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) of a plasma for which a macroscopic description is valid. This parameter is used to compute the average ion density (given the average ionization and electron density) for calculating the ion sphere radius for nonclassical impact parameters.z_mean
is a required parameter ifmethod
is"ls_full_interp"
,"hls_max_interp"
, or"hls_full_interp"
.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: \(μ V^2 \sim 2 k_B T\) where \(μ\) is the reduced mass.method (
str
, optional) – The method by which to compute the Coulomb logarithm. The default method is the classical straightline LandauSpitzer method ("classical"
or"ls"
). The other 6 supported methods are"ls_min_interp"
,"ls_full_interp"
,"ls_clamp_mininterp"
,"hls_min_interp"
,"hls_max_interp"
, and"hls_full_interp"
. Please refer to the docstring ofCoulomb_logarithm
for more information about these methods.
 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 incorrect.
TypeError – If any of
n_e
,T
, orV
are not of typeQuantity
.RelativityError – If the input velocity is same or greater than the speed of light.
 Warns
UnitsWarning
– If units are not provided, SI units are assumedRelativityWarning
– If the input velocity is greater than 5% of the speed of light.
Notes
The Spitzer resistivity is given by 1 2
\[η = \frac{m}{n Z_1 Z_2 q_e^2} ν_{1,2}\]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, \(ν_{1,2}\) 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