Numerical solutions of sheath structures around a moderate negative biased electron-emitting cylindrical probe in low-density isotropic plasma

Abstract

The potential structures around a moderate negative biased electron-emitting cylindrical probe in low-density isotropic plasma are calculated in the collisionless sheath region. The formalisms, equations, and solutions for the entire electron emitting range (i.e., subcritical, critical, and supercritical) from the cylindrical emitter and collector surface are discussed. The plasma-electron and emitted-electron are assumed to have half Maxwellian velocity distributions at their respective sheath entering boundaries with cold plasma ions. Poisson's equation is solved numerically in the sheath region for the subcritical, critical, and supercritical emissions. The I-V characteristics for these three cases are presented in tabular form. The results show that we need very high emitted-electron current to solve Poisson's equation for the critical and spercritical emissions. Thus, the floating potential is far away in these scenarios. Also, the number density of emitted-and plasma-electron are comparable at the sheath edge so we cannot neglect the density of former in comparison with latter at the sheath edge.