Structure of collisional and collisionless sheaths: closed expressions for sheath thickness

Abstract

Precise closed expressions for the sheath thickness are derived on the basis of numerical solutions for a fluid model description of the plasma boundary region, both in the collisional and collisionless limits. The ‘sheath edge’ is defined as the edge of the space in which the electron-free ion-sheath solution is defined, while the ‘plasma edge’ is defined as the edge of the space in which a quasi-neutral plasma solution is defined. For a collisional sheath in the constant collision-frequency model, the plasma edge and the sheath edge thus defined coincide. For a collisional sheath in the constant mean-free-path model and for a collisionless sheath, the two points are different, and an accurate value of the separation distance between the two points is determined. The field strength at the sheath edge is of order kTe/eλDs regardless of collisionality, where Te is the electron temperature and λDs the local Debye length at the sheath edge.