Field inside a cylindrical shell with a central cylinder surrounded by concentric rings

The paper is concerned with the field inside a cylindrical shell, having a central core, surrounded by concentric rings. Such a configuration is found in electronic tubes, circuit breakers, waveguides and transmission lines. The potential functions are derived, subject to the boundary conditions of the problem. For mathematical purposes the actual rings are replaced by flat cylindrical rings whose width is allowed to tend to zero. Then, from the equipotential surfaces surrounding these, one can be chosen to represent the rings. The solutions are in the form of infinite series, and a computer has to be used to evaluate them. The series are modified for computational purposes to accelerate convergence. Calculations were carried out on a large digital computer and some results of the calculations are presented in the paper. The potential derived in this paper does not appear to have been considered before. The numerical solutions, although complex, can be obtained conveniently and inexpensively by computer and can be used in the design of equipment.