Effect of wall secondary electron distribution function on the characteristics of stable sheath near a dielectric wall

Abstract

It is widely known that the energy distribution of secondary electrons induced by a single-energy electron beam presents typical bimodal configuration. However, the total velocity distribution of secondary electrons induced by a Maxwellian plasma electron group has not been revealed clearly, due to the lack of detailed theoretical calculation and calculation and experiment result. Therefore, researchers usually function satisfies single-energy distribution ( 0), half-Maxwellian distribution and so on, in order to study the characteristics of stable fluid sheath near a dielectric wall. For this reason, using the Monte Carlo method to simulate the wall secondary electron emission events based on a detailed probabilistic model of secondary electron emission induced by single-energy incident electron beam, we found that, when the incident electron follows an isotropic Maxwellian distribution, the total perpendicular-to-wall velocity distribution of the secondary electrons emitted from dielectric wall follows a three-temperature Maxwellian distribution. In the simulation, the incident angle of the plasma electrons and the emergence angle of the secondary electrons are considered, so the Monte Carlo method can discriminate whether the secondary electron velocity is perpendicular to or parallel to the wall surface. Then, a one-dimensional stable fluid sheath model is established under the wall boundary condition that the secondary electrons obey the three-temperature Maxwellian distribution; and some contrastive studies are made in order to reveal the effect of wall total secondary electron distribution functions such as single-energy distribution, half-Maxwellian distribution, and three-temperature Maxwellian distribution with the sheath characteristics. It is found that the total secondary electron distribution function can significantly influence the ion energy at the sheath interface, the wall surface potential, the potential and electron/ion-density distributions, and so on. Both the ion energy at sheath interface and the wall surface potential increase monotonously with the increase of wall total secondary electron emission coefficient. But the values of three-temperature Maxwellian distribution differ much from that of half-Maxwellian distribution and single-energy distribution. When the total secondary electron follows a three-temperature Maxwellian distribution, the critical space charge saturated sheath has no solution, indicating that with the increase of the wall total secondary electron emission coefficient, the sheath will directly transit from the classic sheath structure to the anti-sheath one. In the future work, a kinetic, static sheath model will be developed in order to study the characteristics of anti-sheath and space charge saturated sheath near a dielectric wall