Interfacial Potential Barrier Induced Constriction and Stepwise Transition of a Dynamic Arc Root

The current transition from metal to plasma (or vice versa) shows constriction of current density at arc root spot rather than uniform distribution. Possible causes for this phenomenon are the interfacial potential barrier which limits the marginal charge emission, and the effect of magnetic pinch. Experiment shows that the current density at arc root spot can be as high as 10
⁸
A/m
²
, which is orders of magnitude larger than that in arc column. Besides, the stepwise motion of the arc root along the electrode surface has also been observed. The mechanism of stepwise transition probably arises from the negative differential resistance across the sheath. For instance, the measured arc voltage for self-sustained discharge has a negative correction with the discharge current. This "volt-ampere characteristics" can help to deduce the relation between voltage drop (potential gap) and current density across the sheath. Thus, we propose a three-stage relation between current density and voltage drop across the sheath, corresponding to three types of electron emission: photo emission, field-dominant emission and the thermionic-field emission. In this work, an interfacial potential barrier as a function of local current density, derived from thermionic-field emission theory, is proposed to interpret the phenomenon of arc-electrode interaction, and its application on the simulation of arc dynamics inside a Jacob's ladder well matches the experimental observation. This concept can be extended to solve the electrohydrodynamics of ion drive and applied in a broad range of engineering applications, from circuit breakers design at fault current to ion injector for plasma coating.