Investigating ELVE photometric waveforms with elementary electromagnetics

ELVEs are quickly expanding rings of light emissions excited in the lower ionosphere by the electromagnetic pulse of an electric discharge in a thundercloud. They are commonly observed from space platforms and have been reported in conjunction with other atmospheric-electricity events. One motivation to investigate ELVEs is that their signal may provide insight into the discharge that created them. Until now the modeling of ELVES has either relied on strong simplifications or on the Finite-Difference Time-Domain (FDTD) method to directly solve the Maxwell equations. One limitation of the latter is that non-axisymmetrical discharges (with a slanted channel or a non-vertical magnetic field for example) require computationally expensive, fully three-dimensional meshes, which makes parametric studies of the ELVE features slow and cumbersome.  We show here that elementary electromagnetic theory allows one to model ELVEs, even non-axisymmetrical ones, with sufficient accuracy at little computational cost. We then apply our methods to the parametric study of ELVE photometric waveforms as recorded by space-based instruments.