DebyeLänge

DebyeLänge, often written Debye-Länge in German texts, is a characteristic length scale over which electric potentials are screened by mobile charges in a quasi-neutral medium such as a plasma or an electrolyte solution. It emerges from Debye–Hückel theory and the linearized Poisson–Boltzmann equation and describes how a test charge’s field is cancelled by surrounding ions.

The general expression in SI units is λ_D = sqrt(ε k_B T / (Σ_i n_i z_i^2 e^2)), where ε = ε_r ε_0 is the permittivity of the medium, k_B is Boltzmann’s constant, T is temperature, e is the elementary charge, and n_i and z_i are the number density and valence of ionic species. In a one-component plasma this reduces to λ_D = sqrt(ε k_B T / (n e^2)). In electrolytes, using molar concentrations c_i and ionic strength I = 1/2 Σ_i c_i z_i^2, one often writes λ_D = sqrt(ε k_B T / (2 N_A e^2 I)), with N_A Avogadro’s number.

Physically, the Debye length sets the scale for exponential screening of potentials: φ(r) ∝ exp(-r/λ_D)/r in a screened medium. λ_D grows with temperature and decreases with higher charge-carrier density or ionic strength; it also depends on the medium’s dielectric constant.

Limitations: The concept relies on weak potentials and classical statistics (Debye–Hückel theory) and is most accurate for dilute plasmas and moderately concentrated electrolytes. In strongly coupled or highly concentrated regimes, more advanced models are required.