Analytic method for evaluation of the field of a charge traversing a geometric discontinuity

An analytic time-domain method is developed for the electromagnetic field generated by a charge traversing a geometric discontinuity. The essence of the method employed here is to use the linear independence of the exponential functions, that control the temporal behavior of the field. As a result, we avoid the large ('infinite') matrix inversion necessary for a frequency-domain solution. This method was utilized for the investigation of the wake generated by electrons in an optical accelerator as well as evaluation of the emittance growth and energy spread