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 λD is the Debye length, ε0 is the permittivity of free space, k is Boltzmann's constant, Te and Ti are the temperatures of the electrons and ions, respectively, ne is the density of electrons, qe 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)

 

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