A Novel Energy-Density Based Approach: From Confinement to Radiation in Cylindrical EM Structures

This work analyzes the transition between quasi-stationary and propagative regimes in electromagnetic wave propagation, considering cylindrical capacitor and inductor configurations as a case study. Starting from the conditions defined by Max Abraham and the subsequent contributions of Schelkunoff—who emphasized energy balance as a crucial variable—the spatio-temporal energy density as a fundamental state variable is here presented. By applying Maxwell's equations through Hertz's method, a rigorous framework to describe energy confinement phenomena in quasi-stationary regimes and their transition to propagative behaviors has been outlined with respect to any cylindrical geometry. The results aim to provide guidelines for designing and optimizing wireless power systems, reconfigurable metamaterials, and advanced electromagnetic devices operating in stratified or anisotropic media.