collision_rate_electron_ion

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

Momentum relaxation electron-ion collision rate

From [3], equations (2.17) and (2.120)

Considering a Maxwellian distribution of “test” electrons colliding with a Maxwellian distribution of “field” ions.

This result is an electron momentum relaxation rate, and is used in many classical transport expressions. It is equivalent to: * 1/tau_e from ref [1] eqn (1) pp. #, * 1/tau_e from ref [2] eqn (1) pp. #, * nu_ei_S from ref [2] eqn (1) pp. #,

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”.

References

[1]Braginskii, S. I. “Transport processes in a plasma.” Reviews of plasma physics 1 (1965): 205.
[2](1, 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]Callen Chapter 2, http://homepages.cae.wisc.edu/~callen/chap2.pdf

Examples

>>> from astropy import units as u
>>> collision_rate_electron_ion(0.1 * u.eV, 1e6 / u.m ** 3, 'p')
<Quantity 0.00180172 1 / s>
>>> collision_rate_electron_ion(100 * u.eV, 1e6 / u.m ** 3, 'p')
<Quantity 8.6204672e-08 1 / s>
>>> collision_rate_electron_ion(100 * u.eV, 1e20 / u.m ** 3, 'p')
<Quantity 3936037.8595928 1 / s>
>>> collision_rate_electron_ion(100 * u.eV, 1e20 / u.m ** 3, 'p', coulomb_log_method = 'GMS-1')
<Quantity 3872922.52743562 1 / s>
>>> collision_rate_electron_ion(0.1 * u.eV, 1e6 / u.m ** 3, 'p', V = c / 100)
<Quantity 4.41166015e-07 1 / s>
>>> collision_rate_electron_ion(100 * u.eV, 1e20 / u.m ** 3, 'p', coulomb_log = 20)
<Quantity 5812633.74935003 1 / s>