The final geometry of the arc column in quartz‑sand current‑limiting fuses is a key determinant of interruption voltage and energy dissipation. Although the arc typically evolves into a characteristic spindle‑shaped structure before extinction, the underlying interactions among arc pressure, effective arc conductivity, and the resulting final morphology have not been sufficiently clarified. This study investigates these interdependent mechanisms based on a combined analysis of thermal, electrical, and pressure‑driven behaviors occurring during fuse interruption. The work examines how rapid pressure rise in the confined sand‑filled cavity alters electron–neutral collision rates, thereby reducing the effective arc conductivity and enhancing radial arc constriction. The pressure‑induced gas acceleration is also shown to contribute to axial arc elongation, promoting the formation of the final spindle‑shaped plasma column with a thick central region and strongly contracted electrode zones. In turn, the reduced cross‑section and conductivity intensify the electric field required to sustain the arc, leading to a sharp increase in arc voltage prior to extinction. The study further analyzes how these coupled effects collectively determine the ultimate arc radius profile, the maximum stable arc length, and the corresponding equivalent electrical characteristics. The results demonstrate that the final arc geometry is not governed by a single dominant factor but emerges from a strong mutual dependence between pressure‑driven plasma compression and the temperature‑ and pressure‑sensitive effective conductivity. The findings provide a clearer physical understanding of how these mechanisms shape the ultimate arc form, offering valuable insights for optimizing the design and interruption behavior of sand‑filled current‑limiting fuses.
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