Spitzer_resistivity¶

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
Parameters:  T (Quantity) – Temperature in units of temperature. This should be the electron temperature for electronelectron and electronion collisions, and the ion temperature for ionion collisions.
 n (Quantity) – The density in units convertible to per cubic meter. This should be the electron density for electronelectron collisions, and the ion density for electronion and ionion 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 nonclassical 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.
Returns: spitzer – The resistivity of the plasma in Ohm meters.
Return type: Raises: 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 incorrectTypeError
– If the n_e, T, or V are not Quantities.RelativityError
– If the input velocity is same or greater than the speed of light.
Warns:  ~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.
Notes
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 electronion collisions are inelastic and therefore produce resistivity in the plasma.
Examples
>>> 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...e06 m Ohm> >>> Spitzer_resistivity(T, n, species, V=1e6 * u.m / u.s) <Quantity 0.000324... m Ohm>
References
[1] Francis, F. Chen. Introduction to plasma physics and controlled fusion 3rd edition. Ch 5 (Springer 2015). [2] http://homepages.cae.wisc.edu/~callen/chap2.pdf