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 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 nonclassical impact parameters.z_mean
is a required parameter ifmethod
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 straightline LandauSpitzer 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 ofCoulomb_logarithm
for more information about these methods.
 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 incorrect
RelativityError – If the input velocity is same or greater than the speed of light.
 Warns
UnitsWarning
– If units are not provided, SI units are assumedRelativityWarning
– 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 = 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