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

Collisional mean free path (m)

  • T (Quantity) – Temperature in units of temperature or energy per particle, which is assumed to be equal for both the test particle and the target particle
  • n_e (Quantity) – The electron density in units convertible to per cubic meter.
  • 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) 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 (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.

mfp – The collisional mean free path for 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 collisional mean free path is given by [1]

\[\lambda_{mfp} = \frac{v}{\nu}\]

where \(v\) is the inter-particle velocity (typically taken to be the thermal velocity) and \(\nu\) is the collision frequency.


>>> from astropy import units as u
>>> n = 1e19 * u.m ** -3
>>> T = 1e6 * u.K
>>> mean_free_path(T, n, ('e-', 'p+'))
<Quantity 7.839... m>
>>> mean_free_path(T, n, ('e-', 'p+'), V=1e6 * u.m / u.s)
<Quantity 0.0109... m>


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