Four Fundamental Relations in Plasma Flows

Investigations on electron temperatures and potentials in steady or unsteady dilute plasma flows are reported. The analysis is based on the detailed fluid model for electrons due to their high mobility. Ionization and normalized electron number density gradients are neglected. The transport properties are assumed as local constants. With these treatments, the partial differential equation for electron temperature significantly degenerates for both quasi-steady or unsteady plasma flows. Along an electron streamline, fundamental correlations for electron temperature and plasma potential are obtained. These formulas offer significant insights, 1). for steady flow, the electron temperature and plasma potential distributions along an electron streamline include two exponential functions, and the one for plasma potential includes an extra linear distribution function; 2). for unsteady flows, both the temporal and spatial parts include exponential functions. Oscillations in unsteady flows may decay, amplify, or remain stable. Joule heating effect is included in the analysis. Numerical simulations of dilute plasma plume flows with the hybrid methods are performed to demonstrate these behaviors in plasma flows.