Comprehensive kinetic theory of an electron emitting electrode in a low-density isotropic plasma

Abstract

The kinetic theory of an electron emitting electrode immersed in a low-density isotropic plasma is developed for the first time to include the theory of formation of a virtual cathode in this scenario. In addition to virtual cathode solution for supercritical emission, the potential profile solution for subcritical and critical emission is also included. The plasma-electron and emitted-electron are assumed to have half Maxwellian velocity distributions at the sheath entrance and electrode surface, respectively, while the plasma ions are assumed to be cold. Poisson's equation is then solved numerically for charge densities in the assumed negative sheath structure. The resulting potential profiles in the sheath for the floating and current carrying electrode/wall are calculated numerically. These potential profiles show a smooth transition from subcritical to critical and to supercritical emissions with increasing emitted-electron temperature Te,em (decreasing parameter α = Te,pl/Te,em, plasma-electron to emitted-electron temperature ratio). The numerical solution of potential profiles for supercritical emission confirms the formation of a virtual cathode. The structure of the virtual cathode is dependent on the chosen boundary values. These results also show that the virtual cathode potential profile structure exists around α < 5 to α = 1.5 but the solution at α = 1 does not exist in this scenario. It indicates that the present model is applicable only to the situation where the sheath potential is negative relative to plasma potential.