Hall_parameter¶

plasmapy.formulary.parameters.Hall_parameter(n: Unit(‘1 / m3’), T: Unit(‘K’), B: Unit(‘T’), ion: plasmapy.particles.particle_class.Particle, particle: plasmapy.particles.particle_class.Particle, coulomb_log=None, V=None, coulomb_log_method='classical')¶

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

Notes

For calculating the collision frequency fundamental_electron_collision_freq is used when particle is an electron and fundamental_ion_collision_freq when particle is an ion.
The collision frequencies are calculated assuming a slowly moving Maxwellian distribution.

Examples

>>> from astropy import units as u
>>> Hall_parameter(1e10 * u.m**-3, 2.8e3 * u.eV, 2.3 * u.T, 'He-4 +1', 'e-')
<Quantity 7.26446...e+16>
>>> Hall_parameter(1e10 * u.m**-3, 5.8e3 * u.eV, 2.3 * u.T, 'He-4 +1', 'e-')
<Quantity 2.11158...e+17>