Transient electromagnetic field propagation through infinite sheets, into spherical shells, and into hollow cylinders

Abstract

Gaussian electromagnetic field pulses of several durations are propagated through infinite sheets into the interior of hollow cylinders and into the interior of spherical shells. The plates, spheres and cylinders are made of aluminum and contain no slots. The time history of the propagated pulses is computed. Finally, the time sequence of the electric field is calculated in the interior of a cylinder of finite length when connected at its ends by wires to a generator delivering a current pulse of Gaussian shape. The dimensions of the cavities are assumed to be sufficiently small so that resonances are not excited by the highest significant frequency contained in the shortest pulse considered. The numerical study is restricted to thin-walled aluminum shields 1/32 inch, 1/16 inch, 1/8 inch and 1/4 inch thick. The half-amplitude widths of the pulses employed lie in the range 14 \mu sec to 2400 \mu sec. It is shown that the resultant Gaussian pulse electric fields defined on the surface of the plates and cylinders are propagated with little diminution in amplitude. This is understandable due to the requirement that the tangential fields are continuous across the interfaces, and to the fact that skin effect is almost nonexistent at low frequencies. The incident (as contrasted to resultant) field pulse undergoes reflection at the boundary surface. Hence, the attenuation sustained by the incident field is great, since reflection is the chief mechanism of attenuation of fields at low frequencies. Thin spherical shells form effective magnetic shields. The electric field is small in the interior of thin-walled cylinders carrying extremely large transient currents.