Improved and simpler FDTD formulation for axisymmetrical problems

Axisymmetrical structures play an important role in high frequency research and engineering. Examples of application include horn and rod antennas, circular waveguide discontinuities, resonators, and particle accelerators. Two FDTD formulations for axisymmetrical problems have been proposed by Gwarek, Morawski and Mroczkowski (1993) and by Jurgens and Saewert (1995). Both operate on a 2D mesh, and account analytically for azimuthal sin(m/spl phi/)/cos(m/spl phi/) field dependence. The two approaches lead to different field update equations and in practice-to somewhat different results. Both algorithms require special treatment of on-axis components, which may cause instabilities or, as we show in this paper, ambiguous solutions. We propose an FDTD formulation for axisymmetrical problems, based on a new mesh construction scheme and a new set of system variables, which: eliminates the need for special on-axis equations; remains stable, and consistent for different axis locations on the mesh; and requires less computer operations per time step than the scheme of Jurgens. We also show that the differences between the two methods are due to different assumptions regarding local field behaviour in cylindrical coordinates, and that the choice of a better approximation is determined by circuit technology.