collision_frequency¶

plasmapy.formulary.
collision_frequency
(T: Unit("K"), n: Unit("1 / m3"), species, z_mean: Unit(dimensionless) = <Quantity nan>, V: Unit("m / s") = <Quantity nan m / s>, method='classical') > Unit("Hz")¶ Collision frequency of particles in a plasma.
Parameters: T (Quantity) – Temperature in units of temperature. This should be the electron temperature for electronelectron and electronion collisions, and the ion temperature for ionion collisions.  n : ~astropy.units.Quantity
 The density in units convertible to per cubic meter. This should be the electron density for electronelectron collisions, and the ion density for electronion and ionion collisions.
 species : tuple
 A tuple containing string representations of the test particle (listed first) and the target particle (listed second)
 z_mean : ~astropy.units.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 : ~astropy.units.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: freq – The collision frequency of particles in a plasma.
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 collision frequency is given by [1]
\[\nu = n \sigma v \ln{\Lambda}\]where n is the particle density, \(\sigma\) is the collisional crosssection, \(v\) is the interparticle velocity (typically taken as the thermal velocity), and \(\ln{\Lambda}\) is the Coulomb logarithm accounting for small angle collisions.
See eq (2.14) in [2].
Examples
>>> from astropy import units as u >>> n = 1e19*u.m**3 >>> T = 1e6*u.K >>> species = ('e', 'p') >>> collision_frequency(T, n, species) <Quantity 70249... Hz>
References
[1] Francis, F. Chen. Introduction to plasma physics and controlled fusion 3rd edition. Ch 5 (Springer 2015). [2] http://homepages.cae.wisc.edu/~callen/chap2.pdf