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 : ~astropy.units.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 : ~astropy.units.Quantity, optional
The average ionization (arithmetic mean) for a plasma where the a macroscopic description is valid. This is used to recover the average ion density (given the average ionization and electron density) for calculating the ion sphere radius for non-classical impact parameters.
V : ~astropy.units.Quantity, optional
The relative velocity between particles. If not provided, thermal velocity is assumed: \(\mu V^2 \sim 2 k_B T\) where mu is the reduced mass.
method: str, optional
Selects which theory to use when calculating the Coulomb logarithm. Defaults to classical method.

freq – The collision frequency of particles in a plasma.

Return type:

float or numpy.ndarray

  • 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.
  • ~astropy.units.UnitsWarning – If units are not provided, SI units are assumed
  • ~plasmapy.utils.RelativityWarning – If the input velocity is greater than 5% of the speed of light.


The collision frequency is given by [1]

\[\nu = n \sigma v \ln{\Lambda}\]

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

See eq (2.14) in [2].


>>> 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>


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