plasmapy.formulary.Spitzer_resistivity(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("m Ohm")

Spitzer resistivity of a plasma

  • T (Quantity) – Temperature in units of temperature. This should be the electron temperature for electron-electron and electron-ion collisions, and the ion temperature for ion-ion collisions.
  • n (Quantity) – The density in units convertible to per cubic meter. This should be the electron density for electron-electron collisions, and the ion density for electron-ion and ion-ion collisions.
  • z_mean (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 non-classical impact parameters.
  • species (tuple) – A tuple containing string representations of the test particle (listed first) and the target particle (listed second)
  • 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.
  • method (str, optional) – Selects which theory to use when calculating the Coulomb logarithm. Defaults to classical method.

spitzer – The resistivity of the plasma in Ohm meters.

Return type:

float or numpy.ndarray

  • 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 incorrect
  • TypeError – If the n_e, T, or V are not Quantities.
  • RelativityError – If the input velocity is same or greater than the speed of light.
  • ~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.


The Spitzer resistivity is given by [1] [2]

\[\eta = \frac{m}{n Z_1 Z_2 q_e^2} \nu_{1,2}\]

where \(m\) is the ion mass or the reduced mass, \(n\) is the ion density, \(Z\) is the particle charge state, \(q_e\) is the charge of an electron, \(\nu_{1,2}\) is the collisional frequency between particle species 1 and 2.

Typically, particle species 1 and 2 are selected to be an electron and an ion, since electron-ion collisions are inelastic and therefore produce resistivity in the plasma.


>>> from astropy import units as u
>>> n = 1e19*u.m**-3
>>> T = 1e6*u.K
>>> species = ('e', 'p')
>>> Spitzer_resistivity(T, n, species)
<Quantity 2.4915...e-06 m Ohm>
>>> Spitzer_resistivity(T, n, species, V=1e6 * u.m / u.s)
<Quantity 0.000324... m Ohm>


[1]Francis, F. Chen. Introduction to plasma physics and controlled fusion 3rd edition. Ch 5 (Springer 2015).