Potential of an emissive cylindrical probe in plasma

The floating potential of an emissive cylindrical probe in a plasma is calculated for an arbitrary ratio of Debye length to probe radius and for an arbitrary ion composition. In their motion to the probe the ions are assumed to be collisionless. For a small Debye length, a two-scale analysis for the quasineutral plasma and for the sheath provides analytical expressions for the emitted and collected currents and for the potential as functions of a generalized mass ratio. For a Debye length that is not small, it is demonstrated that, as the Debye length becomes larger, the probe potential approaches the plasma potential and that the ion density near the probe is not smaller but rather is larger than it is in the plasma bulk.