The FDTD simulation of very low frequency waves propagation in the ionosphere

The VLF (very low frequency) waves can not only propagate in the ground-ionosphere waveguide, but also enter the ionosphere to form whistler waves that propagate along the magnetic field lines and propagate to the magnetosphere or even to the magnetic conjugate region. But the physical process of the VLF propagation in the ionosphere has not been concluded in detail yet, especially for the nonlinear process of ionospheric heating caused by the powerful VLF waves. Moreover, the properties of the D region are hardly measured by satellites or rockets. Thus, the simulation of the VLF propagation profoundly influences the researches of propagation and wave-particle interaction. This work presents a GPU-accelerated FDTD (finite-different time-domain) scheme which simulates the VLF signals spreading from ground to the higher ionosphere. The scheme divides the space into coarse and fine grids to cope with the great changes of VLF wavelength caused by ionospheric refractive index. This work also combines the numerical results and the detection data of the ionosphere by DEMETER satellite and zh-1 satellite to verify whistler waves transmission path at higher satellite altitude.