plasmapy.formulary.fundamental_ion_collision_freq(T_i: Unit("K"), n_i: Unit("1 / m3"), ion, coulomb_log=None, V=None, coulomb_log_method='classical') -> Unit("1 / s")

Average momentum relaxation rate for a slowly flowing Maxwellian distribution of ions.

[3] provides a derivation of this as an average collision frequency between ions and ions for a Maxwellian distribution. It is thus a special case of the collision frequency with an averaging factor.

  • T_i (Quantity) – The electron temperature of the Maxwellian test ions
  • n_i (Quantity) – The number density of the Maxwellian test ions
  • ion (str) – String signifying a particle type of the test and field ions, including charge state information. This function assumes the test and field ions are the same species.
  • V (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.
  • coulomb_log (float or dimensionless ~astropy.units.Quantity, optional) – Option to specify a Coulomb logarithm of the electrons on the ions. If not specified, the Coulomb log will is calculated using the ~plasmapy.formulary.Coulomb_logarithm function.
  • coulomb_log_method (str, optional) – Method used for Coulomb logarithm calculation (see that function for more documentation). Choose from “classical” or “GMS-1” to “GMS-6”.


Equations (2.36) and (2.122) in [3] provide the original source used to implement this formula, however, in our implementation we use the very same process that leads to the fundamental electron collison rate (2.17), gaining simply a different coefficient:

\[\nu_i = \frac{8}{3 * 4 * \sqrt{\pi}} \nu(v_{Ti})\]

Where \(\nu\) is the general collision frequency and \(v_{Ti}\) is the ion thermal velocity (the average, for a Maxwellian distribution).

Note that in the derivation, it is assumed that electrons are present in such numbers as to establish quasineutrality, but the effects of the test ions colliding with them are not considered here. This is a very typical approximation in transport theory.

This result is an ion momentum relaxation rate, and is used in many classical transport expressions. It is equivalent to: * 1/tau_i from ref [1], equation (2.5i) pp. 215, * nu_i from ref [2] pp. 33,


[1]Braginskii, S. I. “Transport processes in a plasma.” Reviews of plasma physics 1 (1965): 205.
[2]Huba, J. D. “NRL (Naval Research Laboratory) Plasma Formulary, revised.” Naval Research Lab. Report NRL/PU/6790-16-614 (2016).
[3](1, 2) J.D. Callen, Fundamentals of Plasma Physics draft material, Chapter 2,


>>> from astropy import units as u
>>> fundamental_ion_collision_freq(0.1 * u.eV, 1e6 / u.m ** 3, 'p')
<Quantity 2.868...e-05 1 / s>
>>> fundamental_ion_collision_freq(1e6 * u.K, 1e6 / u.m ** 3, 'p')
<Quantity 1.741...e-09 1 / s>
>>> fundamental_ion_collision_freq(100 * u.eV, 1e20 / u.m ** 3, 'p')
<Quantity 63087.5... 1 / s>
>>> fundamental_ion_collision_freq(100 * u.eV, 1e20 / u.m ** 3, 'p', coulomb_log_method='GMS-1')
<Quantity 63085.1... 1 / s>
>>> fundamental_ion_collision_freq(100 * u.eV, 1e20 / u.m ** 3, 'p', V = c / 100)
<Quantity 9.111... 1 / s>
>>> fundamental_ion_collision_freq(100 * u.eV, 1e20 / u.m ** 3, 'p', coulomb_log=20)
<Quantity 95918.7... 1 / s>