Debye length

Debye radius

The distance of the action of the electric field of a single electric charge in a neutral medium consisting of positively and negatively charged particles (a plasma, electrolytes). Outside the sphere of radius equal to the Debye length, the field is shielded as a result of the polarization of the surrounding medium.

The Debye length is defined by the formula:

$$d=\left(\sum_j\frac{4\pi e_j^2N_j}{kT_j}\right)^{-1/2},$$

where $e_j,N_j,T_j$ are, respectively, the electric charge, the number density and the temperature of the particles of kind $j$, and $k$ is the Boltzmann constant. The summation is carried out over all kinds of particles, the neutrality condition $\sum_je_jN_j=0$ being satisfied. An important parameter of the medium is the number of particles in the sphere of radius equal to the Debye length:

$$n_D=\frac{4\pi}{3}d^3\sum_jN_j;$$

it describes the ratio between the average kinetic energy of the particles and the average energy of their Coulomb-type interaction:

$$n_D\sim\left(\frac{E_\mathrm{kin}}{E_\mathrm{coul}}\right)^{3/2}.$$

This number is small, typically $n_D\sim10^{-4}$, for electrolytes, and is large for a plasma in all kinds of physical states. As a result, methods of the kinetic theory may be employed to describe the plasma. The concept of the Debye length was introduced by P. Debye in connection with his studies on electrolytic phenomena.

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