SIMPLE THEORY OF FREE-BURNING ARCS

Analytic expressions are derived to give approximate properties of free-burning arcs such as occur in switch-gear, arc welding and electric arc furnaces. Expressions are given for the arc voltage electric field, arc radius and plasma velocity in terms of the arc length, current, gas pressure and temperature. The energy balance equation relates arc temperature with current. The expressions involve the material functions of the arc plasma, so that predictions can be made for any arc medium whose material functions are known. Properties of free-burning arcs for low currents, for example, less than 30 A for air, are controlled by natural convection, it being assumed that the arc is vertical. At higher currents properties become controlled by convection induced by the self-magnetic field of the arc. Although gross simplifications are made, predictions for arcs in air for currents ranging from 1 to 20000 A are in fair agreement with experiment for a position 1 cm from the lower electrode.