plasmapy.formulary.lengths.inertial_length(n: Quantity, particle: str | int | integer | Particle | CustomParticle | Quantity, *, mass_numb: int | None = None, Z: float | None = None) Quantity[source]

Calculate a charged particle’s inertial length.

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.

Aliases: cwp_

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

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

  • mass_numb (integer, keyword-only, optional) – The mass number, if not provided in particle.

  • Z (real number, keyword-only, optional) – The charge number, if not provided in particle.


d – The particle’s inertial length in meters.

Return type:



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


The inertial length is also known as the skin depth.


>>> import astropy.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>