Debye_length

plasmapy.formulary.lengths.Debye_length( T_e: Annotated[Quantity, Unit('K')], n_e: Annotated[Quantity, Unit('1 / m3')], ) → Annotated[Quantity, Unit('m')][source]

Calculate the exponential scale length for charge screening in an electron plasma with stationary ions.

The Debye length is given by

\[λ_D = \sqrt{\frac{ε_0 k_B T_e}{n_e q_e^2}},\]

where \(n_e\) is the electron number density, \(T_e\) is the electron temperature, \(k_B\) is the Boltzmann constant, \(q_e\) is the elementary charge, and \(ε_0\) is the vacuum permittivity.

Aliases: lambdaD_

Parameters:

T_e (Quantity) – Electron temperature.
n_e (Quantity) – Electron number density.

Returns:

lambda_D – The Debye length in meters.

Return type:

Quantity

Raises:

TypeError – If either argument is not a Quantity.
UnitConversionError – If either argument is in incorrect units.
ValueError – If either argument contains invalid values.

Warns:

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

See also

Debye_number

Notes

Plasmas will generally be quasineutral on length scales significantly longer than the Debye length.

The electrical potential will drop by a factor of \(∼\frac{1}{e}\) every Debye length away from the vicinity of a charged particle.

Examples

>>> import astropy.units as u
>>> Debye_length(5e6 * u.K, 5e15 * u.m**-3)
<Quantity 0.002182... m>