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eppaurora.electrons.fang2008() A

↳ Parent: eppaurora.electrons

Complexity

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Total Lines	39
Code Lines	10

Duplication

Lines	39
Ratio	100 %

Importance

Changes

Metric	Value
eloc	10
dl	39
loc	39
rs	9.9
c	0
b	0
f	0
cc	1
nop	5

# coding: utf-8
# Copyright (c) 2020 Stefan Bender
#
# This file is part of pyeppaurora.
# pyeppaurora is free software: you can redistribute it or modify
# it under the terms of the GNU General Public License as published
# by the Free Software Foundation, version 2.
# See accompanying LICENSE file or http://www.gnu.org/licenses/gpl-2.0.html.
"""Atmospheric ionization rate parametrizations

Includes the atmospheric ionization rate parametrizations for auroral
and medium-energy electron precipitation, 100 eV--1 MeV [1]_, [2]_, and [3]_.

.. [1] Roble and Ridley, Ann. Geophys., 5A(6), 369--382, 1987
.. [2] Fang et al., J. Geophys. Res., 113, A09311, 2008
.. [3] Fang et al., Geophys. Res. Lett., 37, L22106, 2010
"""

import numpy as np

POLY_F2008 = np.array([
	[ 3.49979e-1, -6.18200e-2, -4.08124e-2,  1.65414e-2],
	[ 5.85425e-1, -5.00793e-2,  5.69309e-2, -4.02491e-3],
	[ 1.69692e-1, -2.58981e-2,  1.96822e-2,  1.20505e-3],
	[-1.22271e-1, -1.15532e-2,  5.37951e-6,  1.20189e-3],
	[ 1.57018,     2.87896e-1, -4.14857e-1,  5.18158e-2],
	[ 8.83195e-1,  4.31402e-2, -8.33599e-2,  1.02515e-2],
	[ 1.90953,    -4.74704e-2, -1.80200e-1,  2.46652e-2],
	[-1.29566,    -2.10952e-1,  2.73106e-1, -2.92752e-2]
])

POLY_F2010 = np.array([
	[ 1.24616E+0,  1.45903E+0, -2.42269E-1,  5.95459E-2],
	[ 2.23976E+0, -4.22918E-7,  1.36458E-2,  2.53332E-3],
	[ 1.41754E+0,  1.44597E-1,  1.70433E-2,  6.39717E-4],
	[ 2.48775E-1, -1.50890E-1,  6.30894E-9,  1.23707E-3],
	[-4.65119E-1, -1.05081E-1, -8.95701E-2,  1.22450E-2],
	[ 3.86019E-1,  1.75430E-3, -7.42960E-4,  4.60881E-4],
	[-6.45454E-1,  8.49555E-4, -4.28581E-2, -2.99302E-3],
	[ 9.48930E-1,  1.97385E-1, -2.50660E-3, -2.06938E-3]
])

vpolyval = np.vectorize(np.polyval, signature='(m,n),()->(n)')


def rr1987(energy, flux, scale_height, rho):

	"""Atmospheric electron energy dissipation Roble and Ridley, 1987

	Equations (typo corrected) taken from Fang et al., 2008.

	Parameters
	----------
	energy: array_like (M,...)
		Characteristic energy E_0 [keV] of the Maxwellian distribution.
	flux: array_like (M,...)
		Integrated energy flux Q_0 [keV / cm² / s¹]
	scale_height: array_like (N,...)
		The atmospheric scale heights [cm].
	rho: array_like (N,...)
		The atmospheric mass density [g / cm³]

	Returns
	-------
	en_diss: array_like (M,N)
		The dissipated energy profiles.

