inertial_length

plasmapy.formulary.lengths.inertial_length(n: Unit('1 / m3'), particle: str | Integral | Particle | CustomParticle | Quantity, *, mass_numb=None, Z=None)

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).

• mass_numb (integer, keyword-only, optional) – The mass number associated with particle.

• Z (real number, keyword-only, optional) – The charge number associated with particle.

Returns:

d – The particle’s inertial length in meters.

Return type:

Quantity

Raises:

• TypeError – If n is not a Quantity or particle is not a string.

• UnitConversionError – If n is not in units of a number density.

• ValueError – The particle density does not have an appropriate value.

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.

Examples

>>> 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>