The Application of Paschen's Law to the Re-Ignition of an Arc

An a.c. arc, in order to restrike after passing through current zero, requires a potential considerably higher than the normal burning potential. This re-ignition potential is investigated for short gaps in nitrogen, using pure graphite electrodes with spacings up to two mm and pressures up to 500 cm Hg. The re-ignition potential is found to have two characteristics. One of these characteristics is followed for the arcs in which the cathode spot is maintained by field emission, and the other is followed for the ``thermionic'' arc. Relations are obtained between this re-ignition potential and both the gas pressure and the gap spacing, with the arc current as parameter. These relations may then be combined into a single relation between the reignition potential and the product of the pressure and spacing. This gives a function that is of the same form as the Paschen law for the initial sparking potential of a gap. The constants of this function are dependent on the arc current, the gas in the space, and the constants of the circuit. That the constants of the re-ignition function are not the same as those for the sparking potential law is to be expected from the very dissimilar conditions applying in the space. Extreme purity of electrode materials and of gas, as well as extreme care in obtaining the experimental results, are essential.