	References
	----------

	.. [#] Roble and Ridley, Ann. Geophys., 5A(6), 369--382, 1987
	"""
	_c1 = 2.11685
	_c2 = 2.97035
	_c3 = 2.09710
	_c4 = 0.74054
	_c5 = 0.58795
	_c6 = 1.72746
	_c7 = 1.37459
	_c8 = 0.93296

	beta = (rho * scale_height / (4 * 1e-6))**(1 / 1.65)  # RR 1987, p. 371
	y = beta / energy  # Corrected in Fang et al. 2008 (4)
	f_y = (_c1 * (y**_c2) * np.exp(-_c3 * (y**_c4)) +
		_c5 * (y**_c6) * np.exp(-_c7 * (y**_c8)))
	# Corrected in Fang et al. 2008 (2)
	en_diss = 0.5 * flux / scale_height * f_y
	return en_diss


def rr1987_mod(energy, flux, scale_height, rho):

	"""Atmospheric electron energy dissipation Roble and Ridley, 1987

	Equations (typo corrected) taken from Fang et al., 2008.
	Modified polynomial values to get closer to Fang et al., 2008,
	origin unknown.

	Parameters
	----------
	energy: array_like (M,...)
		Characteristic energy E_0 [keV] of the Maxwellian distribution.
	flux: array_like (M,...)
		Integrated energy flux Q_0 [keV / cm² / s¹]
	scale_height: array_like (N,...)
		The atmospheric scale heights [cm].
	rho: array_like (N,...)
		The atmospheric mass density [g / cm³]

	Returns
	-------
	en_diss: array_like (M,N)
		The dissipated energy profiles.

	References
	----------

	.. [#] Roble and Ridley, Ann. Geophys., 5A(6), 369--382, 1987
	"""
	# Modified polynomial, origin unknown
	_c1 = 3.233
	_c2 = 2.56588
	_c3 = 2.2541
	_c4 = 0.7297198
	_c5 = 1.106907
	_c6 = 1.71349
	_c7 = 1.8835444
	_c8 = 0.86472135

	# Fang et al., 2008, Eq. (4)
	y = (rho * scale_height / (4.6 * 1e-6))**(1 / 1.65) / energy
	f_y = (_c1 * (y**_c2) * np.exp(-_c3 * (y**_c4)) +
		_c5 * (y**_c6) * np.exp(-_c7 * (y**_c8)))
	# energy dissipated [keV]
	en_diss = 0.5 * flux / scale_height * f_y
	return en_diss


def fang2008(energy, flux, scale_height, rho, pij=POLY_F2008):

	"""Atmospheric electron energy dissipation from Fang et al., 2008

	Ionization profile parametrization as derived in Fang et al., 2008 [#]_.

	Parameters
	----------
	energy: array_like (M,...)
		Characteristic energy E_0 [keV] of the Maxwellian distribution.
	flux: array_like (M,...)
		Integrated energy flux Q_0 [keV / cm² / s¹]
	scale_height: array_like (N,...)
		The atmospheric scale height(s) [cm].
	rho: array_like (N,...)
		The atmospheric densities [g / cm³], corresponding to the scale heights.

	Returns
	-------
	en_diss: array_like (M,N)
		The dissipated energy profile(s).

	References
	----------

	.. [#] Fang et al., J. Geophys. Res., 113, A09311, 2008, doi: 10.1029/2008JA013384
	"""
	def _f_y(_cc, _y):
		# Fang et al., 2008, Eq. (6)
		_c = _cc.reshape((8, -1))
		return (_c[0] * (_y**_c[1]) * np.exp(-_c[2] * (_y**_c[3])) +
			_c[4] * (_y**_c[5]) * np.exp(-_c[6] * (_y**_c[7])))
	# Fang et al., 2008, Eq. (7)
	_cs = np.exp(vpolyval(pij[:, ::-1].T, np.log(energy))).T
	# Fang et al., 2008, Eq. (4)
	y = (rho * scale_height / (4e-6))**(1 / 1.65) / energy
	f_y = _f_y(_cs, y)
	# Fang et al., 2008, Eq. (2)
	en_diss = 0.5 * f_y * flux / scale_height
	return en_diss


def fang2010_mono(energy, flux, scale_height, rho, pij=POLY_F2010):

	r"""Atmospheric electron energy dissipation from Fang et al., 2010

	Parametrization for mono-energetic electrons [#]_.

