Voltage‐current relationship for pulsed arc discharges

A theoretical treatment of the electrical behavior of pulsed discharges in gas‐filled flashlamps is presented. The theory is based on a simple model of the plasma and a balance of electrical power input and radiation output. It is assumed that the plasma radiates as a greybody with an emissivity that depends on the electron density. The principal result is an analytic expression for the arc voltage as a function of current, with initial voltage, arc length and diameter, and atom density as parameters. The expression describes the entire voltage pulse, including the initial fall, the following minimum and the peak when the current peaks. The predicted voltages substantially agree with measurements, including dependences on lamp length and diameter and initial voltage. The theory is an improvement on the empirical V‐I relation commonly used in flashlamp circuit analyses.