On full-wave solution for VLF waves in the near-Earth space

Abstract

A VLF wave that propagates in the Earth's plasmasphere in the whistler mode must be converted into free space mode in order to be observed on the ground. This conversion takes place in collisional and highly inhomogeneous ionospheric plasma, which makes the description of the process not easy. Since an understanding of this process is vital for the analysis of VLF data, it has been in the focus of research since the beginning of whistler studies. A general approach to this problem, which is based on Maxwell's equations in magnetized plasma, is well developed and commonly accepted. However, its direct implementation meets serious difficulties which reveal themselves in numerical swamping. The intrinsic reason behind this is the existence of evanescent mode in the whistler frequency band. This leads to exponential growth of numerical solutions to the general set of equations. Various methods that have been developed to suppress this instability shift a solution of the physical problem to the field of simulation skill, so that the essential part of solution remains largely hidden. In this work we develop a new approach to the problem in which the evanescent mode is analytically excluded from consideration, making numerical calculations plain and straightforward. Using this approach, we find the field of whistler mode wave incident on the ionosphere from above in the whole span of altitudes, and calculate the reflection coefficient as a function of frequency for a number of incidence angles. We explain a quasiperiodic behaviour of the reflection coefficient by resonance absorption of the waves in the lower ionosphere.