The Electromagnetic Fields Due to Radial Currents Near a Perfectly Conducting Sphere

摘要

The dyadic Green's function technique is applied to the problem of determining the electromagnetic fields due to radial electron emission near a perfectly conducting sphere. The application of the technique results in formal solutions for the surface current on the sphere and the curlless field within the electron cloud which causes the currents. Two electron velocity functions are used. They are the constant velocity case and the case in which the velocity falls off in a central potential. The analysis of the problem is simplified by ignoring electron-electron interactions, electromagnetic field-electron interactions, and the potential due to ions left on the surface of the sphere. Both time domain and Laplace transform domain solutions are obtained. The singularity expansion method is used to determine the inverse transforms of the Laplace domain field expressions. The final field expressions are in formal series form. The series are not summed. (Author)