	Parameters
	----------
	energy: array_like (M,...)
		Characteristic energy E_0 [keV] of the Maxwellian distribution.
	flux: array_like (M,...)
		Integrated energy flux Q_0 [keV / cm² / s¹]
	scale_height: array_like (N,...)
		The atmospheric scale heights.
	rho: array_like (N,...)
		The atmospheric densities, corresponding to the scale heights.

	Returns
	-------
	en_diss: array_like (M,N)
		The dissipated energy profile(s).

	References
	----------

	.. [#] Fang et al., Geophys. Res. Lett., 37, L22106, 2010, doi: 10.1029/2010GL045406
	"""
	def _f_y(_cc, _y):
		# Fang et al., 2008, Eq. (6), Fang et al., 2010 Eq. (4)
		_c = _cc.reshape((8, -1))
		return (_c[0] * (_y**_c[1]) * np.exp(-_c[2] * (_y**_c[3])) +
			_c[4] * (_y**_c[5]) * np.exp(-_c[6] * (_y**_c[7])))
	# Fang et al., 2010, Eq. (5)
	_cs = np.exp(vpolyval(pij[:, ::-1].T, np.log(energy))).T
	# Fang et al., 2010, Eq. (1)
	y = 2. / energy * (rho * scale_height / (6e-6))**(0.7)
	f_y = _f_y(_cs, y)
	# Fang et al., 2008, Eq. (2)
	en_diss = f_y * flux / scale_height
	return en_diss


def fang2010_spec_int(ens, dfluxes, scale_height, rho, pij=POLY_F2010, axis=-1):

	r"""Integrate over a given energy spectrum

	Integrates over the mono-energetic parametrization `q` from Fang et al., 2010
	using the given differential particle spectrum `phi`:

	:math:`\int_\text{spec} \phi(E) q(E, Q) E \text{d}E`

	Parameters
	----------
	ens: array_like (M,...)
		Central (bin) energies of the spectrum
	dfluxes: array_like (M,...)
		Differential particle fluxes in the given bins
	scale_height: array_like (N,...)
		The atmospheric scale heights
	rho: array_like (N,...)
		The atmospheric densities, corresponding to the
		scale heights.

	Returns
	-------
	en_diss: array_like (N)
		The dissipated energy profile(s).
	"""
	ediss_f10 = fang2010_mono(
		ens[None, None, :],
		dfluxes,
		scale_height[..., None],
		rho[..., None],
		pij=pij,
	)
	return np.trapz(ediss_f10 * ens, ens, axis=axis)


def maxwell_general(en, en_0=10.):
	"""Maxwell number flux spectrum as in Fang2008 [1]

	Defined in Fang et al., JGR 2008, Eq. (1).

	Parameters
	----------
	en: float
		Energy in [keV]
	en_0: float, optional
		Characteristic energy in [keV], i.e. mode of the distribution.
		Default: 10 keV

	Returns
	-------
	phi: float
		Differential hemispherical number flux in [keV-1 cm-2 s-1]
		([keV] or scaled by 1 keV-2 cm-2 s-1, e.g. ).
	"""
	return en * np.exp(-en / en_0)


def maxwell_pflux(en, en_0=10.):
	"""Maxwell particle flux spectrum as in Fang2008 [1]

	Defined in Fang et al., JGR 2008, Eq. (1).
	The total precipitating energy flux is fixed to 1 keV cm-2 s-1,
	multiply by Q_0 [keV cm-2 s-1] to scale the particle flux.

	Parameters
	----------
	en: float
		Energy in [keV]
	en_0: float, optional
		Characteristic energy in [keV], i.e. mode of the distribution.
		Default: 10 keV.

