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 orderofmagnitude 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 nonclassical 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.
Returns: knudsen_param – The dimensionless Knudsen number.
Return type: 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 incorrectTypeError
– If the n_e, T, or V are not Quantities.RelativityError
– If the input velocity is same or greater than the speed of light.
Warns:  ~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.
Notes
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.
Examples
>>> from astropy import units as u >>> L = 1e3 * 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