FDTD propagation of VLF-LF waves in the presence of ions in the earth-ionosphere waveguide

The finite-difference time-domain (FDTD) method has been used for a long time to compute the propagation of very low frequency (VLF) and low frequency (LF) radio waves in the Earth-Ionosphere waveguide. In previously published FDTD schemes, only the electronic density of the ionosphere was accounted for, since in usual natural conditions the effect of the ion density can be neglected. In the present paper, the FDTD scheme is extended to the case where one or several ion species must be accounted for, which may occur in special natural conditions or in such artificial conditions as after high altitude nuclear bursts. The conditions that must hold for the effect of the ions not to be negligible are discussed, the FDTD scheme with ions is derived, and numerical experiments are provided to show that the effect of the ions may be significant when the ionosphere is disturbed by incident flows of gamma or beta rays.