plasmapy.formulary.collisions.Knudsen_number(characteristic_length, 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(dimensionless)

Knudsen number (dimensionless)

  • characteristic_length (Quantity) – Rough order-of-magnitude estimate of the relevant size of the system.
  • 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.

knudsen_param – The dimensionless Knudsen number.

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 Knudsen number is given by [1]

\[Kn = \frac{\lambda_{mfp}}{L}\]

where \(\lambda_{mfp}\) is the collisional mean free path for particles in a plasma and :math`L` is the characteristic scale length of interest.

Typically the characteristic scale length is the plasma size or the size of a diagnostic (such a the length or radius of a Langmuir probe tip). The Knudsen number tells us whether collisional effects are important on this scale length.


>>> from astropy import units as u
>>> L = 1e-3 * u.m
>>> n = 1e19*u.m**-3
>>> T = 1e6*u.K
>>> species = ('e', 'p')
>>> Knudsen_number(L, T, n, species)
<Quantity 7839.5...>
>>> Knudsen_number(L, T, n, species, V=1e6 * u.m / u.s)
<Quantity 10.91773...>