Yong Li

This paper has established a relatively comprehensive model for ultra-low frequency (ULF) current induced by thermal pressure gradients and its propagation. In the ULF current excitation model, we decomposed the current into a constant term unaffected by altitude and a product with a function significantly influenced by altitude. Combining this with the EISCAT background, we determined that for modulation frequencies below 5 Hz, the optimal height for ULF current excitation corresponds to the critical frequency height. We calculated the ionospheric currents at heating altitudes of 332 km for modulation frequencies of 5 Hz; the corresponding maximum currents were 1.03 × 10−10 A·m−2. By incorporating the current into the ULF waves propagation model based on magnetoionic theory, we found that the electromagnetic field energy is mainly concentrated in the horizontal direction, indicating that the energy primarily propagates outward through magnetosonic waves. The dominant components are the electric field component Ey and the magnetic field component Bz, whose maximum values reached 1.1 μV·m−1 and 1.5 pT. Unfortunately, magnetosonic waves cannot propagate downward due to the sharp variation in the real part of the refractive index between 200 and 300 km. However, the shear Alfvén waves component By can propagate downward, and there is still an intensity of approximately 0.1 pT at the bottom of the ionosphere, which is because the refractive index of shear Alfvén waves is most uniform in the parallel magnetic field direction, allowing By to propagate parallel to the magnetic field effectively.

Powerful high-frequency (HF) radio waves can modulate the ionosphere and lead to the current generation. Along these lines, in this work, a numerical model for the investigation of ultralow-frequency (ULF) currents excited by radio waves heating the ionosphere in mid-latitudes was established. The impact of both neutral winds and pressure gradient was taken into account by the proposed model. Combining the ionospheric background data of Beijing, the characterization of ULF ionospheric currents (1 Hz) was numerically calculated and discussed. From our analysis, it was demonstrated that the electron temperature relaxation time gradually increased with increasing the altitude during the day and night. The temperature relaxation time of 1 s was attributed to an altitude of 140 km during the day and 180 km at night. The maxima of neutral wind term current was 22 nA $\cdot$ m $^{-2}$ at daytime, corresponding to the position 102 km. Interestingly, at nighttime, the maximum value of the current was reduced to 0.032 nA $\cdot$ m $^{-2}$ , corresponding to 112 km. The electronic pressure gradient term current exhibited a maximum value of 8 nA $\cdot$ m $^{-2}$ at the position 104 km during the day, while, at nighttime, the maxima of the current was 0.19 nA $\cdot$ m $^{-2}$ , corresponding to the position near 224 km. It was also proved that the properties of the neutral wind term current are strongly dependent on the ionospheric conductivity but are constrained by the electron temperature and the relaxation time. In addition, the current induced by the electronic pressure gradient term is mainly correlated with the electronic Hall conductivity and the electron temperature relaxation time.

The paper starts from the polarization of the electromagnetic wave launched by the transmitter, develops an ionospheric heating model for a wide range of launching angles and polarizations of powerful heating radio waves. The electric field polarization is characterized by Q and ϕ, where Q characterizes the relative amplitude of the electric field components and ϕ characterizes the relative phase of the electric field components. We use similarity transformation and tensor calculation in our calculations and give the optimal polarization equation using the idea of finding the maximum value of a binary function. Combining the ionospheric background data of three widely separated locations—EISCAT (polar region), Beijing (mid-latitude), and Sanya (low latitude)—we have numerically calculated and discussed the three sites based on the heating model. The following conclusions are drawn from the calculations. The Q of the optimal polarization gradually decreases and tends to be stable when the collision frequency becomes negligible relative to the ionospheric cyclotron frequency. Q also depends on the angle between the radio wave launching angle and the magnetic inclination angle. The optimal polarization angle ϕ is generally π/2 in northern hemisphere heating experiments. With the angle between the radio wave launching angle and the magnetic inclination angle increasing from 0, the optimal polarization changes from left-handed circular polarization to left-handed elliptical polarization, and when it reaches π/2, the optimal polarization becomes east–west linear polarization. These results will provide some guidance in future experiments.