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As a possible trigger of the substorm onset, the ballooning instability has been often suggested. The ballooning disturbances in a finite-pressure plasma immersed into a curved magnetic field are described with the system of coupled equations for the Alfven and slow magnetosonic modes. The spectral properties of ballooning disturbances and instabilities can be characterized by the local dispersion equation. The basic system of equations can be reduced to the dispersion equation for the small-scale in transverse direction disturbances. From this relationship the dispersion, instability threshold, and stop-bands of the Alfvenic and slow magnetosonic modes have been determined. The field-aligned structure of unstable mode is described with the solution of the eigenvalue problem in the Voigt model. We have also analyzed in a cylindrical geometry an eigenvalue problem for the stability of ballooning disturbances with a finite scale along the plasma inhomogeneity. The account of a finite scale in the radial direction raises the instability threshold as compared with that in the WKB approximation.

The expected magnitude of extralow-frequency (ELF) electromagnetic response in the upper ionosphere to ground large-scale power transmission lines at low Earth orbit (LEO) is modeled. The full-wave system of Maxwell's equations is numerically solved in a realistic ionosphere whose parameters have been reconstructed with the use of the International Reference Ionosphere (IRI) model. We have calculated the altitudinal structure in the atmosphere and ionosphere of electromagnetic field and Poynting flux excited by an oscillating 50/150 Hz linear current suspended above the ground. The leakage rate into the upper ionosphere was shown to increase during nighttime hours and above a high-resistive crust. The amplitudes of electromagnetic power line emission (PLE) detected by LEO satellites correspond to the unbalanced power line current intensity of about 1-10 A, depending on the crust resistivity.

Nowadays our planet exists in an electromagnetic environment, at least in some frequency bands, created by rather industrial activity than by natural processes. There appear ever growing evidences of man-made influence on natural geophysical processes (Parrot, 2018). This influence was found not only in dedicated active experiments, but also as unintentional by-product of the technosphere development (Rothkaehl & Parrot, 2005). The most ubiquitous type of electromagnetic radiation emanating from the Earth is the 50/60 Hz power line emission (PLE) (Pilipenko et al., 2021).The electromagnetic response of the ionosphere in the very-low-frequency (VLF) band (1-10 kHz) to natural and man-made electromagnetic disturbances (e.g., lightning, radio transmitters) has been thoroughly studied. In contrast to VLF emitters, any noticeable radiation efficiency in the extra-low-frequency (ELF) range (about several tens-hundreds of Hz) may be expected only for a very large emitting system. Such manmade large-scale transmitters do exist-they are networks of electric power transmission 50/60 Hz lines extended to many hundreds of km. A three-phase power transmission line must be balanced (symmetrical) when the voltages and currents of each of the phases have the same amplitude, and the phase shift is 0 120 E . If at least one of these conditions is not met, then the system becomes unbalanced. Such imbalance leads to a decrease in the efficiency of the transmission line and power losses due to the radiation of electromagnetic energy. In most cases, the source of the imbalance is the asymmetry of the load (high-speed railways, induction furnaces in metallurgy, computers, etc.). Substantial distortions into power line operation can be produced by geomagnetically induced currents (GICs) caused by rapid variations of the geomagnetic field, that is high dB dt / values. The detection of PLE at large distances from a three-phase power line is an indicator of its unbalanced operation. Moreover, due to strong non-linear elements (like thyristors) in industrial power lines high harmonics of the 50/60 Hz base frequency are generated. Power line harmonic radiation (PLHR) refers to VLF electromagnetic emissions at equidistant frequencies separated by 50/60 Hz. In this frequency range power lines can operate as running wave antenna (Beverage antenna) and be an efficient VLF emitter (Kostrov et al., 2017). PLHR can effectively penetrate into the ionosphere and magnetosphere and be detected by satellites (Nemec et al., 2006;Wu et al., 2014).

The feasibility of detection of electromagnetic response in the upper ionosphere to ground large‐scale extremely low frequency (ELF) transmitters (e.g., submarine communication systems) by low‐orbiting satellites is discussed. Several times when the DEMETER satellite (660 km) was in the vicinity of the ELF transmitter on the Kola Peninsula, the electric and magnetic sensors operating in a burst mode detected a narrowband 82‐Hz emission. The same emission associated with the ELF transmitter was observed by a ground‐based magnetometer. We modeled the rate of the ELF wave energy leakage into the upper ionosphere from an oscillating 82‐Hz linear current with an infinite length suspended above a high‐resistive ground. A realistic altitudinal profile of the plasma parameters has been reconstructed with the use of the IRI ionospheric model. The modeled amplitudes and polarization of electromagnetic response of the upper ionosphere are in reasonable agreement with the properties of emission recorded by the satellite.

We examine excitation of ultralow frequency (ULF) electromagnetic waves by an atmospheric lightning stroke in the upper ionosphere and the role of the ionospheric Alfvén resonator (IAR) in this process. We have theoretically calculated with the developed numerical model the spatial and spectral structures of electromagnetic disturbance in the ULF frequency range 0.1–6.0 Hz excited by an atmospheric lightning stroke on the ground and at ionospheric altitudes. The frequency band under consideration comprises typical frequencies of the IAR and the ionospheric waveguide. The spectra of horizontal magnetic and electric components reveal a spectral multiband structure in the upper ionosphere. The form of spectra depends significantly on the horizontal distance ρ from the source: spectral peaks associated with the IAR are evident at ρ≤400 km, whereas at ρ≥1,000 km the spectral peaks (>4 Hz) corresponding to the ionospheric waveguide modes can be seen. The model predicts that a vertical electric discharge with the charge moment MQ=106 C·m produces at altitude 500 km and ρ = 40 km a pulse with electric and magnetic amplitudes of about 4 mV/m and 4 nT, correspondingly, and duration ∼0.2 s. The pulse amplitude decays rather slowly with distance ∝ρ−1. Detection of ULF response in the upper ionosphere to isolated intense lightning stroke by low‐orbiting satellites with magnetic or electric sensors onboard is quite feasible.

A characteristic feature of the upper ionosphere is the occurrence of the ionospheric Alfvén resonator (IAR) and MHD waveguide, which can trap electromagnetic wave energy in the range from fractions of a Hz to a few Hz. This wave trapping ensures the strong dependence of the ionospheric transmission/reflective properties on frequency. We have developed a numerical model of the magnetospheric Alfvén wave interaction with the ionosphere and transmission to the ground based on the solution of multifluid magnetohydrodynamic (MHD) full wave equations in a realistic ionosphere, whose parameters were reconstructed from the International Reference Ionosphere model. The MHD modes are coupled owing to the frequency‐dependent Hall conductivity and geomagnetic field line inclination. This model can be applied to the interpretation of the spectral structure of electromagnetic emissions of the magnetospheric origin in the band 0.1–10 Hz observed at various latitudes. The model predicts that the upper part of the ULF spectrum (f > 1 Hz) will be severely absorbed upon wave transmission through the daytime ionosphere to the ground. At nighttime the transmission coefficient of Alfvén waves has an oscillatory dependence on frequency, with “transmission windows” at the lowest IAR eigenfrequencies (<3 Hz). At higher frequencies (3–10 Hz) the reflection/transmission coefficients are dominated by periodic scale‐dependent modulation owing to the waveguide modes. Broad maxima/minima of the transmission coefficient are determined by the phasing between Alfvén and fast magnetosonic waves at the bottom of the ionosphere.

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