collision_rate_ion_ion

plasmapy.physics.transport.collisions.collision_rate_ion_ion(T_i, n_i, ion_particle, coulomb_log=None, V=None, coulomb_log_method='classical')

Momentum relaxation ion-ion collision rate

From [3], equations (2.36) and (2.122)

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

Note, it is assumed that electrons are present in such numbers as to establish quasineutrality, but the effects of the test ions colliding with them are not considered here.

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

Parameters:
  • T_i (Quantity) – The electron temperature of the Maxwellian test ions
  • n_i (Quantity) – The number density of the Maxwellian test ions
  • ion_particle (str) – String signifying a particle type of the test and field ions, including charge state information. This function assumes the test and field ions are the same species.
  • 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 ~plasmapy.physics.transport.Coulomb_logarithm function.
  • coulomb_log_method (str, 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_ion_ion(0.1 * u.eV, 1e6 / u.m ** 3, 'p')
<Quantity 2.97315582e-05 1 / s>
>>> collision_rate_ion_ion(100 * u.eV, 1e6 / u.m ** 3, 'p')
<Quantity 1.43713193e-09 1 / s>
>>> collision_rate_ion_ion(100 * u.eV, 1e20 / u.m ** 3, 'p')
<Quantity 66411.80316364 1 / s>
>>> collision_rate_ion_ion(100 * u.eV, 1e20 / u.m ** 3, 'p', coulomb_log_method='GMS-1')
<Quantity 66407.00859126 1 / s>
>>> collision_rate_ion_ion(100 * u.eV, 1e20 / u.m ** 3, 'p', V = c / 100)
<Quantity 6.53577473 1 / s>
>>> collision_rate_ion_ion(100 * u.eV, 1e20 / u.m ** 3, 'p', coulomb_log=20)
<Quantity 95918.76240877 1 / s>