The plasma channel is a Verlet-integrated rope of points anchored to the two electrode tips. Its unstretched (rest) length is set slightly longer than the electrode gap — ionized gas can always occupy more path than the straight-line distance — so when an upward buoyant force is applied to every point along the rope (hot, low-density plasma rises through the surrounding gas, fastest in light gases like helium), the inextensible rope has nowhere to go but to bow: the classic "upside-down catenary" problem, solved here the same way cloth and rope solvers do it, by alternating force integration with distance-constraint relaxation.
Arc voltage follows the classic Ayrton arc equation, which captures the two real, competing trends of a free-burning arc — voltage falls as current rises (more ionization lowers the plasma's resistance) but rises with arc length (more gas column to sustain):
V = A + B/I + (C + D/I)·L
R = V/I, P = V·I
L is the actual curved length of the rope, not the electrode gap — so raising the buoyant-lift slider elongates the arc, which feeds back into a higher voltage, exactly as it does on a real welding or switchgear arc subject to "arc blow". The constants (A,B,C,D) are representative order-of-magnitude values for a free-burning gas arc, not a measured spec sheet for one specific electrode pair; the functional form and the qualitative trends are the real physics being modelled. Core temperature is estimated from power density (P/L) against a light-gas baseline — illustrative, but scaled to the right order of magnitude for a free-burning arc (several thousand kelvin at the core).
- Current — drives Joule heating (hence buoyancy strength) and lowers resistance via the 1/I terms.
- Electrode gap — sets the rope's anchor separation and its rest length.
- Buoyant lift — the vertical force per rope point; helium's low density makes convective lift on a hot column stronger than in air, which is why a helium arc bows and elongates faster than an equivalent arc in air.