Debye length

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In plasma physics, the Debye length, named after the Dutch physical chemist Peter Debye, is the scale over which mobile charge carriers (e.g. electrons) screen out electric fields in plasmas and other conductors. In other words, the Debye length is the distance over which significant charge separation can occur. In space plasmas where the electron density is relatively low, the Debye length may reach macroscope values, such as in the Magnetosphere, Solar wind, Interstellar medium and Intergalactic medium (See table):

Plasma	Density ne(m3)	Electron Temperature T(K)	Magnetic Field B(T)	Debye Length λD(m)
Gas discharge	1016	104	--	10-4
Tokamak	1020	108	10	10-4
Ionosphere	1012	103	10-5	10-3
Magnetosphere	107	107	10-8	102
Solar core	1032	107	--	10-11
Solar wind	106	105	10-9	10
Interstellar medium	105	104	10-10	10
Intergalactic medium	1	106	--	105

Hannes Alfven pointed out that: "In a low density plasma, localized space charge regions may build up large potential drops over distances of the order of some tens of the Debye lengths. Such regions have been called electric double layers. An electric double layer is the simplest space charge distribution that gives a potential drop in the layer and a vanishing electric field on each side of the layer. In the laboratory, double layers have been studied for half a century, but their importance in cosmic plasmas has not been generally recognized.".

Debye length in a plasma

In SI units, it is

where

λ_D is the Debye length,

ε₀ is the permittivity of free space,

k is Boltzmann's constant,

T_e and T_i are the temperatures of the electrons and ions, respectively,

n_e is the density of electrons,

q_e is the charge on an electron,

Z is the ionization state of the ions,

The ion term is often dropped, giving

although this is only valid when the electrons are much colder than the ions.

Debye length in an Electrolyte

In an electrolyte, the Debye length is given by

.

Reference

Equation for Debye length copied from Goldston & Rutherford's Introduction to Plasma Physics, Institute of Physics Publishing, Philadelphia: 1997, p. 15)

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