# fundamental_electron_collision_freq¶

plasmapy.transport.collisions.fundamental_electron_collision_freq(T_e, n_e, ion_particle, coulomb_log=None, V=None, coulomb_log_method='classical')

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

3 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 is heavily related 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_particle (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: $$\mu V^2 \sim 2 k_B T$$ where mu is the reduced mass.

• coulomb_log (float or dimensionless ~astropy.units.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 (string, optional) – Method used for Coulomb logarithm calculation (see that function for more documentation). Choose from “classical” or “GMS-1” to “GMS-6”.

Notes

Equations (2.17) and (2.120) in 3 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 is this (from 2.17):

$\nu_e = \frac{4}{3 \sqrt{\pi}} \nu(v_{Te})$

Where $$\nu$$ 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 is equivalent to: * 1/tau_e from ref 1 eqn (2.5e) pp. 215, * nu_e from ref 2 pp. 33,

References

1

Braginskii, S. I. “Transport processes in a plasma.” Reviews of plasma physics 1 (1965): 205.

2

Huba, J. D. “NRL (Naval Research Laboratory) Plasma Formulary, revised.” Naval Research Lab. Report NRL/PU/6790-16-614 (2016). https://www.nrl.navy.mil/ppd/content/nrl-plasma-formulary

3(1,2)

J.D. Callen, Fundamentals of Plasma Physics draft material, Chapter 2, http://homepages.cae.wisc.edu/~callen/chap2.pdf

Examples

>>> from astropy import units as u
>>> fundamental_electron_collision_freq(0.1 * u.eV, 1e6 / u.m ** 3, 'p')
<Quantity 0.00180167 1 / s>
>>> fundamental_electron_collision_freq(1e6 * u.K, 1e6 / u.m ** 3, 'p')
<Quantity 1.07221863e-07 1 / s>
>>> fundamental_electron_collision_freq(100 * u.eV, 1e20 / u.m ** 3, 'p')
<Quantity 3935958.7396539 1 / s>
>>> fundamental_electron_collision_freq(100 * u.eV, 1e20 / u.m ** 3, 'p', coulomb_log_method = 'GMS-1')
<Quantity 3872815.52840036 1 / s>
>>> fundamental_electron_collision_freq(0.1 * u.eV, 1e6 / u.m ** 3, 'p', V = c / 100)
<Quantity 5.65897885e-07 1 / s>
>>> fundamental_electron_collision_freq(100 * u.eV, 1e20 / u.m ** 3, 'p', coulomb_log = 20)
<Quantity 5812633.74935004 1 / s>