# mobility¶

plasmapy.transport.collisions.mobility(T, n_e, particles, z_mean=<Quantity nan>, V=<Quantity nan m / s>, method='classical')

Electrical mobility (m^2/(V s))

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 density in units convertible to per cubic meter.

• particles (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) 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. It is also used the obtain the average mobility of a plasma with multiple charge state species. When z_mean is not given, the average charge between the two particles is used instead.

• 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

mobility_value – The electrical mobility of particles in a collisional 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 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 mobility is given by 1

$\mu = \frac{q}{m \nu}$

where $$q$$ is the particle charge, $$m$$ is the particle mass and $$\nu$$ is the collisional frequency of the particle in the plasma.

The mobility describes the forced diffusion of a particle in a collisional plasma which is under the influence of an electric field. The mobility is essentially the ratio of drift velocity due to collisions and the electric field driving the forced diffusion.

Examples

>>> from astropy import units as u
>>> n = 1e19*u.m**-3
>>> T = 1e6*u.K
>>> particles = ('e', 'p')
>>> mobility(T, n, particles)
<Quantity 250505.04164488 m2 / (s V)>
>>> mobility(T, n, particles, V=1e6 * u.m / u.s)
<Quantity 1921.27848189 m2 / (s V)>


References

1

https://en.wikipedia.org/wiki/Electrical_mobility#Mobility_in_gas_phase