🧪 Plasma Lightning Sphere: Dielectric Breakdown Model (2D)

This 2D companion swaps the 3D version's orbiting glass sphere for the physics that actually drives it: the central electrode and grounded shell form a coaxial capacitor, so the radial field falls off exactly as 1/r rather than the 1/r² of a free point charge, and a breakdown-radius readout compares that field against real ionization thresholds — roughly 3 MV/m for sea-level air, about two orders of magnitude lower for the low-pressure noble gas that actually fills a plasma globe. The branch pattern itself comes from a documented Dielectric Breakdown Model (Niemeyer–Pietronero–Wiesmann): every growth tick relaxes Laplace's equation on a grid and extends the discharge into an empty neighboring cell with probability proportional to the local potential gradient raised to a tunable exponent η, which is exactly what produces the fractal, Lichtenberg-figure branching instead of a scripted zigzag. Press and hold on the glass to ground a touch point — the grid's boundary condition dips there, steepens the local gradient, and the growth probabilities visibly pull the spark toward your finger, matching how a real plasma globe behaves.