.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/plot_B_divergence_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_divergence_free.py>`
        to download the full example code.

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

.. _sphx_glr_examples_plot_B_divergence_free.py:


Divergence free magnetic field
------------------------------

This example demonstrates the resulting angular profile of
an SECS pole placed at the north pole. Figure 2 from
Amm and Viljanen 1999.

.. GENERATED FROM PYTHON SOURCE LINES 9-63



.. image-sg:: /examples/images/sphx_glr_plot_B_divergence_free_001.png
   :alt: Amm and Viljanen (1999) Figure 2
   :srcset: /examples/images/sphx_glr_plot_B_divergence_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

    # Pole of the current system at the North Pole
    sec_loc = np.array([90.0, 0.0, R_E + 100e3])

    # Set up the system with a single SEC
    system_df = SECS(sec_df_loc=sec_loc)

    # Fit unit currents since we aren't fitting to any data
    system_df.fit_unit_currents()

    # Scale the system corresponding to Figure 2 of
    # Amm and Viljannen (1999) doi:10.1186/BF03352247
    # 10 kA
    total_current = 10000
    system_df.sec_amps *= total_current

    # Set up the prediction grid
    N = 1000
    pred_loc = np.zeros(shape=(N, 3))
    angles = np.linspace(0, 45, N)

    pred_loc[:, 0] = 90 - angles
    pred_loc[:, 2] = R_E

    B_pred = system_df.predict(pred_loc=pred_loc)

    # B_theta == -Bx == -B_pred[:,0]
    # Convert to nT (1e9)
    B_theta = -B_pred[:, 0] * 1e9
    # B_r == -Bz = -B_pred[:,2]
    B_r = -B_pred[:, 2] * 1e9

    fig, ax = plt.subplots()

    ax.plot(angles, B_theta, c="b", label=r"B$_{\theta}$")
    ax.plot(angles, B_r, c="r", label=r"B$_r$")
    ax.legend(loc="upper right")
    ax.set_xlim(angles[0], angles[-1])
    ax.set_ylim(-5, 10)
    ax.set_xlabel("Angle from pole (deg)")
    ax.set_ylabel("B (nT)")
    ax.axhline(0.0, c="k", alpha=0.5, linewidth=0.5)
    ax.set_title("Amm and Viljanen (1999) Figure 2")

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.126 seconds)


.. _sphx_glr_download_examples_plot_B_divergence_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_divergence_free.ipynb <plot_B_divergence_free.ipynb>`

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

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

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

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


.. only:: html

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

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