Knudsen_number

plasmapy.formulary.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)

Parameters
  • 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 number 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) of a plasma for which a macroscopic description is valid. This parameter is used to compute the average ion density (given the average ionization and electron density) for calculating the ion sphere radius for non-classical impact parameters. z_mean is a required parameter if method is "ls_full_interp", "hls_max_interp", or "hls_full_interp".

  • V (Quantity, optional) – The relative velocity between particles. If not provided, thermal velocity is assumed: \(μ V^2 \sim 2 k_B T\) where \(μ\) is the reduced mass.

  • method (str, optional) – The method by which to compute the Coulomb logarithm. The default method is the classical straight-line Landau-Spitzer method ("classical" or "ls"). The other 6 supported methods are "ls_min_interp", "ls_full_interp", "ls_clamp_mininterp", "hls_min_interp", "hls_max_interp", and "hls_full_interp". Please refer to the docstring of Coulomb_logarithm for more information about these methods.

Returns

knudsen_param – The dimensionless Knudsen number.

Return type

float or numpy.ndarray

Raises
  • 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 any of n_e, T, or V is not a Quantity.

  • RelativityError – If the input velocity is same or greater than the speed of light.

Warns
  • UnitsWarning – If units are not provided, SI units are assumed

  • RelativityWarning – If the input velocity is greater than 5% of the speed of light.

Notes

The Knudsen number is given by 1

\[Kn = \frac{λ_{mfp}}{L}\]

where \(λ_{mfp}\) 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.

Examples

>>> 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...>

References

1

https://en.wikipedia.org/wiki/Knudsen_number