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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 parametrizations for auroral |
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and medium-energy electron precipitation, 100 eV--1 MeV [1]_, [2]_, and [3]_. |
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.. [1] Roble and Ridley, Ann. Geophys., 5A(6), 369--382, 1987 |
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.. [2] Fang et al., J. Geophys. Res., 113, A09311, 2008 |
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.. [3] Fang et al., Geophys. Res. Lett., 37, L22106, 2010 |
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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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from .spectra import pflux_maxwell, ediss_spec_int, ediss_specfun_int |
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__all__ = [ |
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"rr1987", |
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"rr1987_mod", |
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"fang2008", |
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"fang2010_mono", |
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"fang2010_spec_int", |
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"fang2010_maxw_int", |
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] |
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POLY_F2008 = [ |
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[ 3.49979e-1, -6.18200e-2, -4.08124e-2, 1.65414e-2], |
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[ 5.85425e-1, -5.00793e-2, 5.69309e-2, -4.02491e-3], |
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[ 1.69692e-1, -2.58981e-2, 1.96822e-2, 1.20505e-3], |
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[-1.22271e-1, -1.15532e-2, 5.37951e-6, 1.20189e-3], |
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[ 1.57018, 2.87896e-1, -4.14857e-1, 5.18158e-2], |
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[ 8.83195e-1, 4.31402e-2, -8.33599e-2, 1.02515e-2], |
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[ 1.90953, -4.74704e-2, -1.80200e-1, 2.46652e-2], |
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[-1.29566, -2.10952e-1, 2.73106e-1, -2.92752e-2] |
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] |
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POLY_F2010 = [ |
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[ 1.24616E+0, 1.45903E+0, -2.42269E-1, 5.95459E-2], |
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[ 2.23976E+0, -4.22918E-7, 1.36458E-2, 2.53332E-3], |
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[ 1.41754E+0, 1.44597E-1, 1.70433E-2, 6.39717E-4], |
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[ 2.48775E-1, -1.50890E-1, 6.30894E-9, 1.23707E-3], |
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[-4.65119E-1, -1.05081E-1, -8.95701E-2, 1.22450E-2], |
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[ 3.86019E-1, 1.75430E-3, -7.42960E-4, 4.60881E-4], |
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[-6.45454E-1, 8.49555E-4, -4.28581E-2, -2.99302E-3], |
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[ 9.48930E-1, 1.97385E-1, -2.50660E-3, -2.06938E-3] |
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] |
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View Code Duplication |
def rr1987(energy, flux, scale_height, rho): |
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"""Atmospheric electron energy dissipation Roble and Ridley, 1987 [#]_ |
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Equations (typo corrected) taken from Fang et al., 2008. |
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Parameters |
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---------- |
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energy: array_like (M,...) |
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Characteristic energy E_0 [keV] of the Maxwellian distribution. |
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flux: array_like (M,...) |
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Integrated energy flux Q_0 [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 density [g / cm³] |
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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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.. [#] Roble and Ridley, Ann. Geophys., 5A(6), 369--382, 1987 |
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""" |
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_c1 = 2.11685 |
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_c2 = 2.97035 |
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_c3 = 2.09710 |
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_c4 = 0.74054 |
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_c5 = 0.58795 |
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_c6 = 1.72746 |
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_c7 = 1.37459 |
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_c8 = 0.93296 |
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beta = (rho * scale_height / (4 * 1e-6))**(1 / 1.65) # RR 1987, p. 371 |
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y = beta / energy # Corrected in Fang et al. 2008 (4) |
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f_y = (_c1 * (y**_c2) * np.exp(-_c3 * (y**_c4)) + |
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_c5 * (y**_c6) * np.exp(-_c7 * (y**_c8))) |
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# Corrected in Fang et al. 2008 (2) |
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en_diss = 0.5 * flux / scale_height * f_y |
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return en_diss |
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View Code Duplication |
def rr1987_mod(energy, flux, scale_height, rho): |
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"""Atmospheric electron energy dissipation Roble and Ridley, 1987 [#]_ |
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Equations (typo corrected) taken from Fang et al., 2008. |
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Modified polynomial values to get closer to Fang et al., 2008, |
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origin unknown. |
