Hall_parameter

plasmapy.formulary.dimensionless.Hall_parameter(
n: Annotated[Quantity, Unit('1 / m3')],
T: Annotated[Quantity, Unit('K')],
B: Annotated[Quantity, Unit('T')],
ion: str | int | integer | Particle | CustomParticle | Quantity,
particle: str | int | integer | Particle | CustomParticle | Quantity,
coulomb_log: float | None = None,
V: Annotated[Quantity, Unit('m / s')] | None = None,
coulomb_log_method: str = 'classical',
)[source]

Calculate the particle Hall parameter for a plasma.

The Hall parameter for plasma species \(s\) (particle) is given by:

\[β_{s} = \frac{Ω_{c s}}{ν_{s s^{\prime}}}\]

where \(Ω_{c s}\) is the gyrofrequncy for plasma species \(s\) (particle) and \(ν_{s s^{\prime}}\) is the collision frequency between plasma species \(s\) (particle) and species \(s^{\prime}\) (ion).

Aliases: betaH_

Parameters:

  • n (Quantity) – The number density associated with particle.

  • T (Quantity) – The temperature of associated with particle.

  • B (Quantity) – The magnetic field.

  • ion (Particle) – The type of ion particle is colliding with.

  • particle (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 (Quantity) – The relative velocity between particle and ion. If not provided, then the particle thermal velocity is assumed (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 Coulomb_logarithm for more information about these methods.

Returns:

Hall parameter for particle.

Return type:

Quantity

See also

gyrofrequency, fundamental_electron_collision_freq, fundamental_ion_collision_freq, Coulomb_logarithm

Notes

Examples

>>> import astropy.units as u
>>> Hall_parameter(1e10 * u.m**-3, 2.8e2 * u.eV, 2.3 * u.T, "He-4 +1", "e-")
<Quantity 2.500...e+15>