Effective electric field for an arbitrary electromagnetic pulse

In the performance of intense electromagnetic transient, gaseous breakdown experiments, one parameter of interest is the effective electric field. A method of calculating the effective electric field for an arbitrary electromagnetic pulse is presented. This method is based upon the Laplace transform of the Lorentz force equation. Results from previous efforts are reproduced via this method and compared. Examples are calculated for various electromagnetic transients, most of which have never been calculated before. These examples of effective electric fields are used to generate theoretical Paschen curves, which are compared to experimental results.