.. _sphx_glr_api_gallery_plasma_waves:

Cold-plasma waves
-----------------

Linearizes the multi-fluid cold-plasma equations around a uniform
background to get the plasma frequency
(:func:`~physicskit.plasma.waves.plasma_frequency`) and the Stix
dielectric tensor components :math:`S`, :math:`D`, :math:`P`
(:func:`~physicskit.plasma.waves.stix_parameters`), from which every
named cold-plasma wave mode follows as one quartic equation in the
refractive index (:func:`~physicskit.plasma.waves.cold_plasma_dispersion`),
organized by the Clemmow-Mullaly-Allis (CMA) diagram
(:func:`~physicskit.plasma.waves.cma_coordinates`). Beyond this linear,
dispersion-relation picture, the ion-acoustic soliton
(:func:`~physicskit.plasma.waves.ion_acoustic_soliton_profile`,
:func:`~physicskit.plasma.waves.ion_acoustic_soliton_evolve`) is a
genuinely nonlinear traveling wave, propagating without change of shape
under the Washimi-Taniuti Korteweg-de Vries reduction.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="In 1928, Irving Langmuir found that the electron gas in an ionized discharge tube rings at a sharply defined natural frequency: displace the electrons from the (fixed) ion background and their own restoring electric field snaps them back, overshoots, and rings, exactly like a mass on a spring built from nothing but the plasma&#x27;s own charge density,">

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  .. image:: /api/gallery/plasma/waves/images/thumb/sphx_glr_plot_01_plasma_frequency_thumb.png
    :alt:

  :doc:`/api/gallery/plasma/waves/plot_01_plasma_frequency`

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      <div class="sphx-glr-thumbnail-title">Langmuir's plasma frequency</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Thomas Stix&#x27;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&#x27; plasma and cyclotron frequencies,">

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  .. image:: /api/gallery/plasma/waves/images/thumb/sphx_glr_plot_02_cma_diagram_thumb.png
    :alt:

  :doc:`/api/gallery/plasma/waves/plot_02_cma_diagram`

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      <div class="sphx-glr-thumbnail-title">Stix's cold-plasma dielectric tensor and the CMA diagram</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Haruichi Washimi and Tosiya Taniuti (1966) applied the &quot;reductive perturbation&quot; method to the coupled cold-ion-fluid/Boltzmann-electron equations in the weakly nonlinear, weakly dispersive limit and showed the ion-acoustic wave problem reduces exactly to the Korteweg-de Vries (KdV) equation, in its canonical stretched-coordinate form for the normalized density (or potential) perturbation u(\xi, t) in a frame moving at the ion-sound speed:">

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  .. image:: /api/gallery/plasma/waves/images/thumb/sphx_glr_plot_03_ion_acoustic_soliton_thumb.png
    :alt:

  :doc:`/api/gallery/plasma/waves/plot_03_ion_acoustic_soliton`

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      <div class="sphx-glr-thumbnail-title">Ion-acoustic solitons: a KdV pulse that never changes shape</div>
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    </div>


.. toctree::
   :hidden:

   /api/gallery/plasma/waves/plot_01_plasma_frequency
   /api/gallery/plasma/waves/plot_02_cma_diagram
   /api/gallery/plasma/waves/plot_03_ion_acoustic_soliton