New solutions of the corona discharge equation for applications in waveguide filters in SAT-COM

The microwave device designers in the industry of satellite communications systems use analytical solutions of the corona discharge equation, employing the concept of characteristic diffusion length, to determine whether its intensity in a particular device, such as waveguides and filters, is within established margins. The analytical solutions provide the lowest possible breakdown threshold. Until now, the difference of the gap between the electrical breakdown values obtained experimentally and provided by analytical solutions has not yet been explained sufficiently. This paper shows how it is inappropriate to use the characteristic diffusion length (Λ) rather than the effective diffusion length (Λ_eff), although in principle electric fields are considered in terms of its geometry. The presence of an ionic space charge generated during the time evolution of the electron avalanche alters the medium properties in waveguide filters, occasioning signal absorption and reflection anomalies that modify the condition of homogeneous fields in inhomogeneous fields.