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# coding: utf-8 |
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# Copyright (c) 2020 Stefan Bender |
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# |
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# This file is part of pyeppaurora. |
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# pyeppaurora is free software: you can redistribute it or modify |
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# it under the terms of the GNU General Public License as published |
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# by the Free Software Foundation, version 2. |
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# See accompanying LICENSE file or http://www.gnu.org/licenses/gpl-2.0.html. |
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"""Atmospheric ionization rate parametrizations |
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Includes the atmospheric ionization rate parametrization for auroral |
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proton precipitation [1]_. |
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.. [1] Fang, X., Lummerzheim, D., and Jackman, C. H. (2013), |
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Proton impact ionization and a fast calculation method, |
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J. Geophys. Res. Space Physics, 118, 5369--5378, doi:10.1002/jgra.50484. |
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""" |
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import numpy as np |
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from numpy.polynomial.polynomial import polyval |
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__all__ = ["fang2013_protons"] |
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POLY_F2013 = [ |
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[ 2.55050e+0, 2.69476e-1, -2.58425e-1, 4.43190e-2], |
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[ 6.39287e-1, -1.85817e-1, -3.15636e-2, 1.01370e-2], |
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[ 1.63996e+0, 2.43580e-1, 4.29873e-2, 3.77803e-2], |
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[-2.13479e-1, 1.42464e-1, 1.55840e-2, 1.97407e-3], |
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[-1.65764e-1, 3.39654e-1, -9.87971e-3, 4.02411e-3], |
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[-3.59358e-2, 2.50330e-2, -3.29365e-2, 5.08057e-3], |
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[-6.26528e-1, 1.46865e+0, 2.51853e-1, -4.57132e-2], |
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[ 1.01384e+0, 5.94301e-2, -3.27839e-2, 3.42688e-3], |
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[-1.29454e-6, -1.43623e-1, 2.82583e-1, 8.29809e-2], |
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[-1.18622e-1, 1.79191e-1, 6.49171e-2, -3.99715e-3], |
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[ 2.94890e+0, -5.75821e-1, 2.48563e-2, 8.31078e-2], |
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[-1.89515e-1, 3.53452e-2, 7.77964e-2, -4.06034e-3] |
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] |
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def fang2013_protons(energy, flux, scale_height, rho, pij=None): |
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"""Proton ionization parametrization by Fang et al., 2013 |
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Parametrization for mono-energetic protons as described in [#]_. |
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Parameters |
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---------- |
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energy: array_like (M,...) |
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Energy E_0 of the mono-energetic proton beam [keV]. |
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flux: array_like (M,...) |
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Energy flux Q_0 of the mono-energetic proton beam [keV / cm² / s¹]. |
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scale_height: array_like (N,...) |
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The atmospheric scale heights [cm]. |
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rho: array_like (N,...) |
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The atmospheric mass densities [g / cm³], corresponding to the scale heights. |
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pij: array_like (12, 4), optional |
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Polynomial coefficents for the proton energy dissipation |
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per atmospheric depth. Default: `None` (as given in the reference). |
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Returns |
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------- |
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en_diss: array_like (M,N) |
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The dissipated energy profiles [keV]. |
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References |
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---------- |
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.. [#] Fang, X., Lummerzheim, D., and Jackman, C. H. (2013), |
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Proton impact ionization and a fast calculation method, |
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J. Geophys. Res. Space Physics, 118, 5369--5378, doi:10.1002/jgra.50484. |
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""" |
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def _f_y(_c, _y): |
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# Fang et al., 2008, Eq. (6), Fang et al., 2010 Eq. (4) |
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# Fang et al., 2013, Eqs. (6), (7) |
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return ( |
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_c[0] * (_y**_c[1]) * np.exp(-_c[2] * (_y**_c[3])) + |
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_c[4] * (_y**_c[5]) * np.exp(-_c[6] * (_y**_c[7])) + |
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_c[8] * (_y**_c[9]) * np.exp(-_c[10] * (_y**_c[11])) |
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) |
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pij = np.asarray(pij) or np.asarray(POLY_F2013) |
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# Fang et al., 2013, Eqs. (6), (7) |
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_cs = np.exp(polyval(np.log(energy), pij.T)) |
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# Fang et al., 2013, Eq. (5) |
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y = 7.5 / energy * (1e4 * rho * scale_height)**(0.9) |
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f_y = _f_y(_cs, y) |
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# Fang et al., 2013, Eq. (3) |
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en_diss = f_y * flux / scale_height |
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return en_diss |
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st-bender /
pyeppaurora
