Model for the density, temperature, and plasma potential of low-density hot-filament discharges

A theoretical model is developed for the density and temperature of confined electrons and the plasma potential in low-density hot-filament discharges. These three parameters are found from a simultaneous solution of the equations for ion particle balance, electron particle balance, and electron energy balance. In the model, electrons are lost by diffusion in velocity over the potential barrier determined by the plasma potential. The confined electrons are heated by the unconfined electrons that are the secondaries from the wall and, to a lesser extent, by the primary electrons from the filaments. The plasma parameters calculated from the model agree with parameters measured in a double plasma device that has been modified to have a clean wall that gives a single value for the confining potential.