	Returns
	-------
	phi: float
		Hemispherical differential particle flux in [keV-1 cm-2 s-1]
		([kev-2] scaled by unit energy flux).
	"""
	return 0.5 / en_0**3 * maxwell_general(en, en_0)


def fang2010_maxw_int(energy, flux, scale_height, rho, bounds=(0.1, 300.), nstep=128, pij=POLY_F2010):

	"""
	Integrate the mono-energetic parametrization over a Maxwellian

	Parameters
	----------
	bounds: tuple, optional
		(min, max) [keV] of the integration range to integrate the Maxwellian.
		Make sure that this is appropriate to encompass the spectrum.
		Default: (0.1, 300.)
	nsteps: int, optional
		Number of integration steps, default: 128.
	"""
	bounds_l10 = np.log10(bounds)
	ens = np.logspace(*bounds_l10, num=nstep)
	dflux = flux * maxwell_pflux(ens[:, None], energy)
	return fang2010_spec_int(ens, dflux.T, scale_height, rho, pij=pij, axis=-1)


1		# coding: utf-8
2		# Copyright (c) 2020 Stefan Bender
3		#
4		# This file is part of pyeppaurora.
5		# pyeppaurora is free software: you can redistribute it or modify
6		# it under the terms of the GNU General Public License as published
7		# by the Free Software Foundation, version 2.
8		# See accompanying LICENSE file or http://www.gnu.org/licenses/gpl-2.0.html.
9		"""Atmospheric ionization rate parametrizations
10
11		Includes the atmospheric ionization rate parametrizations for auroral
12		and medium-energy electron precipitation, 100 eV--1 MeV [1]_, [2]_, and [3]_.
13
14		.. [1] Roble and Ridley, Ann. Geophys., 5A(6), 369--382, 1987
15		.. [2] Fang et al., J. Geophys. Res., 113, A09311, 2008
16		.. [3] Fang et al., Geophys. Res. Lett., 37, L22106, 2010
17		"""
18
19		import numpy as np
20
21		POLY_F2008 = np.array([
22		[ 3.49979e-1, -6.18200e-2, -4.08124e-2, 1.65414e-2],
23		[ 5.85425e-1, -5.00793e-2, 5.69309e-2, -4.02491e-3],
24		[ 1.69692e-1, -2.58981e-2, 1.96822e-2, 1.20505e-3],
25		[-1.22271e-1, -1.15532e-2, 5.37951e-6, 1.20189e-3],
26		[ 1.57018, 2.87896e-1, -4.14857e-1, 5.18158e-2],
27		[ 8.83195e-1, 4.31402e-2, -8.33599e-2, 1.02515e-2],
28		[ 1.90953, -4.74704e-2, -1.80200e-1, 2.46652e-2],
29		[-1.29566, -2.10952e-1, 2.73106e-1, -2.92752e-2]
30		])
31
32		POLY_F2010 = np.array([
33		[ 1.24616E+0, 1.45903E+0, -2.42269E-1, 5.95459E-2],
34		[ 2.23976E+0, -4.22918E-7, 1.36458E-2, 2.53332E-3],
35		[ 1.41754E+0, 1.44597E-1, 1.70433E-2, 6.39717E-4],
36		[ 2.48775E-1, -1.50890E-1, 6.30894E-9, 1.23707E-3],
37		[-4.65119E-1, -1.05081E-1, -8.95701E-2, 1.22450E-2],
38		[ 3.86019E-1, 1.75430E-3, -7.42960E-4, 4.60881E-4],
39		[-6.45454E-1, 8.49555E-4, -4.28581E-2, -2.99302E-3],
40		[ 9.48930E-1, 1.97385E-1, -2.50660E-3, -2.06938E-3]
41		])
42
43		vpolyval = np.vectorize(np.polyval, signature='(m,n),()->(n)')
44
45
46	View Code Duplication	def rr1987(energy, flux, scale_height, rho):
		0 ignored issues – show Duplication introduced 2020-06-06 16:42 UTC by Report Bug Copy Issue Report This code seems to be duplicated in your project. Loading history...
47		"""Atmospheric electron energy dissipation Roble and Ridley, 1987
48
49		Equations (typo corrected) taken from Fang et al., 2008.
50
51		Parameters
