Townsend avalanche, streamer formation, and the Paschen curve
Townsend's first ionization coefficient α = A·p·exp(−B·p/E) gives the number of ion pairs created per cm. Avalanche multiplication M = e^{αd}. The Paschen curve V_break(p·d) shows a minimum (Paschen minimum) at optimal pd because too few or too many collisions both impede breakdown. Above Meek's criterion (α·d ≈ 18–20), space charge creates a streamer that short-circuits the gap.