Ray Tracing of the Equatorial Extremely Low Frequency Whistlers Detected by the Swarm Mission

Whistlers are generated by the electromagnetic signal from lightning discharges leaking into the
ionosphere and magnetosphere. They propagate upward through the ionosphere, where they can be
detected by satellites. The dispersion of whistler signal during propagation has been empirically
described by Eckersley [1935] by the following law: T = D / √ f , where T is the group delay of the
wave packet, f is its frequency and D is called the dispersion of the whistler.
We focus on events detected during burst-mode campaigns of the Absolute Scalar Magnetometer
(ASM) of the Swarm satellites at orbital altitudes ~475 km (Alpha) and ~510 km (Bravo). Since
the bandwidth of interest of this instrument lies between 10 Hz and 125 Hz, the whistlers detected
are in the Extremely Low Frequency (ELF). In this band, whistler propagation differs from the
more commonly studied Very Low Frequency (VLF) whistlers and presents a unique set of
characteristics. In particular, in the equatorial region (±5° of magnetic inclination), Eckersley’s
empirical dispersion description seems to break down.
To investigate such propagation oddity, we model the ELF whistler propagation of equatorial
whistler with a ray tracing technique using the International Reference Ionosphere 2016 (IRI) and
a local dipolar magnetic field approximation derived from the IGRF-13 as background models.
Ray tracing provides an estimate of the propagation path and the group delay of the whistler. Since
ray tracing is an application of geometric optics, it has inherent limitations for large wavelength
that are characterized in the context of ELF whistler simulation.
Ray tracing allows us to successfully model ELF whistler dispersion as detected by Swarm ASM.
This is tested on both whistler following Eckersley’s law and equatorial whistlers. For the latter
case, the simulated group delay is shown to have two main contributions: the first is related to the
expected wave dispersion and the second to the special propagation geometry of these signals.
Indeed, the various frequency components of equatorial whistlers have ray paths that differs
widely, impacting the length traveled by the rays and thus their group delay. This explains well the
group delay of ELF equatorial seen in Swarm ASM data.