The potential difference between a floating emitting surface and the plasma surrounding it has been described by several sheath models, including the space-charge-limited sheath, the electron sheath with high emission current, and the inverse sheath produced by charge-exchange ion trapping. Our measurements reveal that each of these models has its own regime of validity. We determine the potential of an emissive filament relative to the plasma potential, emphasizing variations in emitted current density and neutral particle density. The potential of a filament in a diffuse plasma is first shown to vanish, consistent with the electron sheath model and increasing electron emission. In a denser plasma with ample neutral pressure, the floating filament potential is positive, as predicted by a derived ion trapping condition. Lastly, the filament floated negatively in a third plasma, where flowing ions and electrons and nonnegligible electric fields may have disrupted ion trapping. Depending on the regime chosen, emitting surfaces can float positively or negatively with respect to the plasma potential.
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