Riccati approach to the propagation of axially symmetric waves in a coaxial guide

The problem of the axially symmetric modes (¿/¿¿ = 0) in a coaxial waveguide has been studied afresh in terms of the first-order nonlinear wave equation of Riccati type in which the dependent variable involves the wave impedance EZ/H¿ looking radially across the guide. This presentation is particularly suitable when ¿ and ¿ are functions of the radial co-ordinate r, while, for the mode in which H¿w is the only component of magnetic field and the guide is narrow enough to cut off the higher-order modes, the nonlinear term behaves as a small correction, leading to an iterative solution. It is shown that, under some conditions, for instance when there is a dielectric layer on or near to the outer conducting wall, there can be a small decrease in attenuation along the guide below the value for the quasi-TEM mode when there is only air in the guide. This effect, however, depends on the actual radius of the inner conductor and on the ratio of the radii of the outer and inner conductors being sufficiently large, and is, moreover, rapidly offset when the loss factor in the dielectric is increased.