# mean_free_path¶

plasmapy.formulary.mean_free_path(T: Unit("K"), n_e: Unit("1 / m3"), species, z_mean: Unit(dimensionless) = <Quantity nan>, V: Unit("m / s") = <Quantity nan m / s>, method='classical') -> Unit("m")

Collisional mean free path (m)

Parameters
• T (Quantity) – Temperature in units of temperature or energy per particle, which is assumed to be equal for both the test particle and the target particle.

• n_e (Quantity) – The electron number density in units convertible to per cubic meter.

• species (tuple) – A tuple containing string representations of the test particle (listed first) and the target particle (listed second).

• 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 if method is "ls_full_interp", "hls_max_interp", or "hls_full_interp".

• 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 of Coulomb_logarithm for more information about these methods.

Returns

mfp – The collisional mean free path for particles in a plasma.

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, or V is not a Quantity.

• 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 collisional mean free path is given by 1

$λ_{mfp} = \frac{v}{ν}$

where $$v$$ is the inter-particle velocity (typically taken to be the thermal velocity) and $$ν$$ is the collision frequency.

Examples

>>> from astropy import units as u
>>> n = 1e19 * u.m ** -3
>>> T = 1e6 * u.K
>>> mean_free_path(T, n, ('e-', 'p+'))
<Quantity 7.839... m>
>>> mean_free_path(T, n, ('e-', 'p+'), V=1e6 * u.m / u.s)
<Quantity 0.0109... m>


References

1

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