Diffusion-free charge relaxation in a conducting medium

The commonly used two-term relaxation equation can lead to inconsistencies, which researchers have sought to resolve by introducing diffusion and scattering-time effects. It is shown here that the complete equation ∂n^~/∂t + σ/ε n^~+ E^→ċ grad^→(nµ) = 0 is sufficient to account for charge flow, propagation effects and surface-charge induction, as well as instabilities in negative-differential-conductivity materials.