Numerical solutions of sheath structures in front of an electron-emitting electrode immersed in a low-density plasma

The exact theoretical expressions involved in the formation of sheath in front of an electron emitting electrode immersed in a low-density plasma have been derived. The potential profile in the sheath region has been calculated for subcritical, critical, and supercritical emissions. The potential profiles of critical and supercritical emissions reveals that we must take into account a small, instead of zero, electric field at the sheath edge to satisfy the boundary conditions used to integrate the Poisson's equation. The I-V curves for critical emission shows that only high values of plasma-electron to emitted-electron temperature ratio can meet the floating potential of the emissive electrode. A one-dimensional fluid like model is assumed for ions, while the electron species are treated as kinetic. The distribution of emitted-electron from the electrode is assumed to be half Maxwellian. The plasma-electron enters the sheath region at sheath edge with half Maxwellian velocity distribution, while the reflected ones have cut-off velocity distribution due to the absorption of super thermal electrons by the electrode. The effect of varying emitted-electron current on the sheath structure has been studied with the help of a parameter G (the ratio of emitted-electron to plasma-electron densities)