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# coding: utf-8 |
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# Copyright (c) 2021 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 conductivity from electron densities [1]_ [2]_ [3]_ |
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.. [1] A. Brekke, J. R. Doupnik, P. M. Banks, |
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Incoherent scatter measurements of E region conductivities and currents in the auroral zone, |
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J. Geophys. Res., 79(25), 3773--3790, Sept. 1974, |
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doi: `10.1029/JA079i025p03773 <https://doi.org/10.1029/JA079i025p03773>`_ |
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.. [2] James F. Vickrey, Richard R. Vondrak, Stephen J. Matthews, |
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The diurnal and latitudinal variation of auroral zone ionospheric conductivity, |
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J. Geophys. Res., 86(A1), 65--75, Jan. 1981, |
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doi: `10.1029/JA086iA01p00065 <https://doi.org/10.1029/JA086iA01p00065>`_ |
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.. [3] R. M. Robinson, R. R. Vondrak, K. Miller, T. Dabbs, D. Hardy, |
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On calculating ionospheric conductances from the flux and energy of precipitating electrons, |
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J. Geophys. Res. Space Phys., 92(A3), 2565--2569, Mar. 1987, |
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doi: `10.1029/JA092iA03p02565 <https://doi.org/10.1029/JA092iA03p02565>`_ |
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""" |
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import numpy as np |
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__all__ = [ |
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"ion_coll", |
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"ion_gyro", |
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"pedersen", |
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"hall", |
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"SigmaP_robinson1987", |
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"SigmaH_robinson1987", |
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] |
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E_CHARGE = 1.602176634e-19 # [C] = [As] |
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def ion_coll(n_neutral): |
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"""Ion--neutral collision frequency |
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Derived from the atmospheric neutral density [#]_ |
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e.g., from NRLMSISE-00. |
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Parameters |
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---------- |
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n_neutral: float or array_like (M, ...) |
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Atmospheric density in [cm⁻³] |
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Returns |
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------- |
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ion_coll: float or array_like (M, ...) |
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Ion--neutral collision frequency [s⁻¹] |
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References |
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---------- |
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.. [#] Vickrey et al., J. Geophys. Res., 86(A1), 65--75, Jan. 1981, |
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doi: `10.1029/JA086iA01p00065 <https://doi.org/10.1029/JA086iA01p00065>`_ |
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""" |
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return 3.75e-10 * n_neutral |
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def ion_gyro(bmag, m_ion=30.): |
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"""Ion gyro (cyclotron) frequency |
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Parameters |
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---------- |
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bmag: float or array_like (M,...) |
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Magnitude of the magnetic B-field [T]. |
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m_ion: float or array_like (M, ...), optional (default 30.0) |
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Ion mass [GeV / c²] |
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Returns |
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------- |
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ion_gyro: float or array_like (M, ...) |
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Ion cyclotron frequency [s⁻¹] |
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""" |
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return 2 * np.pi * 2.8e10 * bmag * (511e-6 / m_ion) |
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def pedersen(ne, bmag, ion_gyro, ion_coll): |
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"""Pedersen conductivity σP |
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Formulae and parameters as described in [#]_ [#]_, |
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neglecting electron--neutral collisions. |
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Parameters |
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---------- |
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ne: float or array_like (M, ...) |
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Electron density in [m⁻³] |
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bmag: float or array_like (M, ...) |
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Magnitude of the magnetic B-field [T]. |
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ion_gyro: float or array_like (N, ...) |
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The ion gyro frequency [s⁻¹] |
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ion_coll: float or array_like (N, ...) |
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The ion collision frequency [s⁻¹] |
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Returns |
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------- |
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σP: float or array_like (M, N) if broadcastable |
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Pedersen conductivity [S m⁻¹]. |
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References |
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---------- |
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.. [#] Brekke et al., J. Geophys. Res., 79(25), 3773--3790, Sept. 1974, |
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doi: `10.1029/JA079i025p03773 <https://doi.org/10.1029/JA079i025p03773>`_ |
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.. [#] Vickrey et al., J. Geophys. Res., 86(A1), 65--75, Jan. 1981, |
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doi: `10.1029/JA086iA01p00065 <https://doi.org/10.1029/JA086iA01p00065>`_ |
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""" |
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return ne * E_CHARGE / bmag * ion_gyro * ion_coll / (ion_gyro**2 + ion_coll**2) |
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def hall(ne, bmag, ion_gyro, ion_coll): |
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"""Hall conductivity σH |
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Formulae and parameters as described in [#]_ [#]_, |
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neglecting electron--neutral collisions. |
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Parameters |
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---------- |
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ne: float or array_like (M, ...) |
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Electron density in [m⁻³] |
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bmag: float or array_like (M,...) |
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Magnitude of the magnetic B-field [T]. |
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ion_gyro: float or array_like (N, ...) |
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The ion gyro frequency [s⁻¹] |
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ion_coll: float or array_like (N, ...) |
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The ion collision frequency [s⁻¹] |
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Returns |
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------- |
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σH: float or array_like (M, N) if broadcastable |
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Hall conductivity [S m⁻¹]. |
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References |
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---------- |
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.. [#] Brekke et al., J. Geophys. Res., 79(25), 3773--3790, Sept. 1974, |
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doi: `10.1029/JA079i025p03773 <https://doi.org/10.1029/JA079i025p03773>`_ |
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.. [#] Vickrey et al., J. Geophys. Res., 86(A1), 65--75, Jan. 1981, |
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doi: `10.1029/JA086iA01p00065 <https://doi.org/10.1029/JA086iA01p00065>`_ |
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""" |
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return ne * E_CHARGE / bmag * ion_coll**2 / (ion_gyro**2 + ion_coll**2) |
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def SigmaP_robinson1987(en_avg, flx): |
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"""Pedersen conductance [#]_ |
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Directly derived from the electron mean energy and energy flux. |
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Parameters |
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---------- |
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en_avg: float or array_like (M, ...) |
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Electron average energy in [keV] |
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flx: float or array_like (M, ...) |
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Energy flux [ergs cm⁻² s⁻¹]. |
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Returns |
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------- |
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ΣP: float or array_like (M, N) if broadcastable |
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Pedersen conductance [S]. |
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References |
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---------- |
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.. [#] Robinson et al., J. Geophys. Res. Space Phys., 92(A3), 2565--2569, Mar. 1987, |
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doi: `10.1029/JA092iA03p02565 <https://doi.org/10.1029/JA092iA03p02565>`_ |
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""" |
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return 40 * en_avg / (16. + en_avg**2) * np.sqrt(flx) |
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def SigmaH_robinson1987(en_avg, flx): |
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"""Hall conductance [#]_ |
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Directly derived from the electron mean energy and energy flux. |
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Parameters |
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---------- |
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en_avg: float or array_like (M, ...) |
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Electron average energy in [keV] |
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flx: float or array_like (M, ...) |
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Energy flux [ergs cm⁻² s⁻¹]. |
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Returns |
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------- |
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ΣH: float or array_like (M, N) if broadcastable |
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Hall conductance [S]. |
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References |
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---------- |
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.. [#] Robinson et al., J. Geophys. Res. Space Phys., 92(A3), 2565--2569, Mar. 1987, |
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doi: `10.1029/JA092iA03p02565 <https://doi.org/10.1029/JA092iA03p02565>`_ |
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""" |
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return 0.45 * en_avg**(0.85) * SigmaP_robinson1987(en_avg, flx) |
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st-bender /
pyeppaurora
