Pulsed Radiation From A Parabolic Reflector

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Abstract
We consider a transient point dipole current turned on at time zero, with the time-derivative being discontinuous at zero. This point current source generates an electromagnetic field incident on a perfectly conducting smooth surface having a boundary. Surface current is induced in the conductor, producing a scattered field. The objective is to analyze the leading edge of the scattered field. Cases are shown in which the edge singularity is strong enough to generate an electromagnetic missile. This report includes a rigorous formulation of the problem in terms of Maxwell's equations and a review of the incident and scattered wave fronts associated with these equations. These fronts are used to extract information about the leading edge of the scattered field. A "tangent-plane" approximation is studied and applied to a case of a bounded paraboloidal reflector illuminated by a transient point dipole. This results in a missile with a radiated energy den-sity that drops off as slowly as the inverse logarithm of the distance. Steps toward the establishment of bounds on the error of the approximation are described.

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