Theory of negative differential conductivity of electrons caused by electron–electron scattering in low-temperature plasma

Abstract

A simplified quantitative analysis of the mechanism of negative differential conductivity (NDC) of electrons in low-temperature plasma due to electron–electron scattering (EES) is presented for the first time. On the basis of an analytical treatment of the Boltzmann equation, it is shown that with the constraint νε≪νee≪νm the necessary condition for displaying of the N- and S-type NDC induced by EES can be written as ν̂mU=δ̂U>0.5 and <−0.5, respectively, where νε=νε(U), νee=νee(U), and νm=νm(U) are the total electron energy exchange, effective electron–electron, and momentum transfer collision frequencies, respectively [U is the electron mean energy, δ=(E/N)/W, where E/N is the reduced electric field (E=E(U) is the intensity of the electric field, N is the gas number density), W=W(U) is the drift velocity of electrons, and ŷx=d ln y/d ln x]. Simple analytical criteria for prediction of the EES induced NDC are obtained. It is shown that the EES induced NDC may be responsible for triggering of a broad category of spatial and temporal instabilities taking place in various gases and gas mixtures in glow-discharge plasma. The validity of the proposed theory is confirmed by comparison with numerous experimental and numerical works of other authors.