plasmapy.transport.collisions.collision_frequency(T, n, particles, z_mean=<Quantity nan>, V=<Quantity nan m / s>, method='classical')

Collision frequency of particles in a plasma.


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.


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.


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
>>> particles = ('e', 'p')
>>> collision_frequency(T, n, particles)
<Quantity 702492.01188504 Hz>



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