# inertial_length¶

plasmapy.formulary.parameters.inertial_length(n: Unit(‘1 / m3’), particle: plasmapy.particles.particle_class.Particle)

Calculate a charged particle’s inertial length.

Aliases: cwp_

Parameters
• n (Quantity) – Particle number density in units convertible to m-3.

• particle (Particle) – Representation of the particle species (e.g., ‘p+’ for protons, ‘D+’ for deuterium, or ‘He-4 +1’ for singly ionized helium-4).

Returns

d – The particle’s inertial length in meters.

Return type

Quantity

Raises
Warns

UnitsWarning – If units are not provided and SI units are assumed.

Notes

The inertial length of a particle of species $$s$$ is given by

$d = \frac{c}{ω_{ps}}$

The inertial length is the characteristic length scale for a particle to be accelerated in a plasma. The Hall effect becomes important on length scales shorter than the ion inertial length.

The inertial length is also known as the skin depth.

Example

>>> from astropy import units as u
>>> inertial_length(5 * u.m ** -3, 'He+')
<Quantity 2.02985...e+08 m>
>>> inertial_length(5 * u.m ** -3, 'e-')
<Quantity 2376534.75... m>