# Minimum Voltage to Sustain an Arc

I've read that after a plasma channel is created in air, the resistance decreases significantly and the arc can be sustained with a much lower voltage, as long as the heat dissipated by the plasma is enough to sustain the plasma. I've been trying to calculate the minimum voltage required (if one exists) to sustain an arc with a given separation distance, air pressure, etc, assuming that the current depends only on the resistance of the plasma.

I have tried setting the rate of heat loss from the plasma into the surroundings (from Newton's law of cooling) equal to the power as given by Ohm's law (using Spitzer resistivity), but the unknown proportionality constant in the former means I cannot solve for any real numbers.

Am I approaching this completely wrong? What am I missing?

Thank you!

• Hence they blow out arcs when opening high voltage switches. See for example. circuitglobe.com/air-blast-circuit-breaker.html . Not really an answer but there some fun youtube videos around. – Hilmar Apr 5 at 19:01
• this is hard, because arcs exhibit negative resistance: pumping more current through the arc increases the size of the conductive channel and thereby decreases the resistance of the channel. – niels nielsen Apr 5 at 19:59
• The resistance of an arc is nearly zero. Plasmas are extremely conductive. The only current that matters there is the maximum current that the power supply can give. – Sartem Cacartem Jun 26 at 2:03