Plasma Lightning Sphere: Dielectric Breakdown Model (2D)

Discharge Source

Applied voltage 10.0 kV

DBM growth exponent η 2.2

Growth grid resolution 58

Touch Point (grounding)

Press and hold on the glass in the view to ground a point with your finger — real plasma globes route the discharge toward it.

Live Readout

Elapsed time

0.0 s

Sparks completed

Field @ electrode

— MV/m

Breakdown radius

— mm

Filament tips

Touch grounding

off

How it works

The central electrode and the grounded glass shell form a coaxial capacitor, so the radial field falls off exactly as 1/r (not 1/r² — that's the point/line-charge coaxial-cylinder result, not a free point charge):

E(r) = V / (r · ln(R/r0))
R = 90 mm shell, r0 = 15 mm electrode

Air ionizes near 3 MV/m at sea level; the low-pressure noble-gas fill of a real plasma globe breaks down roughly two orders of magnitude lower (~30 kV/m), which is why a few kilovolts is enough to sustain visible filaments. The slider computes where E(r) crosses that threshold — beyond the "breakdown radius" a candidate site's growth weight is suppressed by (E/E_threshold)³.

Branch shape comes from a real Dielectric Breakdown Model (Niemeyer–Pietronero–Wiesmann, 1984): Laplace's equation ∇²φ = 0 is relaxed on a grid every growth tick (structure fixed at φ=1, shell at φ=0, and a grounded touch patch pulled to φ=−0.2), and each empty site touching the discharge grows with probability

p_i ∝ (1 − φ_i)^η

Low η (~1) gives dense, bush-like trees; high η (~4) starves side branches and produces a few needle-like leaders — exactly the fractal-dimension control real DBM literature reports. Because the touch patch locally deepens φ, sites along the path toward it see a steeper gradient (larger 1−φ_i) and are preferentially selected, so the spark visibly bends toward a grounded finger.

Discharge filament Central electrode Grounded touch point

Press & hold on the glass to ground it