fundamental_electron_collision_freq

plasmapy.formulary.collisions.frequencies.fundamental_electron_collision_freq(T_e: Unit('K'), n_e: Unit('1 / m3'), ion, coulomb_log=None, V=None, coulomb_log_method='classical')

Average momentum relaxation rate for a slowly flowing Maxwellian distribution of electrons.

Note

The fundamental_electron_collision_freq function has been replaced by the more general MaxwellianCollisionFrequencies class. To replicate the functionality of fundamental_electron_collision_freq, create a MaxwellianCollisionFrequencies class and access the Maxwellian_avg_ei_collision_freq attribute.

Braginskii [1965] provides a derivation of this as an average collision frequency between electrons and ions for a Maxwellian distribution. It is thus a special case of the collision frequency with an averaging factor, and is on many occasions in transport theory the most relevant collision frequency that has to be considered. It commonly occurs in relation to diffusion and resistivity in plasmas.

Parameters
  • T_e (Quantity) – The electron temperature of the Maxwellian test electrons.

  • n_e (Quantity) – The number density of the Maxwellian test electrons.

  • ion (str) – String signifying a particle type of the field ions, including charge state information.

  • 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.

  • coulomb_log (float or dimensionless Quantity, optional) – Option to specify a Coulomb logarithm of the electrons on the ions. If not specified, the Coulomb log will is calculated using the Coulomb_logarithm function.

  • coulomb_log_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

nu_e

Return type

Quantity

Notes

Equations (2.17) and (2.120) in Callen [n.d.] provide the original source used to implement this formula, however, the simplest form that connects our average collision frequency to the general collision frequency is this (from 2.17):

\[ν_e = \frac{4}{3 \sqrt{π}} ν(v_{Te})\]

Where \(ν\) is the general collision frequency and \(v_{Te}\) is the electron thermal velocity (the average, for a Maxwellian distribution).

This implementation of the average collision frequency is equivalent to:

  • \(1/τ_e\) from equation (2.5e) on page 215 of Braginskii [1965]

  • \(ν_e\) from page 33 of Richardson [2019]

Examples

>>> import astropy.units as u
>>> from astropy.constants import c
>>> fundamental_electron_collision_freq(0.1 * u.eV, 1e6 / u.m ** 3, 'p')
<Quantity 0.001801... 1 / s>
>>> fundamental_electron_collision_freq(1e6 * u.K, 1e6 / u.m ** 3, 'p')
<Quantity 1.07221...e-07 1 / s>
>>> fundamental_electron_collision_freq(100 * u.eV, 1e20 / u.m ** 3, 'p')
<Quantity 3935958.7... 1 / s>
>>> fundamental_electron_collision_freq(100 * u.eV, 1e20 / u.m ** 3, 'p', coulomb_log_method = 'GMS-1')
<Quantity 3872815.5... 1 / s>
>>> fundamental_electron_collision_freq(0.1 * u.eV, 1e6 / u.m ** 3, 'p', V = c / 100)
<Quantity 5.6589...e-07 1 / s>
>>> fundamental_electron_collision_freq(100 * u.eV, 1e20 / u.m ** 3, 'p', coulomb_log = 20)
<Quantity 5812633... 1 / s>