Stepped Leader Growth: Dielectric Breakdown Model

Discharge Parameters

Branching exponent η 2.5

Cloud field strength 1.0

Step interval (μs) 35

Grounded structure position 0.0

Controls

Live Readouts

Leader initiating…

Elapsed time

0 μs

Avg. descent speed

0 ×10⁵ m/s

Active branch tips

Steps taken

How it works

A negative stepped leader descends from a thundercloud in discrete jumps, not a continuous arc. Each ~10–50 m step ionizes in about a microsecond, then the channel pauses for roughly 20–50 μs before the next step — the characteristic "stepping" seen in high-speed lightning photography.

This simulation grows the channel with a dielectric breakdown model (Niemeyer–Pietronero–Wiesmann, the standard stochastic model for both lab spark discharges and lightning branching statistics). Between the charged cloud base and the grounded surface below, an approximate potential field φ obeys Laplace's equation, and each candidate next-step site is chosen with probability proportional to the local field raised to a branching exponent η:

P(i) = E(p_i)^η / Σⱼ E(p_j)^η

E(p) ≈ E_cloud · [enhancement as p nears ground]
       + E_structure / d(p, rod)²   (attraction toward grounded objects)

η (branching exponent) — low η makes every direction nearly equally likely, producing a bushy fractal; high η forces growth almost straight down the strongest-field path.
Cloud field strength — scales the driving potential difference, changing how aggressively new branches spawn.
Step interval — the assumed real time between steps, used to convert simulated steps into the elapsed-time and descent-speed readouts (real measured stepped-leader speeds average ≈1–2.6×10⁵ m/s).
Grounded structure position — moves a tall grounded object whose own field enhancement competes to attract the nearest leader tip, illustrating why lightning preferentially strikes elevated conductors (the same physics behind lightning rods).

When a tip's field exceeds the local breakdown threshold near the ground or the structure, the downward leader connects with the upward streamer it induces — the attachment process that triggers the bright return stroke. Distances here are illustrative (1 unit ≈ 50 m), not a full numerical Laplace solve.

Leader channel Branch (deeper generation) Grounded structure

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