Debye length (${\lambda }_D=\sqrt{{ϵ}_0{k}_B{T}_e/(n_e{e}^2)}$)

For mobile thermal electrons with a fixed neutralizing background, the Debye length is the characteristic distance over which plasma screening suppresses an electrostatic perturbation. Linearizing the Boltzmann density response and using Poisson's equation gives the displayed scale. Other mobile species contribute additively to ${\lambda }_D^{-2}$ through $n_s{q}_s^2/({ϵ}_0{k}_B{T}_s)$.

A sphere of radius equal to the Debye length. Its particle count defines one common normalization of the plasma parameter.

For a three-dimensional ideal degenerate electron gas, let $r=\hslash {\omega }_{\mathrm{pe}}/E_F$. If one heuristically defines a Debye length by replacing $k_{\mathrm{B}}T$ with the Fermi energy, then $k_F{\lambda }_D=\sqrt{2}/r$ and the associated electron count is the displayed expression. A count below one signals failure of the classical many-particle screening interpretation. It does not prohibit plasmons. The zero-temperature compressibility instead gives the Thomas-Fermi screening length squared $2{ϵ}_0{E}_F/(3n_e{e}^2)$.