52		----------
53		energy: array_like (M,...)
54		Characteristic energy E_0 [keV] of the Maxwellian distribution.
55		flux: array_like (M,...)
56		Integrated energy flux Q_0 [keV / cm² / s¹]
57		scale_height: array_like (N,...)
58		The atmospheric scale heights [cm].
59		rho: array_like (N,...)
60		The atmospheric mass density [g / cm³]
61
62		Returns
63		-------
64		en_diss: array_like (M,N)
65		The dissipated energy profiles.
66
67		References
68		----------
69
70		.. [#] Roble and Ridley, Ann. Geophys., 5A(6), 369--382, 1987
71		"""
72		_c1 = 2.11685
73		_c2 = 2.97035
74		_c3 = 2.09710
75		_c4 = 0.74054
76		_c5 = 0.58795
77		_c6 = 1.72746
78		_c7 = 1.37459
79		_c8 = 0.93296
80
81		beta = (rho * scale_height / (4 * 1e-6))**(1 / 1.65) # RR 1987, p. 371
82		y = beta / energy # Corrected in Fang et al. 2008 (4)
83		f_y = (_c1 * (y*_c2) np.exp(-_c3 * (y**_c4)) +
84		_c5 * (y*_c6) np.exp(-_c7 * (y**_c8)))
85		# Corrected in Fang et al. 2008 (2)
86		en_diss = 0.5 * flux / scale_height * f_y
87		return en_diss
88
89
90	View Code Duplication	def rr1987_mod(energy, flux, scale_height, rho):
		0 ignored issues – show Duplication introduced 2020-06-06 16:42 UTC by Report Bug Copy Issue Report This code seems to be duplicated in your project. Loading history...
91		"""Atmospheric electron energy dissipation Roble and Ridley, 1987
92
93		Equations (typo corrected) taken from Fang et al., 2008.
94		Modified polynomial values to get closer to Fang et al., 2008,
95		origin unknown.
96
97		Parameters
98		----------
99		energy: array_like (M,...)
100		Characteristic energy E_0 [keV] of the Maxwellian distribution.
101		flux: array_like (M,...)
102		Integrated energy flux Q_0 [keV / cm² / s¹]
103		scale_height: array_like (N,...)
104		The atmospheric scale heights [cm].
105		rho: array_like (N,...)
106		The atmospheric mass density [g / cm³]
107
108		Returns
109		-------
110		en_diss: array_like (M,N)
111		The dissipated energy profiles.
112
113		References
114		----------
115
116		.. [#] Roble and Ridley, Ann. Geophys., 5A(6), 369--382, 1987
117		"""
118		# Modified polynomial, origin unknown
119		_c1 = 3.233
120		_c2 = 2.56588
121		_c3 = 2.2541
122		_c4 = 0.7297198
123		_c5 = 1.106907
124		_c6 = 1.71349
125		_c7 = 1.8835444
126		_c8 = 0.86472135
127
128		# Fang et al., 2008, Eq. (4)
129		y = (rho * scale_height / (4.6 * 1e-6))**(1 / 1.65) / energy
130		f_y = (_c1 * (y*_c2) np.exp(-_c3 * (y**_c4)) +
131		_c5 * (y*_c6) np.exp(-_c7 * (y**_c8)))
132		# energy dissipated [keV]
133		en_diss = 0.5 * flux / scale_height * f_y
134		return en_diss
135
136
137	View Code Duplication	def fang2008(energy, flux, scale_height, rho, pij=POLY_F2008):
		0 ignored issues – show Duplication introduced 2020-06-06 16:42 UTC by Report Bug Copy Issue Report This code seems to be duplicated in your project. Loading history...
138		"""Atmospheric electron energy dissipation from Fang et al., 2008
139
140		Ionization profile parametrization as derived in Fang et al., 2008 [#]_.
141
142		Parameters
143		----------
144		energy: array_like (M,...)
