Summary form only given. Atmospheric pressure plasma arcs are used extensively in material processing applications such as welding and metallurgy. An experimental arc furnace operating in air with graphite cathode and steel anode at 100-250 A exhibits large (/spl sim/10% rms) voltage and current fluctuations for certain cathode geometries, with the arc assuming a rotating helical shape persistent for many cycles. The instability occurs for cathode tip diameters of 1.5 to 3 times the cathode spot diameter, with the amplitude strongly dependent on current. A model for the instability is developed in which ordered cathode spot motion and the cathode jet give rise to the observed arc shape. Previous experiments on arc dynamics in applied AC magnetic field are used as a diagnostic for jet velocity. The model gives a good description of arc shape for low amplitudes. Possible mechanisms for spot motion on the cathode and its dependence on geometry will be proposed. Cathode shape is seen as an important means of controlling arc stability and broadening effective arc volume.