Constant DC supply and 3 phase AC (in mercury rectifier) can produce a continuous arc. But can single phase AC also produce a continuous arc? Because it is written on the web that arc extinguishes at zero crossing. Also high voltage is needed to initiate arc. But what is needed to maintain the arc (high voltage or high current)?
tl; dr version: With AC the arc current does drop to zero, but the plasma hangs around, so the visual arcing effect is continuous even if the arc current is not.
When the arc fires up it makes a plasma cloud - a region of ionized gases with lower resistance than air. This plasma persists for a time even during the AC zero-cross interval, allowing the arc jump once more at a lower strike voltage than it would in normal air. So the zero-current time is lessened in the presence of plasma for a given gap - so much so that your eye can hardly see it.
This plasma is why a ‘Jacob’s Ladder’ can work with ever-widening electrodes, even on single-phase AC: the heated plasma travels upward, making a lowest-impedance path for the arc to strike.
Here's a slow-motion video showing an AC-arc Jacob's ladder which clearly shows the arc extinguishing and relighting between cycles. Notice that the arc alternates sides as it re-strikes, while following the rising plasma cloud. https://www.youtube.com/watch?v=4zxGK0hoqIc
The mercury-vapor lamp uses a plasma arc to generate light, and they're almost always powered by single-phase AC. The lamp's arc absolutely fluctuates, but like the Jacob's ladder this isn't visible due to the human eye persistence of vision, plus the glowing of the still-excited plasma, and not the least of which the lowered strike voltage of the activated plasma. So we don't see flickering on this kind of lamp either, though its variation is measureable.
Unrectified 3-phase AC arcing behavior is the same as single-phase. Each phase has single-phase AC potential to neutral, ground, or either of two phases. So arcs phase-to-phase or phase-to-ground (or neutral, if used) will also have intervals of zero-current and cross-plasma re-strike. Likewise, so would a discharge lamp powered by two legs of a 3-phase feed.
When an electric arc first starts it ionized the air and reduces the resistance of the air. This causes the arc to be maintained easier. The arc will usually last until the metal causing the arc burns away or the electricity source is turned off. The sine wave crossing the zero axis will not extinguish the arc. Voltage is what is required to establish and maintain the arc. Current will exist but it's the difference in potential that causes the arc.