The double sheath associated with electron emission into a plasma containing negative ions

The double sheath formed by thermal electrons and negative ions in a plasma and electrons emitted from an electrode is investigated. The ion energy at the sheath edge and the electric field at the electrode surface are calculated for several values of the ratio of negative-ion density to electron density. The maximum beam density above which a virtual cathode appears is given. The relation to the Langmuir limit is shown. The numerical results for the electric potential, the electric field and the space charge density are presented. The floating potential is calculated from the current balance of all components.