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Parameters |
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---------- |
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energy: array_like (M,...) |
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Characteristic energy E_0 [keV] of the Maxwellian distribution. |
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flux: array_like (M,...) |
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Integrated energy flux Q_0 [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 density [g / cm³] |
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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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.. [#] Roble and Ridley, Ann. Geophys., 5A(6), 369--382, 1987 |
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""" |
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# Modified polynomial, origin unknown |
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_c1 = 3.233 |
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_c2 = 2.56588 |
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_c3 = 2.2541 |
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_c4 = 0.7297198 |
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_c5 = 1.106907 |
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_c6 = 1.71349 |
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_c7 = 1.8835444 |
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_c8 = 0.86472135 |
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# Fang et al., 2008, Eq. (4) |
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y = (rho * scale_height / (4.6 * 1e-6))**(1 / 1.65) / energy |
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f_y = (_c1 * (y**_c2) * np.exp(-_c3 * (y**_c4)) + |
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_c5 * (y**_c6) * np.exp(-_c7 * (y**_c8))) |
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# energy dissipated [keV] |
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en_diss = 0.5 * flux / scale_height * f_y |
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return en_diss |
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def _fang_f_y(_c, _y): |
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"""Polynomial evaluation helper |
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Fang et al., 2008, Eq. (6), Fang et al., 2010 Eq. (4) |
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""" |
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ret = ( |
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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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) |
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return ret |
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def fang2008(energy, flux, scale_height, rho, pij=None): |
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"""Atmospheric electron energy dissipation from Fang et al., 2008 |
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Ionization profile parametrization as derived in Fang et al., 2008 [#]_. |
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Parameters |
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---------- |
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energy: array_like (M,...) |
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Characteristic energy E_0 [keV] of the Maxwellian distribution. |
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flux: array_like (M,...) |
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Integrated energy flux Q_0 [keV / cm² / s¹] |
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scale_height: array_like (N,...) |
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The atmospheric scale height(s) [cm]. |
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rho: array_like (N,...) |
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The atmospheric densities [g / cm³], corresponding to the scale heights. |
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pij: array_like (8, 4), optional |
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Polynomial coefficents for the electron 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 et al., J. Geophys. Res., 113, A09311, 2008, doi: 10.1029/2008JA013384 |
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""" |
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pij = np.asarray(pij) or np.asarray(POLY_F2008) |
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# Fang et al., 2008, Eq. (7) |
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_cs = np.exp(polyval(np.log(energy), pij.T)) |
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# Fang et al., 2008, Eq. (4) |
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y = (rho * scale_height / (4e-6))**(1 / 1.65) / energy |
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f_y = _fang_f_y(_cs, y) |
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# Fang et al., 2008, Eq. (2) |
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en_diss = 0.5 * f_y * flux / scale_height |
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return en_diss |
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def fang2010_mono(energy, flux, scale_height, rho, pij=None): |
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r"""Atmospheric electron energy dissipation from Fang et al., 2010 |
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Parametrization for mono-energetic electrons [#]_. |
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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 electron beam [keV]. |
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flux: array_like (M,...) |
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Energy flux Q_0 of the mono-energetic electron 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 (8, 4), optional |
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Polynomial coefficents for the electron 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 et al., Geophys. Res. Lett., 37, L22106, 2010, doi: 10.1029/2010GL045406 |
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""" |
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pij = np.asarray(pij) or np.asarray(POLY_F2010) |
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# Fang et al., 2010, Eq. (5) |
