Time constants for nonstationary arcs

The time constants associated with the initial deviations of an arc column from a static state have been studied analytically. The basic approach is to use a Taylor series expansion in powers of time of the energy balance equation. It is assumed that the arc gas is optically thin and is in local thermal equilibrium. Initially the effects of radial gas flow (which must exist for dynamic arcs) are neglected, but this simplification is later relaxed. The initial conditions are given by the properties of a cylindrically symmetric, wall-stabilized DC positive column. The interrupted (freely decaying) and the step-modulated arcs are considered, and initial time constants for conductance, electric field, and heat flux potential are computed. For numerical results the best available values of thermodynamic and transport properties have been used.