Spitzer_resistivity
- plasmapy.formulary.collisions.misc.Spitzer_resistivity(T: Unit("K"), n: Unit("1 / m3"), species, z_mean: ~numbers.Real = nan, V: Unit("m / s") = <Quantity nan m / s>, method='classical') -> Unit("Ohm m")
Spitzer resistivity of a plasma.
- Parameters:
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) 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 non-classical 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 straight-line Landau-Spitzer 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 assumed.RelativityWarning
– If the input velocity is greater than 5% of the speed of light.
Notes
The Spitzer resistivity (see Ch. 5 of Chen [2016]) is given by:
\[η = \frac{m}{n Z_1 Z_2 q_e^2} ν_{1,2}\]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 electron-ion collisions are inelastic and therefore produce resistivity in the plasma.
Examples
>>> import astropy.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 Ohm m> >>> Spitzer_resistivity(T, n, species, V=1e6 * u.m / u.s) <Quantity 0.000324... Ohm m>