RESONATICA
Safety

Spark gap: breakdown voltage in air

At what voltage does the spark jump? The tool calculates the breakdown voltage between flat electrodes in air by Paschen's law and compares it with the rule of thumb of 3 kV per millimetre.

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Abbreviations and symbols on this page (5)
Paschen's law
Breakdown voltage of a gas between flat electrodes as a function of pressure × distance: U = B p d ÷ (ln(A p d) − ln(ln(1 + 1/γ))).
p · d
Product of gas pressure and electrode gap, here in mbar·cm; in Paschen's law it determines the breakdown voltage.
γ
Secondary electron emission coefficient of the electrode (second Townsend coefficient); here 0.01 as in the source for stainless steel electrodes.
mbar
Millibar, pressure: air at sea level about 1013 mbar, at 1000 m altitude about 900 mbar.
kV
Kilovolt = 1000 volts.
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mm
mbar
kV
Breakdown (Paschen)5.059 kV
Rule of thumb 3 kV/mm2.999 kV
p · d101.3 mbar·cm
Paschen minimum312 V · 1.14 mbar·cm
Breaks down at 6 kV?yes
+−1 mm
Spark as soon as the applied voltage reaches the breakdown voltage.
0.11101001,00010,000100 V1 kV10 kV100 kV1 MVp · d (mbar·cm)
Paschen curve for air (log-log); orange: your gap and pressure.

Formula

Paschen: U = B p d ÷ (ln(A p d) − ln(ln(1 + 1/γ))) with A = 11 /(mbar·cm), B = 274 V/(mbar·cm), γ = 0.01 (air, stainless steel electrodes). Minimum at p d = e · ln(1 + 1/γ) ÷ A. Rule of thumb: about 3 kV/mm at 1 bar, proportional to pressure.

Example

1 mm at 1013 mbar: Paschen about 5.1 kV, rule of thumb 3 kV. 10 mm: Paschen about 36 kV, rule of thumb 30 kV. Minimum of the Paschen curve about 312 V at 1.14 mbar·cm.

Notes

  • Paschen's law applies to a uniform field between flat electrodes. Points and edges fire considerably earlier; spheres with a large radius are close to the value.
  • Humidity, temperature, contamination and electrode material shift the voltage; use it as a planning value with margin.
  • For Tesla coils and protective spark gaps, set and check the gap on the device, do not just calculate it.
  • Sparks produce ozone, UV light and radio interference; high voltage is life-threatening.