Particle and energy balance in low-density plasma discharges

For nearly-collisionless, unmagnetized plasma discharges, it is shown that electron particle and energy balance can be found from a model that includes 1) the energy distribution of the newborn electrons, 2) the rate of heating of confined electrons by collisions with more energetic electrons, and 3) the rate at which confined electrons are lost over the confining potential barrier. The ion flux density at the wall is reduced by charge-exchange collisions, thus these ion collisions must be included in particle balance. The model is applied to a simple, low-density, hot-filament discharges such as those in the double plasma device. The plasma density, electron temperature, and confining potential are shown to have approximately the values given by the model.