Theory for formation of a low-pressure, current-free double layer

A diffusion-controlled theory is developed for the formation of a low-pressure, current-free double layer just inside an upstream insulating source chamber connected to a larger diameter, downstream chamber. The double layer is described using four groups of charged particles: thermal ions, monoenergetic accelerated ions flowing downstream, accelerated electrons flowing upstream, and thermal electrons. The condition of particle balance upstream is found to determine the double layer potential. The double layer disappears at very low pressures due to loss of ionization balance upstream and due to energy relaxation processes for ionizing electrons at higher pressures, in good agreement with experiments.