  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.
