.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "gallery/04_advanced_examples/p05_plotting_q.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_gallery_04_advanced_examples_p05_plotting_q.py: Plotting the Squashing Factor ========================================= This example demonstrates how to use and plot the :func:`~mapflpy.scripts.compute_q_on_surface` to visualize key topology and morphology metrics of the magnetic field. The :func:`~mapflpy.scripts.compute_q_on_surface` combines :func:`~mapflpy.scripts.expansion_factor` with :func:`~mapflpy.utils.calc_jacobian` and :func:`~mapflpy.utils.calc_q` using :func:`~mapflpy.scripts.map_pt_forward` or :func:`~mapflpy.scripts.map_pt_backward` to calculate the squashing factor. For a more complete description of the squashing factor, see `Titov et al. 2007 `_. Generally, the squashing factor indicates how much a given flux tube distorts. Other ways to imagine the squashing factor, Q, includes places where current sheets are likely (but not guaranteed) to form as high Q lines indicate quasi-separatrix layers (QSLs). Alternatively, high Q lines indicate different magnetic flux domains. Additionally, this plots :func:`~mapflpy.scripts.expansion_factor`, critical to models such as WSA (see `Wang & Sheeley 1990 `_, `Arge & Pizzo 2000 `_, and `Arge et al. 2004 `_). .. GENERATED FROM PYTHON SOURCE LINES 24-31 .. code-block:: Python import os from psi_data import fetch_mas_data import numpy as np import matplotlib.pylab as plt from mapflpy.scripts import map_pt_forward, expansion_factor, compute_q_on_surface .. GENERATED FROM PYTHON SOURCE LINES 38-43 The squashing factor, Q, is a measure of the topology of the magnetic field. So, let's read in magnetic field files. We're loading in from a CORHEL-MAS thermodynamic MHD calculation for CR2282. These aren't currently standard datasets in mapflpy or psi-io, so we're fetching them manually and placing them in the default cache location. .. GENERATED FROM PYTHON SOURCE LINES 43-47 .. code-block:: Python files = fetch_mas_data(domains="cor", variables="br,bt,bp,t") magnetic_field_files = files.cor_br, files.cor_bt, files.cor_bp .. GENERATED FROM PYTHON SOURCE LINES 48-50 As a quick look, we can immediately calculate Q specifying only the magnetic field files and visualize the output. .. GENERATED FROM PYTHON SOURCE LINES 50-63 .. code-block:: Python # compute Q squashing_factor_default = compute_q_on_surface(magnetic_field_files) # plot Q ax = plt.figure().add_subplot() q_map = ax.pcolormesh(np.rad2deg(squashing_factor_default.p), 90 - np.rad2deg(squashing_factor_default.t), np.log10(squashing_factor_default.q), cmap='Grays') ax.set_aspect("equal", adjustable="box") ax.set_title('Log$_{10}$ Q') plt.colorbar(q_map) plt.show() .. image-sg:: /gallery/04_advanced_examples/images/sphx_glr_p05_plotting_q_001.png :alt: Log$_{10}$ Q :srcset: /gallery/04_advanced_examples/images/sphx_glr_p05_plotting_q_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none fwd mapping .. GENERATED FROM PYTHON SOURCE LINES 64-70 That should run fairly quickly, as the resolution is a little bit more than 1 degree. However, we can customize the map. We can, for example, change the direction of mapping to "bwd" and choose a trace_radius of 3. We can either specify a [start, end] for theta and phi with t_range and p_range, or specify our own array with t_arr and p_arr. We are intentionally picking a low resolution so this runs fast, you should use more points! .. GENERATED FROM PYTHON SOURCE LINES 70-84 .. code-block:: Python squashing_factor_3_bwd = compute_q_on_surface(magnetic_field_files, direction='bwd', nproc=4, trace_radius=3, p_arr=np.linspace(0, 2 * np.pi, 80), t_arr=np.linspace(0, np.pi, 40)) # and visualizing: ax = plt.figure().add_subplot() q_map = ax.pcolormesh(np.rad2deg(squashing_factor_3_bwd.p), 90 - np.rad2deg(squashing_factor_3_bwd.t), np.log10(squashing_factor_3_bwd.q), cmap='Grays') ax.set_aspect("equal", adjustable="box") ax.set_title('Log$_{10}$ Q') plt.colorbar(q_map) plt.show() .. image-sg:: /gallery/04_advanced_examples/images/sphx_glr_p05_plotting_q_002.png :alt: Log$_{10}$ Q :srcset: /gallery/04_advanced_examples/images/sphx_glr_p05_plotting_q_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none bwd mapping .. GENERATED FROM PYTHON SOURCE LINES 85-87 This wrapper makes it easy to get the squashing factor. If we're interested in just say, the expansion factor, we can plot that. .. GENERATED FROM PYTHON SOURCE LINES 87-104 .. code-block:: Python # We first need to calculate a mapping on a set of given points p_to_trace = np.linspace(0, 2 * np.pi, 100) t_to_trace = np.linspace(0, np.pi, 50) # let's map and get the expansion factor mapping = map_pt_forward(*magnetic_field_files, p_to_trace, t_to_trace) ef, p_ef, t_ef = expansion_factor(magnetic_field_files, mapping, 3, p_to_trace, t_to_trace) # and now we can visualize ax = plt.figure().add_subplot() ef_map = ax.pcolormesh(np.rad2deg(p_to_trace), 90 - np.rad2deg(t_to_trace), np.log10(ef).T, cmap='plasma') ax.set_aspect("equal", adjustable="box") ax.set_title('expansion factor') plt.colorbar(ef_map) plt.show() .. image-sg:: /gallery/04_advanced_examples/images/sphx_glr_p05_plotting_q_003.png :alt: expansion factor :srcset: /gallery/04_advanced_examples/images/sphx_glr_p05_plotting_q_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 13.499 seconds) .. _sphx_glr_download_gallery_04_advanced_examples_p05_plotting_q.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: p05_plotting_q.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: p05_plotting_q.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: p05_plotting_q.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_