By heating the ionosphere with ELF/VLF-modulated high-power HF wave, a virtual antenna is produced in the ionosphere, which is an effective means to launch ELF/VLF waves. This paper uses the modulatedheating models of Wang Feng [2009] to calculate the strength of the LF radiation source produced by HF heating, and analyzes attenuation and reflection of the LF wave transmitting downward using full-wave algorithm. With HAARP experiment parameter, this work simulates magnetic field of the LF signals on the sea, which is of PT order of magnitude, consistent with the experimental data.

Powerful high-frequency radio waves modulated at extremely low frequency (ELF) and very low frequency (VLF) can efficiently modify the lower ionospheric current which can act as an equivalent ionospheri'c antenna for the generation of ELF/VLF wave and these signals can propagate into the magnetosphere and the investigation of the propagation properties is of significance for understanding of radiation belt energetic electrons precipitation. In this paper, based on the raytracing theory, the ray paths of ELF waves in the magnetosphere are obtained using numerical modeling and the properties are analyzed. The results shows that the ELF waves generated from the low latitude reflect between the southern and northern hemisphere and propagate to the farther place gradually. For the signals with different frequencies, the higher their frequencies, the shorter their propagation distances are, the lower their frequencies, the longer their propagtion distances are. In the process, ELF waves tend to reflect near a fixed region. The normal angel increases to 90° gradually and ray direction tends to propagate along the direction of geomagnetic field.

Ionospheric modulation can artificially trigger ELF/VLF whistler waves, which can leak into the inner magnetosphere and contribute to resonant interactions with energetic electrons. Combining the ray tracing method and test particle simulations, we investigate the propagation of these artificially generated ELF/VLF waves through the high ionosphere into the inner magnetosphere, and evaluate the subsequent effects of resonant scattering energetic electrons near the heart of the outer radiation belt. The results show that the artificially triggered ELF/VLF waves become highly oblique in the magnetosphere and their spatial extent of L shell and magnetic latitude can be significantly controlled by the initial launch latitude. Corresponding to the principal first-order resonance, the energetic electrons from ～ 100 keV to 3 MeV can resonate with the artificial VLF waves with frequency above 10 kHz in the inner radiation belt, while in the outer radiation belt these hazardous electrons can resonate with ELF waves from ～100 Hz to 1 kHz. At L=4.5 as the focus in this study, the artificial ELF waves can resonate with 1 MeV electron at the harmonics N=-1, 1, 2. In contrast, the Landau resonance rarely occurs for these energetic electrons. The results of test particle simulations indicate that while wave-induced changes in pitch angle and kinetic energy of a single electron are stochastic, the change averaged over all test electrons increases monotonically within the resonance timescale, which implies that resonant scattering is an overall characteristic of energetic electrons under the influence of the artificial whistler waves. Computed resonant scattering rates based on the test particle simulations indicate that aritificial ELF/VLF waves with an observable in situ wave amplitude of ～ 10 pT can drive efficient local pitch angle scattering of energetic electrons at the magnetic equator, thereby contributing considerably to their precipitation loss and magnetospheric electron dynamics. When the waves become highly oblique during the propagation, besides the fundamental first order resonance, higher order resonances can also drive efficient electron scattering. The results support the feasibility of generating artificially ELF/VLF whistler waves for controlled removal of energetic electrons in the Earth radiation belts.

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Modulated high frequency (HF) heating of the ionosphere provides a feasible means of artificially generating extremely low frequency (ELF)/very low frequency (VLF) whistler waves, which can leak into the inner magnetosphere and contribute to resonant interactions with high energy electrons. Combining the ray tracing method and test particle simulations, we evaluate the effects of energetic electron resonant scattering driven by the discrete, multi-frequency artificially generated ELF/VLF waves. The simulation results indicate a stochastic behavior of electrons and a linear profile of pitch angle and kinetic energy variations averaged over all test electrons. These features are similar to those associated with single-frequency waves. The computed local diffusion coefficients show that, although the momentum diffusion of relativistic electrons due to artificial ELF/VLF whistlers with a nominal amplitude of ∼ 1 pT is minor, the pitch angle scattering can be notably efficient at low pitch angles near the loss cone, which supports the feasibility of artificial triggering of multi-frequency ELF/VLF whistler waves for the removal of high energy electrons from the magnetosphere. We also investigate the dependences of diffusion coefficients on the frequency interval (∆ f ) of the discrete, multi-frequency waves. We find that there is a threshold value of ∆ f for which the net diffusion coefficient of multi-frequency whistlers is inversely proportional to ∆ f (proportional to the frequency components N w ) when ∆ f is below the threshold value but it remains unchanged with increasing ∆ f when ∆ f is larger than the threshold value. This is explained as being due to the fact that the resonant scattering effect of broadband waves is the sum of the effects of each frequency in the 'effective frequency band'. Our results suggest that the modulation frequency of HF heating of the ionosphere can be appropriately selected with reasonable frequency intervals so that better performance of controlled precipitation of high energy electrons in the plasmasphere by artificial ELF/VLF whistler waves can be achieved.