def Hall_parameter(n,
T,
B,
ion_particle,
particle='e-',
coulomb_log=None,
V=None,
coulomb_log_method="classical"):
r"""Calculate the ratio between the particle gyrofrequency and the
particle-ion particle collision rate.
All parameters apply to `particle`.
Parameters
----------
n : ~astropy.units.quantity.Quantity
The density of particle s
T : ~astropy.units.quantity.Quantity
The temperature of particles
B : ~astropy.units.quantity.Quantity
The magnetic field
ion_particle : str
String signifying the type of ion.
particle : str, optional
String signifying the type of particles. Defaults to electrons.
coulomb_log : float, optional
Preset value for the Coulomb logarithm. Used mostly for testing purposes.
V : ~astropy.units.quantity.Quantity
The relative velocity between `particle` and ion particles.
coulomb_log_method : str, optional
Method used for Coulomb logarithm calculation. Refer to its documentation.
See Also
--------
plasmapy.formulary.parameters.gyrofrequency
plasmapy.formulary.parameters.fundamental_electron_collision_freq
plasmapy.formulary.collisions.Coulomb_logarithm
Returns
-------
astropy.units.quantity.Quantity
"""
from plasmapy.formulary.collisions import (fundamental_ion_collision_freq,
fundamental_electron_collision_freq)
gyro_frequency = gyrofrequency(B, particle)
gyro_frequency = gyro_frequency / u.radian
if atomic.Particle(particle).particle == 'e-':
coll_rate = fundamental_electron_collision_freq(T,
n,
ion_particle,
coulomb_log,
V,
coulomb_log_method=coulomb_log_method)
else:
coll_rate = fundamental_ion_collision_freq(T, n, ion_particle, coulomb_log, V)
return gyro_frequency / coll_rate
def Hall_parameter(
n: u.m**-3,
T: u.K,
B: u.T,
ion,
particle="e-",
coulomb_log=None,
V=None,
coulomb_log_method="classical",
):
r"""Calculate the ratio between the particle gyrofrequency and the
particle-ion particle collision rate.
All parameters apply to `particle`.
Parameters
----------
n : ~astropy.units.quantity.Quantity
The density of particle s
T : ~astropy.units.quantity.Quantity
The temperature of particles
B : ~astropy.units.quantity.Quantity
The magnetic field
ion : str
String signifying the type of ion.
particle : str, optional
String signifying the type of particles. Defaults to electrons.
coulomb_log : float, optional
Preset value for the Coulomb logarithm. Used mostly for testing purposes.
V : ~astropy.units.quantity.Quantity
The relative velocity between `particle` and ion particles.
coulomb_log_method : str, optional
Method used for Coulomb logarithm calculation. Refer to its documentation.
See Also
--------
plasmapy.formulary.parameters.gyrofrequency
plasmapy.formulary.parameters.fundamental_electron_collision_freq
plasmapy.formulary.collisions.Coulomb_logarithm
Returns
-------
astropy.units.quantity.Quantity
Examples
--------
>>> from astropy import units as u
>>> Hall_parameter(1e10 * u.m**-3, 2.8e3 * u.eV, 2.3 * u.T, 'He-4 +1')
<Quantity 7.26446...e+16>
>>> Hall_parameter(1e10 * u.m**-3, 5.8e3 * u.eV, 2.3 * u.T, 'He-4 +1')
<Quantity 2.11158...e+17>
"""
from plasmapy.formulary.collisions import (
fundamental_ion_collision_freq,
fundamental_electron_collision_freq,
)
gyro_frequency = gyrofrequency(B, particle)
gyro_frequency = gyro_frequency / u.radian
if particles.Particle(particle).particle == "e-":
coll_rate = fundamental_electron_collision_freq(
T, n, ion, coulomb_log, V, coulomb_log_method=coulomb_log_method)
else:
coll_rate = fundamental_ion_collision_freq(T, n, ion, coulomb_log, V)
return gyro_frequency / coll_rate
def Hall_parameter(
n: u.m**-3,
T: u.K,
B: u.T,
ion: Particle,
particle: Particle,
coulomb_log=None,
V=None,
coulomb_log_method="classical",
):
r"""
Calculate the ``particle`` Hall parameter for a plasma.