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_cs = np.exp(polyval(np.log(energy), pij.T)) |
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# Fang et al., 2010, Eq. (1) |
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y = 2. / energy * (rho * scale_height / (6e-6))**(0.7) |
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f_y = _fang_f_y(_cs, y) |
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# Fang et al., 2008, Eq. (2) |
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en_diss = f_y * flux / scale_height |
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return en_diss |
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def fang2010_spec_int(ens, dfluxes, scale_height, rho, pij=None, axis=-1): |
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r"""Integrate over a given energy spectrum |
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Integrates over the mono-energetic parametrization `q` from [#]_ |
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using the given differential particle spectrum `phi`: |
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:math:`\int_\text{spec} \phi(E) q(E, Q) E \text{d}E` |
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Parameters |
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---------- |
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ens: array_like (M,...) |
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Central (bin) energies of the spectrum |
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dfluxes: array_like (M,...) |
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Differential particle fluxes in the given bins |
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scale_height: array_like (N,...) |
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The atmospheric scale heights |
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rho: array_like (N,...) |
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The atmospheric densities, corresponding to the |
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scale heights. |
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pij: array_like (8, 4), optional |
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Polynomial coefficents for the electron energy dissipation |
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per atmospheric depth. Default: `None` (as given in the reference). |
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axis: int, optional |
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The axis to use for integration, default: -1 (last axis). |
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Returns |
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------- |
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en_diss: array_like (N) |
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The dissipated energy profiles [keV]. |
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References |
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---------- |
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.. [#] Fang et al., Geophys. Res. Lett., 37, L22106, 2010, doi: 10.1029/2010GL045406 |
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See Also |
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-------- |
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fang2010_mono, ediss_spec_int |
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""" |
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return ediss_spec_int( |
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ens, dfluxes, scale_height, rho, fang2010_mono, |
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axis=axis, |
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func_kws=dict(pij=pij), |
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) |
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def fang2010_maxw_int(energy, flux, scale_height, rho, bounds=(0.1, 300.), nstep=128, pij=None): |
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"""Integrate Fang et al., 2010 over a Maxwellian spectrum |
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Integrates the mono-energetic parametrization from Fang et al., 2010 [#]_ |
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over a Maxwellian spectrum with characteristic energy `energy` and |
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total energy flux `flux`. |
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Parameters |
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---------- |
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|
energy: float or array_like (M,...) |
|
290
|
|
|
Characteristic energy E_0 [keV] of the Maxwellian distribution. |
|
291
|
|
|
flux: float or array_like (M,...) |
|
292
|
|
|
Integrated energy flux Q_0 [keV / cm² / s¹] |
|
293
|
|
|
scale_height: float or array_like (N,...) |
|
294
|
|
|
The atmospheric scale heights [cm]. |
|
295
|
|
|
rho: float or array_like (N,...) |
|
296
|
|
|
The atmospheric mass density [g / cm³] |
|
297
|
|
|
bounds: tuple, optional |
|
298
|
|
|
(min, max) [keV] of the integration range to integrate the Maxwellian. |
|
299
|
|
|
Make sure that this is appropriate to encompass the spectrum. |
|
300
|
|
|
Default: (0.1, 300.) |
|
301
|
|
|
nsteps: int, optional |
|
302
|
|
|
Number of integration steps, default: 128. |
|
303
|
|
|
pij: array_like (8, 4), optional |
|
304
|
|
|
Polynomial coefficents for the electron energy dissipation |
|
305
|
|
|
per atmospheric depth. Default: `None` (as given in the reference). |
|
306
|
|
|
|
|
307
|
|
|
Returns |
|
308
|
|
|
------- |
|
309
|
|
|
en_diss: array_like (M,N) |
|
310
|
|
|
The dissipated energy profiles [keV]. |
|
311
|
|
|
|
|
312
|
|
|
References |
|
313
|
|
|
---------- |
|
314
|
|
|
.. [#] Fang et al., Geophys. Res. Lett., 37, L22106, 2010, doi: 10.1029/2010GL045406 |
|
315
|
|
|
|
|
316
|
|
|
See Also |
|
317
|
|
|
-------- |
|
318
|
|
|
fang2010_mono, fang2010_specfun_int, pflux_maxwell |
|
319
|
|
|
""" |
|
320
|
|
|
return ediss_specfun_int( |
|
321
|
|
|
energy, flux, scale_height, rho, fang2010_mono, |
|
322
|
|
|
ediss_kws=dict(pij=pij), |
|
323
|
|
|
bounds=bounds, |
|
324
|
|
|
nstep=nstep, |
|
325
|
|
|
spec_fun=pflux_maxwell, |
|
326
|
|
|
) |
|
327
|
|
|
|
st-bender /
pyeppaurora
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