Expression for momentum-transfer scattering in inelastic collisions in electron transport in a collisional plasma

An expression for the inelastic momentum-transfer scattering on the collision integral of the Boltzmann equation is derived in order to reflect the effect of an inelastic collision of an electron with a molecule on the electron kinetics in gases and collisional plasmas. To our knowledge, this is the first attempt to formulate the explicit effect of the momentum-transfer scattering of an inelastic collision. The present procedure is a traditional one in which the Boltzmann equation of electrons is expanded in spherical-harmonics in velocity space. It is shown that the effect of the inelastic momentum-transfer on the electron transport is expressed only when we consider the first anisotropic part of the velocity distribution in the expanded Boltzmann equation. In addition, case studies are performed by considering the dependence of the scattering angle and the magnitude distribution.