Effective electric field for arbitrary waveforms

Summary form only given. When performing gaseous electrical breakdown experiments one parameter of interest is the effective electric field. This field is required to calculate the ionization rate of the gaseous medium. A new method of calculating the effective electric field for any arbitrary waveform is presented. Simple examples are calculated for various electromagnetic transients and compared to previous efforts, and to one another. The method is then expanded to include relativistic effects, and again compared and contrasted with classical results.