The Hall parameter for plasma species :math:`s` (``particle``) is given by:
.. math::
β_{s} = \frac{Ω_{c s}}{ν_{s s^{\prime}}}
where :math:`Ω_{c s}` is the gyrofrequncy for plasma species :math:`s`
(``particle``) and :math:`ν_{s s^{\prime}}` is the collision frequency
between plasma species :math:`s` (``particle``) and species
:math:`s^{\prime}` (``ion``).
**Aliases:** `betaH_`
Parameters
----------
n : `~astropy.units.quantity.Quantity`
The number density associated with ``particle``.
T : `~astropy.units.quantity.Quantity`
The temperature of associated with ``particle``.
B : `~astropy.units.quantity.Quantity`
The magnetic field.
ion : `~plasmapy.particles.particle_class.Particle`
The type of ion ``particle`` is colliding with.
particle : `~plasmapy.particles.particle_class.Particle`
The particle species for which the Hall parameter is calculated for.
Representation of the particle species (e.g., ``'p'`` for protons,
``'D+'`` for deuterium, or ``'He-4 +1'`` for singly ionized helium-4).
If no charge state information is provided, then the particles are
assumed to be singly charged.
coulomb_log : `float`, optional
Preset value for the Coulomb logarithm. Used mostly for testing purposes.
V : `~astropy.units.quantity.Quantity`
The relative velocity between ``particle`` and ``ion``. If not provided,
then the ``particle`` thermal velocity is assumed
(`~plasmapy.formulary.speeds.thermal_speed`).
coulomb_log_method : `str`, optional
The method by which to compute the Coulomb logarithm.
The default method is the classical straight-line Landau-Spitzer
method (``"classical"`` or ``"ls"``). The other 6 supported methods
are ``"ls_min_interp"``, ``"ls_full_interp"``, ``"ls_clamp_mininterp"``,
``"hls_min_interp"``, ``"hls_max_interp"``, and ``"hls_full_interp"``.
Please refer to the docstring of
`~plasmapy.formulary.collisions.Coulomb_logarithm` for more
information about these methods.
See Also
--------
~plasmapy.formulary.frequencies.gyrofrequency
~plasmapy.formulary.collisions.fundamental_electron_collision_freq
~plasmapy.formulary.collisions.fundamental_ion_collision_freq
~plasmapy.formulary.collisions.Coulomb_logarithm
Returns
-------
`~astropy.units.quantity.Quantity`
Hall parameter for ``particle``.
Notes
-----
* For calculating the collision frequency
`~plasmapy.formulary.collisions.fundamental_electron_collision_freq` is used
when ``particle`` is an electron and
`~plasmapy.formulary.collisions.fundamental_ion_collision_freq` when
``particle`` is an ion.
* The collision frequencies are calculated assuming a slowly moving
Maxwellian distribution.
Examples
--------
>>> import astropy.units as u
>>> import pytest
>>> from plasmapy.utils.exceptions import RelativityWarning
>>> Hall_parameter(1e10 * u.m**-3, 2.8e2 * u.eV, 2.3 * u.T, 'He-4 +1', 'e-')
<Quantity 2.500...e+15>
>>> with pytest.warns(RelativityWarning):
... Hall_parameter(1e10 * u.m**-3, 5.8e3 * u.eV, 2.3 * u.T, 'He-4 +1', 'e-')
<Quantity 2.11158...e+17>
"""
from plasmapy.formulary.collisions import (
fundamental_electron_collision_freq,
fundamental_ion_collision_freq,
)
gyro_frequency = frequencies.gyrofrequency(B, particle)
gyro_frequency = gyro_frequency / u.radian
if Particle(particle).symbol == "e-":
coll_rate = fundamental_electron_collision_freq(
T, n, ion, coulomb_log, V, coulomb_log_method=coulomb_log_method)
else:
coll_rate = fundamental_ion_collision_freq(T, n, ion, coulomb_log, V)
return gyro_frequency / coll_rate