Fourierndash;Bessel representation of periodic electrostatic systems of juxtaposed coaxial cylinders separated by finite gaps

摘要

An iterative procedure is described by means of which the potential distribution can be found in axially symmetrical periodic configurations of juxtaposed coaxial electrodes. The solution is in the form of Fourierndash;Bessel series, and the procedure involves the potential calculation in the gap by an overrelaxation process in respect of points located on a mesh covering a small region which includes a cross section of the gap. The gap potential is represented either by a polynomial or by the sum of a linear function and a Fourier series. Using this method, the errors on axial potentials are found to be approximately two orders of magnitude smaller than those on potentials calculated by assuming that the potential in a gap is a linear function. Compared to the relaxation method, the present procedure represents a considerable saving on computing time and memory.