.. _sphx_glr_api_gallery_plasma_mhd:

Magnetohydrodynamics
--------------------

Treats the plasma as a single conducting fluid rather than a collection of
orbiting particles: the characteristic Alfven and magnetosonic wave speeds
(:func:`~physicskit.plasma.mhd.alfven_speed`,
:func:`~physicskit.plasma.mhd.magnetosonic_speeds`); static toroidal
equilibrium via the Grad-Shafranov equation
(:func:`~physicskit.plasma.mhd.solve_grad_shafranov`,
:func:`~physicskit.plasma.mhd.safety_factor_large_aspect_ratio`); and
resistive magnetic reconnection, comparing the classic Sweet-Parker model
against Petschek's faster X-point revision
(:func:`~physicskit.plasma.mhd.sweet_parker_rate`,
:func:`~physicskit.plasma.mhd.petschek_rate`).


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


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

.. thumbnail-parent-div-open

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    <div class="sphx-glr-thumbcontainer" tooltip="In 1942, Hannes Alfven proposed that a magnetized, highly conducting fluid should support a wave nobody had previously imagined: magnetic field lines, frozen into the plasma by its high conductivity, behave like strings under tension B^2/\mu_0, plucked sideways by the fluid&#x27;s own inertia. The result -- the Alfven wave -- travels at v_A = B/\sqrt{\mu_0\rho}, purely transverse and non-compressive, and founded magnetohydrodynamics (MHD) as a discipline treating the plasma as a single conducting fluid.">

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  .. image:: /api/gallery/plasma/mhd/images/thumb/sphx_glr_plot_01_alfven_and_magnetosonic_waves_thumb.png
    :alt:

  :doc:`/api/gallery/plasma/mhd/plot_01_alfven_and_magnetosonic_waves`

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      <div class="sphx-glr-thumbnail-title">Alfven waves and the magnetosonic wave-speed diagram</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Peter Sweet and Eugene Parker (1957-1958) proposed the first quantitative model of magnetic reconnection: oppositely directed field lines are driven together into a long, thin resistive current sheet of length L, where finite conductivity \eta finally lets them break and reconnect. The relevant dimensionless control parameter is the Lundquist number S=Lv_A/\eta, the ratio of the resistive diffusion time L^2/\eta to the Alfven crossing time L/v_A. Mass conservation through the sheet&#x27;s narrow exit throttles the whole process to">

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  .. image:: /api/gallery/plasma/mhd/images/thumb/sphx_glr_plot_02_sweet_parker_reconnection_thumb.png
    :alt:

  :doc:`/api/gallery/plasma/mhd/plot_02_sweet_parker_reconnection`

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      <div class="sphx-glr-thumbnail-title">The Sweet-Parker reconnection-rate bottleneck</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Harold Grad and Hanan Rubin, and independently Vitalii Shafranov, derived (1958) the equation governing any static, axisymmetric magnetized-plasma equilibrium: force balance between the pressure gradient and the \mathbf{J}\times\mathbf{B} force reduces, in toroidal geometry, to a single nonlinear elliptic PDE for the poloidal flux function \psi(R,Z),">

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  .. image:: /api/gallery/plasma/mhd/images/thumb/sphx_glr_plot_03_grad_shafranov_equilibrium_thumb.png
    :alt:

  :doc:`/api/gallery/plasma/mhd/plot_03_grad_shafranov_equilibrium`

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      <div class="sphx-glr-thumbnail-title">Solving the Grad-Shafranov equation for nested flux surfaces</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Harry Petschek (1964) proposed a resolution to the Sweet-Parker rate problem (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, 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.">

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  .. image:: /api/gallery/plasma/mhd/images/thumb/sphx_glr_plot_04_petschek_reconnection_thumb.png
    :alt:

  :doc:`/api/gallery/plasma/mhd/plot_04_petschek_reconnection`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Petschek vs. Sweet-Parker reconnection</div>
    </div>


.. thumbnail-parent-div-close

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    </div>


.. toctree::
   :hidden:

   /api/gallery/plasma/mhd/plot_01_alfven_and_magnetosonic_waves
   /api/gallery/plasma/mhd/plot_02_sweet_parker_reconnection
   /api/gallery/plasma/mhd/plot_03_grad_shafranov_equilibrium
   /api/gallery/plasma/mhd/plot_04_petschek_reconnection