Is the Sheath Potential Positive or Negative at Strongly Emitting Surfaces?

In the recent literature, two distinct sheath solutions under strong electron emission have been reported in theoretical models, simulations, and in experiments [1], a “space-charge limited” (SCL) sheath and an “inverse” sheath. It is important to determine which sheath occurs under what conditions because they lead to sharply different particle and energy fluxes. Our current study [2] offers a unifying analysis of the strong emission problem, addressing both the presheath and sheath. We confirm from first principles that two equilibria, one with SCL sheaths and Bohm presheaths, and one with inverted sheaths/presheaths, are indeed possible whenever the emission coefficient exceeds unity, regardless of the plasma’s upstream properties (e.g., N and Te). However, we also show [3] that if cold ions are born in the potential dip of a SCL sheath, the accumulating ion space charge forces a transition to an inverse sheath. This explains why stable SCL sheaths were only observed in simulation studies without collisions in the plasma domain [4]. Assuming some ionization or CX collisions are always present in real sheaths, we predict only a monotonic inverse sheath should exist at any surface under strong emission conditions, whether a divertor plate, emissive probe, dust grain, Hall thruster channel wall, or sunlit object in space. Our new 1D simulations [2] illustrate that SCL and inverse equilibria have major differences of ion flow velocities and density gradients over presheath length scales. This will enable future experimental studies to identify the sheath state without having to probe inside the sheath itself.