.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/geophysics/plot_10_larmor_self_exciting_dynamo.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_geophysics_plot_10_larmor_self_exciting_dynamo.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

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

.. _sphx_glr_api_gallery_geophysics_plot_10_larmor_self_exciting_dynamo.py:


Larmor's self-exciting dynamo (1919)
====================================

Joseph Larmor asked how a body such as the Sun could be a magnet, and proposed
that conducting fluid moving through a magnetic field could induce the currents
that sustain that field, like a self-exciting dynamo. The Earth needs one: a
field left in a still iron core would decay in tens of thousands of years, yet
rocks record a field for over three billion years. The core's flow of a fraction
of a millimetre per second gives a magnetic Reynolds number in the hundreds,
enough for induction to beat diffusion.

.. GENERATED FROM PYTHON SOURCE LINES 13-39



.. image-sg:: /api/gallery/geophysics/images/sphx_glr_plot_10_larmor_self_exciting_dynamo_001.png
   :alt: A still core forgets its field, Induction beats diffusion
   :srcset: /api/gallery/geophysics/images/sphx_glr_plot_10_larmor_self_exciting_dynamo_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.geophysics import magnetic_decay_time, magnetic_reynolds_number
    from earthsciencekit.units import convert

    core_radius, shell = 3.48e6, 2.26e6
    conductivity = np.logspace(5, 6, 100)
    decay = convert(magnetic_decay_time(core_radius, conductivity), "s", "kyr")
    assert decay.max() < 100 and convert(3.5, "Ga", "kyr") / decay.max() > 1e4
    speed = np.logspace(-5, -2, 100)
    reynolds = magnetic_reynolds_number(speed, shell, 5e5)
    assert magnetic_reynolds_number(5e-4, shell, 5e5) > 100

    fig, (left, right) = plt.subplots(1, 2, figsize=(10, 4))
    left.loglog(conductivity, decay)
    left.set(xlabel="core conductivity [S/m]", ylabel="free decay time [kyr]", title="A still core forgets its field")
    right.loglog(convert(speed, "m/s", "cm/year"), reynolds)
    right.axhspan(10, 100, color="0.85", label="typical dynamo threshold")
    right.axvline(convert(5e-4, "m/s", "cm/year"), color="C3", ls="--", label="core flow from secular variation")
    right.set(xlabel="flow speed [cm/year]", ylabel="magnetic Reynolds number", title="Induction beats diffusion")
    right.legend(fontsize="small")
    fig.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.387 seconds)


.. _sphx_glr_download_api_gallery_geophysics_plot_10_larmor_self_exciting_dynamo.py:

.. only:: html

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

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../lite/lab/index.html?path=api/gallery/geophysics/plot_10_larmor_self_exciting_dynamo.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_10_larmor_self_exciting_dynamo.ipynb <plot_10_larmor_self_exciting_dynamo.ipynb>`

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

      :download:`Download Python source code: plot_10_larmor_self_exciting_dynamo.py <plot_10_larmor_self_exciting_dynamo.py>`

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

      :download:`Download zipped: plot_10_larmor_self_exciting_dynamo.zip <plot_10_larmor_self_exciting_dynamo.zip>`


.. only:: html

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

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