Paschen's Curve

Plate 80 speaks for itself: “There's an easiest way for air to break.”

The Physics

The voltage to spark across a gap depends on the product of pressure and gap. Too little gas and electrons make too few collisions; too much and they cannot gain enough energy. In between is a minimum.

V_b = B pd / (ln(A pd) − C)

• V_b: breakdown voltage, V
• p: pressure, Pa (quoted in Torr)
• d: gap, m (quoted in cm)
• A, B: gas constants
• C: ln(1 + 1/γ), dimensionless
• γ: secondary electron emission coefficient, dimensionless

C = ln(1 + 1/γ); γ: secondary emission. Air (tabulated): ≈ 327 V at pd ≈ 0.57 Torr·cm.

Honest caveat: The minimum depends on electrode material and conditions; 327 V is a typical tabulated value for air.

Sources

• F. Paschen, Ann. Phys. 273, 69 (1889).
• Y. P. Raizer, Gas Discharge Physics (1991).

On the poster

Plate 080, “Paschen's Curve”: the pixel-art plate with its slogan “There's an easiest way for air to break.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.