Energetical characteristics of transient electromagnetic field excited by step-like current

Abstract

Background. In contrast to classical radiators with harmonic excitation, whose directional characteristics are well studied and determined by the amplitude and phase distribution on the source surface, pulsed antennas exhibit a significantly more complex dependence that considers both the amplitude distribution and the time dynamics of the source. It is known that a sharp amplitude jump can generate a wave with large amplitude and extremely high directivity. Therefore, the analysis of such processes is highly relevant, particularly in the time domain, as it allows for a more consistent and explicit observation of all energy conversion processes in the area surrounding the radiator. Such studies are not only of theoretical significance for understanding the physics of rectangular pulses radiation without carrier frequency but are also of practical importance. They enable the development of effective methods for increasing the transmission range of information signals, improving their noise immunity, and enhancing the resolution of radar and radiolocation systems based on pulsed ultrawideband waves. Furthermore, the application of such approaches facilitates the optimization of energy resources required for organizing radio communication or radar research, while also minimizing unwanted exposure to nearby objects and personnel.

Objectives. To derive analytical expressions for the flux of a pulsed electromagnetic field generated by an aperture radiator through the transverse cross-section, to calculate the total energy of the pulse, and to apply numerical methods in cases where analytical solutions cannot be obtained. To perform a physical analysis of the results and investigate the contribution of various components of the derived solutions. Moreover, the construction of graphical dependencies of energy parameters on time and spatial coordinates will verify the accuracy of both analytical and numerical results and provide a deeper understanding of the physical processes occurring in the near zone of pulsed radiators.

Materials and methods. The three-dimensional transient problem is solved analytically in the time domain using the evolutionary equations method and the Riemann function. To determine the energy characteristics, integral transformations of special functions are performed to simplify their analytical representation.

Results. Analytical expressions are obtained for the Poynting vector of the pulsed electromagnetic field of an aperture radiator with a uniform current amplitude distribution on its surface. The total energy of the radiated field through an infinite transverse plane is derived in the far-field approximation, which, in the transient case, corresponds to the field at large values of the longitudinal coordinate. Using numerical methods, the energy characteristics are calculated at arbitrary distances from the radiator, enabling a detailed analysis of their dependence on spatial and temporal coordinates.

Conclusions. The obtained dependencies illustrate the process of transforming static field components into wave components. This is clearly demonstrated by the fact om the fact that the far-field approximation yields an energy value near the radiator that significantly exceeds the true magnitude. This phenomenon indicates that the wave component of the radiated field borrows energy from the quasi-static field components, which rapidly decay as the distance from the source increases. It is also worth noting that the faster attenuation of the field energy flux with distance implies a greater concentration of energy near the longitudinal axis. The almost perfectly linear decrease in the energy flux on the radiator’s surface confirms that, after reaching the field originating from the farthest point on the aperture, no further energy transfer from the aperture is possible. However, when not all terms of the series are accounted for, this dependence deviates from the ideal triangular form, sometimes leading to situations where energy returns to the aperture at some point in time. These erroneous results are very similar to the Gibbs phenomenon, which is sometimes observed when information transmission speeds greater than the speed of light are obtained. Taking into account a sufficient number of necessary series terms prevents these inaccuracies and ensures the correctness of the obtained results.