Modeling Low Frequency EM Signals in the Ionosphere*

First-principles propagation of low frequency (0.01-100 Hz) electromagnetic signals from the ionosphere to the Earth's surface requires algorithms that are accurate over orders of magnitude in electron and neutral density.

Starting from Maxwell's equations with a tensor conductivity, we present an algorithm for propagating EM signals from the ionosphere down to the surface of the Earth. This algorithm is shown to be stable at all altitudes for the parallel, Hall, and Pedersen conductivities. For unconditional stability, the parallel and Pedersen terms must be solved implicitly, and the Hall term must be solved via a Crank-Nicolson scheme. Despite its mixed-implicit nature, the novel algorithm is local in space, and hence is easy to implement efficiently on parallel architectures.

We demonstrate the advantage of the new mixed-implicit algorithm compared to the standard diffusion approximation for treating vacuum regions. Using the code Topanga, we model propagation of EM signals around the X-ray ionization patch formed in the aftermath of a high-altitude nuclear explosion. We show that the novel algorithm recovers the EMP blast signal from the Starfish nuclear test, whereas a standard diffusion model fails to match the data.