A method to estimate whistler wave vector from polarization using three-component electric field data



Satellites in the Earth's magnetosphere can be used to record the rich electromagnetic wave activity due to terrestrial lightning, typically up to several tens of kilohertz. With simultaneous recordings of the three components of wave electric field E and of the three components of wave magnetic field B, the entire wavefield, polarization, and wave vector can be specified without any appeal to a priori assumptions about the wave mode and without any reliance on the validity of a dispersion relation. However, some satellites lack such a complete suite of measurements. We develop a method which assumes the theoretical dispersion relation for whistler waves then uses recordings of the three components of wave electric field E but no magnetic components to derive the wave polarization and the wave vector (up to a sign ambiguity on the latter). The method can work only because the dispersion relation, which is assumed, already contains information from the full Maxwell's equations. We illustrate the method with 12 s duration simultaneous recordings, at 32 kilosample/s, of three orthogonal components of wave electric field E from the C/NOFS satellite in low-Earth orbit. Our particular example in this article is shown to contain two broadband whistler features in the range of 4–15 kHz, whose wave vectors differ both according to their polar angles from the geomagnetic field B0 and according to their azimuth around the geomagnetic field B0.