Collector and source sheaths of a finite ion temperature plasma

Abstract

The region between a Maxwellian plasma source and an absorbing surface is described theoretically with a static, kinetic plasma–sheath model and modeled numerically with a dynamic, electrostatic particle simulation. In the kinetic theory, Poisson’s equation and Vlasov equations govern the non-Maxwellian velocity distribution of the ions and electrons. The results in this paper for collector potential and plasma transport agree with the bounded model of Emmert et al. [Phys. Fluids 23, 803 (1980)]. However, this approach differs from those using traditional Bohm sheath analysis by ±0.25 (in units of electron temperature) for potential drop through the collector sheath of a hydrogen plasma. In both the theory and simulation, the plasma source injects equal fluxes of ions and electrons with half-Maxwellian velocities and various mass and temperature ratios and is assumed to have a zero electric field. The potential change within a spatially distributed, full Maxwellian source region is represented with the source sheath potential drop that depends primarily on temperature ratio. This source sheath evolves over a few Debye lengths from the source to neutralize the injected plasma. The plasma flows to an electrically floating collector where the more familiar electron-repelling collector sheath appears. The collector potential ψC and source sheath potential drop ψP (in units of electron temperature) are evaluated as a function of mass and temperature ratio. The velocity moments of density, drift velocity, temperature, kinetic energy flux, and heat flux are also derived as a function of ψC and ψP. Comparisons with electrostatic particle simulations are shown for the ion/electron mass ratios of 40 and 100 and temperature ratios of 0.1, 1, and 10. For a deuterium–tritium plasma (single-ion species with a mass of 2.5 amu) with equal ion and electron temperatures, then, ψC=−3.3 and ψP=−0.3. At the collector, the ions dominate the kinetic energy flux whereas the electrons dominate the heat flux. Ions reach the Bohm minimum energy well within the source sheath, obviating the need for a presheath acceleration.