Expansion of hydrogen arcs driven by oscillating currents

Calculations of the arc channel radius using the arc current as the independent variable are presented and discussed. Previously reported experimental results for the expansion of ~300-A to ~3000-A discharges in 460-torr hydrogen are compared with the theoretical radius calculations presented. Errors introduced in the calculated channel radius are investigated by first assuming the channel conductivity to vary according to the Spitzer conductivity, and then assuming the channel conductivity to be constant and comparing the numerical results of these two methods with the experimentally measured values of channel radius. It is shown that according to Hugoniot adiabatics, the apparent relationship between the arc channel pressure and the directed energy of the shock front is given by the pressure-velocity relationship of the gas leaving the shock front instead of the more commonly used pressure-velocity relationship for the gas entering the shock front