Ray tracing study of whistlers guided by a field-aligned depression of electron density in the magnetosphere

Abstract

The properties of VLF waves guided by a field-aligned depression of electron density in different models of the magnetosphere are studied. Ray tracing calculations show that the guidance of VLF waves from one hemisphere to the other is made possible by the existence of Gaussian cross-section trough. The guidance of VLF waves occurs only at the inner side of the trough, when it is located at L ⩽ 2.2 and L ⩾ 4.0 for the winter night model and at L ⩾ 1.5 for the summer day model of the magnetosphere. All analyzed troughs are modelled with the same electron density depression of 15% and with the effective width of 215 km in the equatorial plane. Initial latitude ranges for various wave normal directions, from which rays are successfully guided, are moved equatorward from the trough centre. For one trough the initial latitude ranges are defined so that corresponding rays reach 300 km altitude in the conjugate hemisphere with a final wave normal angle inside the ionospheric transmission cone. The guidance of VLF waves by a trough is possible in a para-longitudinal mode or a gradient trapping mode, depending on initial positions. Changing these positions, there is a continuous transition from one ray path to the other. The main difference in the characteristics of rays guided in a para-longitudinal mode and a gradient trapping mode is the behaviour of the wave normal angle to the geomagnetic field. A para-longitudinal mode has lower value of this parameter than a gradient trapping mode. A ray guided in a gradient trapping mode deeply enters a trough. A slight difference of latitudinal gradients of the geomagnetic field and electron density in the lower altitude magnetosphere is responsible for determining a type of mode for guiding whistlers by a trough. These whistlers are characterized by an upper cut-off frequency which is almost 0.5 ƒBmin.