Transient Currents on a Perfectly-Conducting Cylinder Illuminated by Unit-Step and Impulsive Plane Waves

摘要

An analytical study of the transient current density induced upon the surface of a perfectly conducting circular cylinder has been carried out. Both TE and TM incident plane waves are considered. The time dependence of the incident wave is chosen to be either that of a unit impulse or a unit step. Since exact, closed form solutions for the induced current density cannot be derived, it is necessary to separately consider the current density for small and large time intervals after the arrival of the incident plane wavefront. Using this approach, a symptotic representations of the induced current density are derived which are valid in the two extreme time ranges. The large and small-time approximations do not overlap in the moderate time zone. With the aid of two independent numerical approaches, it is found that the transient current waveforms in the moderate time zone can be reasonably approximated by a functional interpolation between the short and large-time solutions. Hence a complete analytic approximation of the current density is obtained. The numerical results which stem from this representation are presented graphically by two methods. One method presents a series of graphs of current density versus time for specific locations on the surface of the cylinder. The alternate presentation presents 'snapshots' of the current density distribution on the circular cylinder at specific instants of time. The numerical results are interpreted in terms of specular reflection and creeping wave contributions. Finally a method is proposed by which the circular cylinder results are extended to more arbitrary convex cylinders for short time intervals after the arrival of the incident wavefront. (Author)