.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/plot_B_curl_free.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_plot_B_curl_free.py>`
        to download the full example code.

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

.. _sphx_glr_examples_plot_B_curl_free.py:


Curl free magnetic field
------------------------

The magnetic field of a curl-free SECS (with its associated radial
field-aligned currents) is identically zero at and below the current
shell -- Fukushima's theorem -- which is why ground magnetometers can
never constrain curl-free amplitudes. Above the shell the field is
purely azimuthal (Vanhamäki and Juusola 2020, Equation 2.15). This
example shows the angular profile at satellite altitude and on the
ground.

.. GENERATED FROM PYTHON SOURCE LINES 13-55



.. image-sg:: /examples/images/sphx_glr_plot_B_curl_free_001.png
   :alt: Curl-free SECS magnetic field (10 kA)
   :srcset: /examples/images/sphx_glr_plot_B_curl_free_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from pysecs import SECS


    # Radius of Earth
    R_E = 6378e3
    # Current shell at 100 km altitude
    R_I = R_E + 100e3

    # Pole of the current system at the North Pole
    sec_loc = np.array([90.0, 0.0, R_I])

    system_cf = SECS(sec_cf_loc=sec_loc)

    # Fit unit currents since we aren't fitting to any data,
    # then scale to a 10 kA system
    system_cf.fit_unit_currents()
    I0 = 10000

    # Observation points along a meridian, from the pole to the equator
    angles = np.linspace(0.5, 90, 500)
    lats = 90 - angles

    # On the ground (below the shell) and at 450 km altitude (above it)
    obs_ground = np.column_stack([lats, np.zeros_like(lats), np.full_like(lats, R_E)])
    obs_sat = np.column_stack([lats, np.zeros_like(lats), np.full_like(lats, R_E + 450e3)])

    B_ground = I0 * system_cf.predict_B(obs_ground)
    B_sat = I0 * system_cf.predict_B(obs_sat)

    fig, ax = plt.subplots()
    # The azimuthal (eastward) component carries the entire field
    ax.plot(angles, B_sat[:, 1] * 1e9, label="450 km altitude (above shell)")
    ax.plot(angles, B_ground[:, 1] * 1e9, label="ground (below shell)")
    ax.set_xlabel("angle from SECS pole (deg)")
    ax.set_ylabel(r"B$_\phi$ (nT)")
    ax.set_title("Curl-free SECS magnetic field (10 kA)")
    ax.legend()
    plt.show()


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

   **Total running time of the script:** (0 minutes 0.137 seconds)


.. _sphx_glr_download_examples_plot_B_curl_free.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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