Electromagnetic radiation from abrupt current changes in electrical discharges

We treat electromagnetic radiation from narrow electrical discharges, with particular emphasis on the asymptotic behavior at high frequencies f. We show that discontinuities in the discharge current and its derivatives dominate the high-frequency part of the radiated spectrum. Specifically, when a current discontinuity is present, the envelope of the radiated fields falls off with large f as f-1 for almost all observation angles. If the current is continuous but has discontinuities in its first derivatives, then the envelope of the radiated field falls off as f -(1+1/n) at large f for a range of observation angles. If the discharge current and its first derivatives are continuous, then the radiated fields fall off at least as fast as f-2 at large f. The characteristic high-frequency dependence associated with abrupt current change persists for some large range of f, even when current variation is not precisely abrupt. We illustrate the general results with radiation from AWA discharge models (previously referred to as arc welder's ansatz models) featuring a constant electric field associated with dissipative discharge processes