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 arc quantities when the arc current is perturbed from its steady-state. The current perturbation is assumed to be very small and the mathematical approach assumes that the arc behavior is linear. This paper investigates how well a linear model describes the small-signal behavior of the arc. The derived formula gives an insight into which are properties are responsible for the dynamic behavior of the arc about its steady-state operating point. Application of the method has been illustrated with arcs in argon. Results calculated with the formula are compared to time-constants deduced from equilibrium model predictions of the decay in the electric field when the current is stepped