Characteristics of whistler wave normal distributions at the exit of low-latitude duct

According to the direction-finding observation of whistler at low latitudes, the whistlers come from a narrow region of the zenith and exhibit morphology at ionospheric exits. When ionospheric transmission characteristics of the very low-frequency (VLF) radio wave emitted to the ground from the magnetic field-aligned duct due to the irregularity of the ionosphere are computed, or when the results of the VLF direction-finding observation on the ground are discussed, distribution of the wave normal of the radio wave at the duct exits is important. Here, the wave-normal distribution of the VLF whistlers at the duct exit, namely the wave normal of the VLF whistlers at each part of the duct exit, is computed by means of the two-dimensional ray tracing based on the duct propagation model assuming low latitudes. It was found that there are two kinds of wave-normal distributions, i.e., upward and downward. The cause of the generation of the two kinds of distributions was clarified qualitatively by the duct-propagation theory. Also, the factors for various characteristics of the wave-normal distributions at the duct exit were investigated. Especially, for the downward wave-normal distributions, there is a region at the center of the duct where the wave normals are directed vertically downward due to the effect of the vertical gradient of the ionosphere applied in the duct. This region contributes to the transmission of the whistler to the ground.