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Debye length

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

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

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

$\lambda_D = \sqrt{\frac{\epsilon_0 k T_e}{n_e q_e^2}}$

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

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

Reference

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

Categories: Electricity

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10-26-2009 08:16:03
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