Radiation from Circular Current Sheets

An analysis of the radiation from a system of coplanar concentric circular current sheets, in which the current elements are perpendicular to the plane of the circles, is carried out. The current elements are of negligible length, and are continuous along the periphery of the circles. The formation of beams in the horizontal plane, and also in the vertical plane, are examined. The solution of the three-dimensional field is given in two forms: one as a Fourier series, and the other as a Bessel-Fourier series. The solutions are adapted to show how a prescribed horizontal pattern may be synthesized. In one method the pattern is represented as a Fourier series, in the other it is represented as a Bessel-Fourier series. It is also shown that by combining these two types of solution, it is possible to synthesize simultaneously a pattern in both the vertical and horizontal planes.