Emergence of sprite streamers from screening-ionization waves in the lower ionosphere

Sprite discharges above thunderclouds at altitudes of 40–90 km (refs 1–5) are usually created by a strong positive cloud-to-ground lightning flash6. Sometimes these sprite discharges emerge from a visible halo5,7–9, and during the first stage they always propagate downwards and branch on their way5,7,9–11. Modelling efforts have been restricted to conditions of non-ionized air of constant density and show double-headed sprites12 or sprites starting from metal electrodes, but they do not explain why observations exclusively record sprites that propagate downwards. Here we present simulations with a numerical discharge model on a non-uniform, dynamically adapted computational grid13 to capture the wide range of emerging spatial scales, and we use realistic air and electron densities that vary with altitude. Our model shows a downward-propagating screening-ionization wave in the lower ionosphere that sharpens and collapses into a sprite streamer as it propagates farther down. Streamer velocity, diameter and length until branching agree with observations9 within measuring accuracy. We speculate that sprites generically emerge through the collapse of a wide screening-ionization wave into a sprite streamer, although this wave is only sometimes visible as a luminous halo. Electrical breakdown in the upper atmosphere above a thundercloud was predicted1 in 1925. However, only in 1990 was an ‘unusual luminous electrical discharge’ actually reported2 in the scientific literature. The most frequent transient luminous events4 are elves7 and sprites14. Sprites are strongly luminous11, filamentary15 discharges in the mesosphere. Continued progress in instrumentation has uncovered their complex dynamics in ever increasing temporal9,16, spatial15 and spectral7,14 resolution. Sprites start as downward-propagating filaments, often emerging from a diffuse glow, called a halo7–9,14. Only after these initial discharges have propagated about 10 km down within milliseconds, a new phase of upward-propagating discharges is observed5. After estimates of electric breakdown high above thunderclouds more than 80 years ago1, sprite theory was largely shaped in the past 13 years17,18. The thin filaments of sprites are streamers19: thin plasma channels that propagate into a non-ionized medium exposed to a high electric field. The streamer nature of sprites was confirmed by telescopic imaging15 and by movies with submillisecond time steps5,11,16. As lengths and times for streamers scale with air density, small streamers at atmospheric pressure and large sprites at high altitudes5,16,20 are physically similar12,20,21. Streamer models have been used12 to study sprites, but only over short propagation lengths where the variation of air density can be neglected. Also background ionization was neglected. Rather the streamers were initiated by arbitrary localized ionization seeds, creating either double-headed streamers extending at both ends simultaneously, or streamers were launched from a pointed metal