Debye length - Definition and Overview

The Debye length is the scale over which mobile charge carriers screen out electric fields in plasmas and other conductors.

Debye length in a plasma

In SI units, it is

<math> \lambda_D = \sqrt{\frac{\epsilon_0 k T_e T_i}{n_e q_e^2 (T_i + Z T_e)}} <math>

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

<math> \lambda_D = \sqrt{\frac{\epsilon_0 k T_e}{n_e q_e^2}}<math>

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

<math> \lambda_D = \sqrt{\frac{\epsilon_0 \epsilon_r k T}{2 N_A e^2 I}} <math>.

Reference

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