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

.. only:: html

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

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

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

.. _sphx_glr_auto_examples_em_plot_static_vector_potentials.py:


Magnetostatic Vector Potentials: Dipole and Loop Sources
========================================================

In this example, we plot the vector potential for a dipole and a loop source
in a wholespace.

We can vary the magnetic permeability of the wholespace, location and
orientation of the sources. For the dipole source, we can vary the moment, and
for the loop source, we can vary the radius and current through the loop.

:author: Lindsey Heagy (`@lheagy <https://github.com/lheagy>`_)
:date: June 6, 2018

.. GENERATED FROM PYTHON SOURCE LINES 16-26

.. code-block:: default



    import numpy as np
    import matplotlib.pyplot as plt
    from matplotlib.colors import LogNorm
    from scipy.constants import mu_0, epsilon_0

    from geoana import utils, spatial
    from geoana.em import static








.. GENERATED FROM PYTHON SOURCE LINES 27-32

Setup
-----

define the location orientation and source, physical properties of the
wholespace and source parameters

.. GENERATED FROM PYTHON SOURCE LINES 32-45

.. code-block:: default


    mu = mu_0  # permeability of free space (this is the default)
    location=np.r_[0., 0., 0.]  # location of the dipole
    orientation='Z'  # vertical dipole (can also be a unit-vector)

    # dipole parameters
    moment = 1

    # loop source parameters
    current = 1
    radius = 20









.. GENERATED FROM PYTHON SOURCE LINES 46-55

Magnetostatic Dipole and Loop
-----------------------------

Here, we build the geoana magnetic dipole in a wholespace and circular loop
in a wholespace using the parameters defined above.
For a full list of the properties you can set on a dipole, see the
:class:`geoana.em.static.MagneticDipoleWholeSpace` docs and for the
circular loop source, see the
:class:`geoana.em.static.CircularLoopWholeSpace` docs

.. GENERATED FROM PYTHON SOURCE LINES 55-67

.. code-block:: default


    dipole = static.MagneticDipoleWholeSpace(
        mu=mu, location=location,
        orientation=orientation , moment=moment
    )

    loop = static.CircularLoopWholeSpace(
        mu=mu, location=location,
        orientation=orientation, current=current,
        radius=radius
    )








.. GENERATED FROM PYTHON SOURCE LINES 68-73

Evaluate vector potential
--------------------------

Next, we construct a grid where we want to plot the vector potential and
evaluate

.. GENERATED FROM PYTHON SOURCE LINES 73-82

.. code-block:: default


    x = np.linspace(-50, 50, 100)
    y = np.linspace(-50, 50, 100)
    xyz = utils.ndgrid([x, y, np.r_[0]])

    # evaluate the vector potential
    a_dipole = dipole.vector_potential(xyz)
    a_loop = loop.vector_potential(xyz)








.. GENERATED FROM PYTHON SOURCE LINES 83-85

and define plotting code to plot an image of the amplitude of the vector
field / flux as well as the streamlines

.. GENERATED FROM PYTHON SOURCE LINES 86-106

.. code-block:: default


    def plot_amplitude(ax, v):
        v = spatial.vector_magnitude(v)
        plt.colorbar(
            ax.pcolormesh(
                x, y, v.reshape(len(x), len(y), order='F'), norm=LogNorm()
            ), ax=ax
        )
        ax.axis('square')
        ax.set_xlabel('x (m)')
        ax.set_ylabel('y (m)')


    # plot streamlines
    def plot_streamlines(ax, v):
        vx = v[:, 0].reshape(len(x), len(y), order='F')
        vy = v[:, 1].reshape(len(x), len(y), order='F')
        ax.streamplot(x, y, vx.T, vy.T, color='k')









.. GENERATED FROM PYTHON SOURCE LINES 107-109

Create subplots for plotting the results. Loop over frequencies and plot the
electric and magnetic fields along a slice through the center of the dipole.

.. GENERATED FROM PYTHON SOURCE LINES 110-131

.. code-block:: default


    fig, ax = plt.subplots(1, 2, figsize=(12, 5))

    # plot dipole vector potential
    plot_amplitude(ax[0], a_dipole)
    plot_streamlines(ax[0], a_dipole)

    # plot loop vector potential
    plot_amplitude(ax[1], a_loop)
    plot_streamlines(ax[1], a_loop)


    # set the titles
    ax[0].set_title("$\\vec{A}$: dipole")
    ax[1].set_title("$\\vec{A}$: loop")

    # format so text doesn't overlap
    fig.tight_layout()
    plt.show()





.. image-sg:: /auto_examples/em/images/sphx_glr_plot_static_vector_potentials_001.png
   :alt: $\vec{A}$: dipole, $\vec{A}$: loop
   :srcset: /auto_examples/em/images/sphx_glr_plot_static_vector_potentials_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 1.060 seconds)


.. _sphx_glr_download_auto_examples_em_plot_static_vector_potentials.py:

.. only:: html

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




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

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

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

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


.. only:: html

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

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