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).

If the Hall parameter is low, the trajectory of electrons between two encounters of heavy particles is approximately linear. If the Hall parameter is high, the motion of the electrons is highly curved.

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>