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

A theory is developed for the formation of a low pressure, current-free double layer just inside an upstream dielectric source chamber connected to a larger diameter, downstream metallic expansion chamber. The double layer is described using four groups of charged particle: thermal ions, mono-energetic accelerated ions flowing downstream, accelerated electrons flowing upstream and thermal electrons. The accelerated electrons are formed downstream from an initially nearly half-Maxwellian electron distribution. A fifth group of counter-streaming electrons formed by the reflection of the accelerated electrons from the sheath at the insulated end wall of the source chamber is used to enforce the condition that the double layer be current-free. The condition of particle balance upstream is found to determine the double layer potential. The double layer is found to disappear at very low pressures due to loss of ionization balance upstream and due to energy relaxation processes for ionizing electrons at higher pressures. The theory is found to be in good agreement with the experiments.