145		Characteristic energy E_0 [keV] of the Maxwellian distribution.
146		flux: array_like (M,...)
147		Integrated energy flux Q_0 [keV / cm² / s¹]
148		scale_height: array_like (N,...)
149		The atmospheric scale height(s) [cm].
150		rho: array_like (N,...)
151		The atmospheric densities [g / cm³], corresponding to the scale heights.
152
153		Returns
154		-------
155		en_diss: array_like (M,N)
156		The dissipated energy profile(s).
157
158		References
159		----------
160
161		.. [#] Fang et al., J. Geophys. Res., 113, A09311, 2008, doi: 10.1029/2008JA013384
162		"""
163		def _f_y(_cc, _y):
164		# Fang et al., 2008, Eq. (6)
165		_c = _cc.reshape((8, -1))
166		return (_c[0] * (_y*_c[1]) np.exp(-_c[2] * (_y**_c[3])) +
167		_c[4] * (_y*_c[5]) np.exp(-_c[6] * (_y**_c[7])))
168		# Fang et al., 2008, Eq. (7)
169		_cs = np.exp(vpolyval(pij[:, ::-1].T, np.log(energy))).T
170		# Fang et al., 2008, Eq. (4)
171		y = (rho * scale_height / (4e-6))**(1 / 1.65) / energy
172		f_y = _f_y(_cs, y)
173		# Fang et al., 2008, Eq. (2)
174		en_diss = 0.5 * f_y * flux / scale_height
175		return en_diss
176
177
178	View Code Duplication	def fang2010_mono(energy, flux, scale_height, rho, pij=POLY_F2010):
		0 ignored issues – show Duplication introduced 2020-06-06 16:42 UTC by Report Bug Copy Issue Report This code seems to be duplicated in your project. Loading history...
179		r"""Atmospheric electron energy dissipation from Fang et al., 2010
180
181		Parametrization for mono-energetic electrons [#]_.
182
183		Parameters
184		----------
185		energy: array_like (M,...)
186		Characteristic energy E_0 [keV] of the Maxwellian distribution.
187		flux: array_like (M,...)
188		Integrated energy flux Q_0 [keV / cm² / s¹]
189		scale_height: array_like (N,...)
190		The atmospheric scale heights.
191		rho: array_like (N,...)
192		The atmospheric densities, corresponding to the scale heights.
193
194		Returns
195		-------
196		en_diss: array_like (M,N)
197		The dissipated energy profile(s).
198
199		References
200		----------
201
202		.. [#] Fang et al., Geophys. Res. Lett., 37, L22106, 2010, doi: 10.1029/2010GL045406
203		"""
204		def _f_y(_cc, _y):
205		# Fang et al., 2008, Eq. (6), Fang et al., 2010 Eq. (4)
206		_c = _cc.reshape((8, -1))
207		return (_c[0] * (_y*_c[1]) np.exp(-_c[2] * (_y**_c[3])) +
208		_c[4] * (_y*_c[5]) np.exp(-_c[6] * (_y**_c[7])))
209		# Fang et al., 2010, Eq. (5)
210		_cs = np.exp(vpolyval(pij[:, ::-1].T, np.log(energy))).T
211		# Fang et al., 2010, Eq. (1)
212		y = 2. / energy * (rho * scale_height / (6e-6))**(0.7)
213		f_y = _f_y(_cs, y)
214		# Fang et al., 2008, Eq. (2)
215		en_diss = f_y * flux / scale_height
216		return en_diss
217
218
219	View Code Duplication	def fang2010_spec_int(ens, dfluxes, scale_height, rho, pij=POLY_F2010, axis=-1):
		0 ignored issues – show Duplication introduced 2020-06-06 16:42 UTC by Report Bug Copy Issue Report This code seems to be duplicated in your project. Loading history...
220		r"""Integrate over a given energy spectrum
221
222		Integrates over the mono-energetic parametrization `q` from Fang et al., 2010
223		using the given differential particle spectrum `phi`:
