Theory and simulations of cylindrical plasma sheaths

Many probe measurements rely on the understanding of plasma sheath that forms around a plasma-immersed material. However, probes typically establish a plasma sheath in cylindrical and spherical coordinates. For cylindrical and spherical sheaths, two types of theories are used in the plasma physics community: thin sheath and thick sheath. While the thin sheath approximation considers a 1D sheath in which the Bohm condition is derived, one of the most common approaches for thick sheaths is the orbital motion limited (OML) theory. In particular, the ion saturation current requires the understanding of the Bohm condition, in which the minimum ion bulk velocity into the sheath edge is the ion acoustic speed for a 1D planar sheath. In this study, we derive the Bohm condition for cylindrical and spherical plasma sheaths. A 1D cylindrical particle-in-cell simulation is used to verify and assess the cylindrical plasma sheath theory.