collision_frequency

plasmapy.formulary.collisions.collision_frequency(T: Unit("K"), n: Unit("1 / m3"), species, z_mean: Unit(dimensionless) = <Quantity nan>, V: Unit("m / s") = <Quantity nan m / s>, method='classical') -> Unit("Hz")

Collision frequency of particles in a plasma.

Parameters
  • T (Quantity) – Temperature in units of temperature. This should be the electron temperature for electron-electron and electron-ion collisions, and the ion temperature for ion-ion collisions.

  • n (Quantity) – The density in units convertible to per cubic meter. This should be the electron density for electron-electron collisions, and the ion density for electron-ion and ion-ion collisions.

  • species (tuple) – A tuple containing string representations of the test particle (listed first) and the target particle (listed second).

  • z_mean (Quantity, optional) – The average ionization (arithmetic mean) of a plasma for which a macroscopic description is valid. This parameter is used to compute the average ion density (given the average ionization and electron density) for calculating the ion sphere radius for non-classical impact parameters. z_mean is a required parameter if method is "ls_full_interp", "hls_max_interp", or "hls_full_interp".

  • V (Quantity, optional) – The relative velocity between particles. If not provided, thermal velocity is assumed: \(μ V^2 \sim 2 k_B T\) where \(μ\) is the reduced mass.

  • 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

freq – The collision frequency of particles in a plasma.

Return type

float or numpy.ndarray

Raises
  • ValueError – If the mass or charge of either particle cannot be found, or any of the inputs contain incorrect values.

  • UnitConversionError – If the units on any of the inputs are incorrect

  • TypeError – If the n_e, T, or V are not Quantities.

  • RelativityError – If the input velocity is same or greater than the speed of light.

Warns
  • UnitsWarning – If units are not provided, SI units are assumed

  • RelativityWarning – If the input velocity is greater than 5% of the speed of light.

Notes

The collision frequency is given by 1

\[ν = n σ v \ln{Λ}\]

where \(n\) is the particle density, \(σ\) is the collisional cross-section, \(v\) is the inter-particle velocity (typically taken as the thermal velocity), and \(\ln{Λ}\) is the Coulomb logarithm accounting for small angle collisions.

See Equation (2.14) in 2.

Examples

>>> from astropy import units as u
>>> n = 1e19*u.m**-3
>>> T = 1e6*u.K
>>> species = ('e', 'p')
>>> collision_frequency(T, n, species)
<Quantity 70249... Hz>

References

1

Francis, F. Chen. Introduction to plasma physics and controlled fusion 3rd edition. Ch 5 (Springer 2015).

2

http://homepages.cae.wisc.edu/~callen/chap2.pdf