Comprehensive kinetic theory of inverse sheath for a strong electron-emitting electrode in a low-pressure isotropic plasma

The basic kinetic theory of an electron emitting inverse sheath was presented in T Gyergyek, J Kovacic, I Gomez, J P Gunn, S Costea and M Mozetic (2020 Phys. of Plasmas 27, 023 520). Here we extend this theory to find the potential profile and kinetic energy flux in inverse sheath for floating and current carrying electron emitting electrode/wall. The values of emitted-electron temperature, number and current densities are explored for the existence and nonexistence of inverse sheath for floating and current carrying electrode/wall. For this we consider half Maxwellian velocity distribution functions of species (emitted-electron, plasma-electron and ions) at their respective emerging boundaries. The species charge densities are calculated self-consistently from the prior assumed positive sheath structure. The Poisson's equation is then solved numerically for floating and current carrying electrode/wall with varying normalized emitted-electron and ion temperatures. The resulting inverse sheath solution is valid for limited range of emitted-electron and ion temperatures in case of floating electrode/wall. The kinetic energy flux relations for each species are derived in inverse sheath. The numerical solutions of these relations for floating and current carrying electrode/wall are presented for valid range of parameters. These solutions shows that the total or kinetic flux received by floating electrode/wall surface decreases with increasing of emitted-electron temperature and even approaches to zero for equal values of emitted-electron and plasma-electron temperatures.

Automated summary

This study extends the basic kinetic theory of an electron emitting inverse sheath to floating and current carrying electrode/wall scenarios, exploring the potential profile and kinetic energy flux. By considering velocity distribution functions and solving the Poisson's equation numerically, the relationship between emitted-electron and ion temperatures is investigated, leading to a valid inverse sheath solution for specific temperature ranges. The numerical solutions show a decrease in total or kinetic flux received by the electrode/wall surface with increasing emitted-electron temperature, approaching zero for equal values of emitted-electron and plasma-electron temperatures.