PERTURBATION ANALYSIS OF AN ENERGY-BALANCE MODEL - TIME CONSTANTS OF LOW-CURRENT CASCADE ARCS IN ARGON

A time-constant formula is derived from a perturbation analysis of an equilibrium energy-balance equation of arc plasmas. The formula gives the time constant associated with changes in are quantities when the a re current is perturbed from its steady-state. The current perturbatio n is assumed to be very small and the mathematical approach assumes th at the are behavior is linear. This paper investigates how well a line ar model describes the small-signal behavior of the are. The derived f ormula gives an insight into which are properties are responsible for the dynamic behavior of the are about its steady-state operating point . Application of the method has been illustrated with arcs in argon. R esults calculated with the formula are compared to time-constants dedu ced from equilibrium model predictions of the decay in the electric fi eld when the current is stepped.