224
225		:math:`\int_\text{spec} \phi(E) q(E, Q) E \text{d}E`
226
227		Parameters
228		----------
229		ens: array_like (M,...)
230		Central (bin) energies of the spectrum
231		dfluxes: array_like (M,...)
232		Differential particle fluxes in the given bins
233		scale_height: array_like (N,...)
234		The atmospheric scale heights
235		rho: array_like (N,...)
236		The atmospheric densities, corresponding to the
237		scale heights.
238
239		Returns
240		-------
241		en_diss: array_like (N)
242		The dissipated energy profile(s).
243		"""
244		ediss_f10 = fang2010_mono(
245		ens[None, None, :],
246		dfluxes,
247		scale_height[..., None],
248		rho[..., None],
249		pij=pij,
250		)
251		return np.trapz(ediss_f10 * ens, ens, axis=axis)
252
253
254		def maxwell_general(en, en_0=10.):
255		"""Maxwell number flux spectrum as in Fang2008 [1]
256
257		Defined in Fang et al., JGR 2008, Eq. (1).
258
259		Parameters
260		----------
261		en: float
262		Energy in [keV]
263		en_0: float, optional
264		Characteristic energy in [keV], i.e. mode of the distribution.
265		Default: 10 keV
266
267		Returns
268		-------
269		phi: float
270		Differential hemispherical number flux in [keV-1 cm-2 s-1]
271		([keV] or scaled by 1 keV-2 cm-2 s-1, e.g. ).
272		"""
273		return en * np.exp(-en / en_0)
274
275
276		def maxwell_pflux(en, en_0=10.):
277		"""Maxwell particle flux spectrum as in Fang2008 [1]
278
279		Defined in Fang et al., JGR 2008, Eq. (1).
280		The total precipitating energy flux is fixed to 1 keV cm-2 s-1,
281		multiply by Q_0 [keV cm-2 s-1] to scale the particle flux.
282
283		Parameters
284		----------
285		en: float
286		Energy in [keV]
287		en_0: float, optional
288		Characteristic energy in [keV], i.e. mode of the distribution.
289		Default: 10 keV.
290
291		Returns
292		-------
293		phi: float
294		Hemispherical differential particle flux in [keV-1 cm-2 s-1]
295		([kev-2] scaled by unit energy flux).
296		"""
297		return 0.5 / en_0*3 maxwell_general(en, en_0)
298
299
300	View Code Duplication	def fang2010_maxw_int(energy, flux, scale_height, rho, bounds=(0.1, 300.), nstep=128, pij=POLY_F2010):
		0 ignored issues – show Duplication introduced 2020-06-06 16:42 UTC by Report Bug Copy Issue Report This code seems to be duplicated in your project. Loading history...
301		"""
302		Integrate the mono-energetic parametrization over a Maxwellian
303
304		Parameters
305		----------
306		bounds: tuple, optional
307		(min, max) [keV] of the integration range to integrate the Maxwellian.
308		Make sure that this is appropriate to encompass the spectrum.
309		Default: (0.1, 300.)
310		nsteps: int, optional
311		Number of integration steps, default: 128.
312		"""
313		bounds_l10 = np.log10(bounds)
314		ens = np.logspace(*bounds_l10, num=nstep)
315		dflux = flux * maxwell_pflux(ens[:, None], energy)
316		return fang2010_spec_int(ens, dflux.T, scale_height, rho, pij=pij, axis=-1)
317

st-bender / pyeppaurora

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eppaurora.electrons.fang2008() A

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