.. _sphx_glr_api_gallery_plasma_single_particle:

Single-particle motion
----------------------

Charged-particle motion in electromagnetic fields, in two complementary
pictures: the exact Lorentz-force orbit integrated with the
energy-conserving Boris pusher
(:func:`~physicskit.plasma.single_particle.boris_integrate`), and the
guiding-center picture that averages over the fast gyration to track only
the slow drift of the orbit's center
(:func:`~physicskit.plasma.single_particle.exb_drift`,
:func:`~physicskit.plasma.single_particle.grad_b_drift`,
:func:`~physicskit.plasma.single_particle.curvature_drift`) and the
adiabatic invariant responsible for magnetic mirror confinement
(:func:`~physicskit.plasma.single_particle.magnetic_moment`,
:func:`~physicskit.plasma.single_particle.magnetic_mirror_bounce`).


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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="Rather than integrate every fast gyration of a charged particle around a field line, plasma theorists of the 1950s (with foundational contributions from Alfven and later systematized by Northrop) showed that the orbit separates cleanly into a rapid gyration plus a slow drift of the gyration&#x27;s center -- the guiding center -- driven by any force or field gradient perpendicular to \mathbf{B}. The gyration itself conserves an adiabatic invariant, the magnetic moment \mu=mv_\perp^2/2B, to very high accuracy whenever the field changes slowly compared to the gyration period; as a particle&#x27;s guiding center drifts into stronger field, \mu conservation forces v_\perp to grow at the expense of v_\parallel. That conversion is the reaction of a parallel mirror force,">

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  .. image:: /api/gallery/plasma/single_particle/images/thumb/sphx_glr_plot_01_guiding_center_drifts_and_mirror_thumb.png
    :alt:

  :doc:`/api/gallery/plasma/single_particle/plot_01_guiding_center_drifts_and_mirror`

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      <div class="sphx-glr-thumbnail-title">Guiding-center drifts and magnetic mirror confinement</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Jay Boris, developing early particle-in-cell plasma codes, needed a numerical integrator for the Lorentz force m\dot{\mathbf{v}}=q(\mathbf{E}+\mathbf{v}\times\mathbf{B}) that would not spuriously heat or cool a particle over millions of simulated gyro-orbits. His 1970 scheme splits each leapfrog step into an electric half-kick, an exact rotation about \mathbf{B} computed without any trigonometry (the &quot;Boris rotation&quot; trick), and a second electric half-kick; the rotation step conserves speed to machine precision in a pure magnetic field, regardless of step size.">

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  .. image:: /api/gallery/plasma/single_particle/images/thumb/sphx_glr_plot_02_boris_pusher_thumb.png
    :alt:

  :doc:`/api/gallery/plasma/single_particle/plot_02_boris_pusher`

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      <div class="sphx-glr-thumbnail-title">Energy-conserving gyration with the Boris pusher</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Modern magnetic-confinement fusion research is dominated by gyrokinetic theory: rather than track a particle&#x27;s full gyration (as the Boris pusher does, plot_02_boris_pusher) or reduce all the way to a fluid (as MHD does), gyrokinetics analytically averages the Vlasov equation over the fast gyro-angle while retaining the finite-Larmor-radius physics needed for turbulence. This closes the gap between the guiding-center drift theory of the 1950s (plot_01_guiding_center_drifts_and_mirror) and full kinetic simulation, and is the theoretical foundation of every modern turbulent-transport code (GENE, GYRO, GS2) used to predict a fusion reactor&#x27;s confinement performance.">

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  .. image:: /api/gallery/plasma/single_particle/images/thumb/sphx_glr_plot_03_exb_drift_gyroaverage_thumb.png
    :alt:

  :doc:`/api/gallery/plasma/single_particle/plot_03_exb_drift_gyroaverage`

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      <div class="sphx-glr-thumbnail-title">Recovering the ExB drift as a time-average of the full orbit</div>
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    </div>


.. toctree::
   :hidden:

   /api/gallery/plasma/single_particle/plot_01_guiding_center_drifts_and_mirror
   /api/gallery/plasma/single_particle/plot_02_boris_pusher
   /api/gallery/plasma/single_particle/plot_03_exb_drift_gyroaverage