk.plasma.stix_parameters(omega=2e9, B=B0, species=species)
    theta = np.linspace(0, np.pi / 2, 200)
    n2 = np.array([pk.plasma.cold_plasma_dispersion(th, S, D, P) for th in theta])

    fig, axes = plt.subplots(1, 2, figsize=(10, 4))
    pk.plasma.plot_cma_diagram(X, Y, ax=axes[0])
    axes[0].set_title("CMA trajectory vs. wave frequency")

    axes[1].plot(theta, n2[:, 0], label=r"$n^2_+$")
    axes[1].plot(theta, n2[:, 1], label=r"$n^2_-$")
    axes[1].axhline(0.0, color="gray", linestyle="--", linewidth=0.8)
    axes[1].set_xlabel(r"$\theta$ (rad)")
    axes[1].set_ylabel(r"$n^2$")
    axes[1].set_title("Cold-plasma dispersion branches")
    axes[1].legend()
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/plasma/waves/images/sphx_glr_plot_02_cma_diagram_001.png
   :alt: CMA trajectory vs. wave frequency, Cold-plasma dispersion branches
   :srcset: /api/gallery/plasma/waves/images/sphx_glr_plot_02_cma_diagram_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.091 seconds)


.. _sphx_glr_download_api_gallery_plasma_waves_plot_02_cma_diagram.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_02_cma_diagram.ipynb <plot_02_cma_diagram.ipynb>`

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

      :download:`Download Python source code: plot_02_cma_diagram.py <plot_02_cma_diagram.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_02_cma_diagram.zip <plot_02_cma_diagram.zip>`


.. only:: html

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

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