Regarding the Theory of Power Lines Emission Propagation to the Space

Abstract

AbstractThe analytical theory is presented that describes the propagation of power lines emission (PLE) with frequency of 50/60 Hz in the heights range from the Earth surface to the magnetosphere. Validation of the theory is made by the comparison with earlier published results of numerical modeling. It is shown that the actual source of emission is a magnetic dipole formed by the power line current and by the secondary image current in the ground. The emission is propagating to the lower boundary of ionosphere, where its main part is reflected back, but some of the energy (a few percent) penetrates into the ionosphere. There it is transformed into a quasi‐flat whistler wave. The generation of current in ground and the reflection from the ionosphere are the main factors that reduce the emission into space. In the ionosphere wave fronts propagate approximately vertically, and the energy propagates in a certain direction that depends on the geomagnetic field inclination. Thus, the ionosphere acts as a focusing system that collects PLE into a unidirectional beam. The PLE intensity does not change with altitude within the total range of ionospheric heights. In the magnetosphere PLE is transformed to both magnetosonic and Alfvén waves and the emission splits into two rays: one propagates along the wave vector and the other one—along the geomagnetic field lines. A set of analytical solutions is presented allowing determining the change in PLE parameters with altitude depending on the source parameters and ionospheric conditions.