Theory of the non-stationary arc column

Abstract

The equations that describe the behaviour of a time-unsteady plasma column have been simplified by neglecting energy transfer by radiation and convection. Furthermore, the thermal diffusivity of the plasma was assumed to be constant and a simplified expression for the electrical conductivity was adopted. Thus the energy equation was cast into a universal form, requiring the specification of only two parameters to obtain solutions. Although some approximate closed form solutions were obtained it was necessary to solve the general a.c. arc problem on a digital computer. In view of the good agreement between the theoretically derived voltage waveforms and those found from a specially designed a.c. cascade it is concluded that the behaviour of the low current a.c. arc can be described by the solution of a complicated heat conduction problem. These solutions have the advantage over older theories that they can be directly related to measurable or calculable quantities that characterize a particular gas.