.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/plasma/mhd/plot_04_petschek_reconnection.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_mhd_plot_04_petschek_reconnection.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_plasma_mhd_plot_04_petschek_reconnection.py:


Petschek vs. Sweet-Parker reconnection
===========================================

Harry Petschek (1964) proposed a resolution to the Sweet-Parker
rate problem (:doc:`plot_02_sweet_parker_reconnection`): if the
resistive diffusion region shrinks to a small X-point rather than
extending the full length of the current sheet, four standing
slow-mode shocks radiating from that X-point can carry away most of
the inflowing magnetic flux and energy. The resulting reconnection
rate falls only *logarithmically* with the Lundquist number,
:math:`v_{in}/v_A\approx\pi/(8\ln S)`, fast enough to plausibly explain
solar flare and magnetospheric substorm energy-release timescales that
Sweet-Parker reconnection could not.

:func:`~physicskit.plasma.mhd.petschek_rate` -- compare directly
against :func:`~physicskit.plasma.mhd.sweet_parker_rate` at the same
Lundquist number to see the difference explode as :math:`S` grows.

.. GENERATED FROM PYTHON SOURCE LINES 22-27

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    import physicskit as pk








.. GENERATED FROM PYTHON SOURCE LINES 28-33

Compare the two reconnection rates across the same S range
------------------------------------------------------------------
From laboratory to solar-flare-scale Lundquist numbers, Sweet-Parker's
S^(-1/2) collapses toward zero while Petschek's logarithmic
pi/(8 ln S) stays observationally plausible.

.. GENERATED FROM PYTHON SOURCE LINES 33-47

.. code-block:: Python


    S_vals = np.logspace(4, 14, 50)
    sp_rate = np.array([pk.plasma.sweet_parker_rate(S) for S in S_vals])
    pet_rate = np.array([pk.plasma.petschek_rate(S) for S in S_vals])

    fig, axes = plt.subplots(1, 2, figsize=(10, 4))
    axes[0].loglog(S_vals, sp_rate, label=r"Sweet-Parker $S^{-1/2}$")
    axes[0].loglog(S_vals, pet_rate, label=r"Petschek $\pi/(8\ln S)$")
    axes[0].axvline(1e12, color="gray", linestyle="--", linewidth=0.8, label="solar flare S")
    axes[0].set_xlabel("Lundquist number S")
    axes[0].set_ylabel(r"reconnection rate $v_{in}/v_A$")
    axes[0].set_title("Petschek's logarithmic rate vs. Sweet-Parker's S^(-1/2)")
    axes[0].legend()




.. image-sg:: /api/gallery/plasma/mhd/images/sphx_glr_plot_04_petschek_reconnection_001.png
   :alt: Petschek's logarithmic rate vs. Sweet-Parker's S^(-1/2)
   :srcset: /api/gallery/plasma/mhd/images/sphx_glr_plot_04_petschek_reconnection_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <matplotlib.legend.Legend object at 0x16b500620>



.. GENERATED FROM PYTHON SOURCE LINES 48-54

How far apart the two predictions actually are
------------------------------------------------------------------------
Overlaid on a log-log rate axis, the two curves' separation is easy to
underestimate; plotting their ratio directly shows Petschek's rate
pulling ahead by many orders of magnitude precisely where it matters --
solar-flare-scale Lundquist numbers.

.. GENERATED FROM PYTHON SOURCE LINES 54-67

.. code-block:: Python


    ratio = pet_rate / sp_rate
    axes[1].semilogy(S_vals, ratio, color="darkorange")
    axes[1].axvline(1e12, color="gray", linestyle="--", linewidth=0.8)
    s_flare_idx = np.argmin(np.abs(S_vals - 1e12))
    axes[1].annotate(f"{ratio[s_flare_idx]:.0e}x at solar-flare S", (S_vals[s_flare_idx], ratio[s_flare_idx]))
    axes[1].set_xscale("log")
    axes[1].set_xlabel("Lundquist number S")
    axes[1].set_ylabel(r"Petschek rate / Sweet-Parker rate")
    axes[1].set_title("The reconnection-rate gap, made explicit")
    fig.tight_layout()

    plt.show()








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

   **Total running time of the script:** (0 minutes 0.136 seconds)


.. _sphx_glr_download_api_gallery_plasma_mhd_plot_04_petschek_reconnection.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_04_petschek_reconnection.ipynb <plot_04_petschek_reconnection.ipynb>`

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

      :download:`Download Python source code: plot_04_petschek_reconnection.py <plot_04_petschek_reconnection.py>`

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

      :download:`Download zipped: plot_04_petschek_reconnection.zip <plot_04_petschek_reconnection.zip>`


.. only:: html

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

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