A relativistic fluid model for reproducing thundercloud hard radiation including ALOFT’s flickering gamma-ray flashes

Thunderclouds are the largest natural gamma-ray laboratories on Earth, producing a large variety of gamma-ray phenomena of different shape, duration, and intensity. In our previous parametric study of a 0.5D fluid model of relativistic runaway electrons (RRE) in a thundercloud high-field region [1] – based on relativistic feedback discharge (RFD) theory [2] – we systematically reproduced the entire zoo of thundercloud gamma-ray signals, including the flickering gamma-ray flashes (FGFs) as detected by ALOFT [3], indicating that RFD may potentially play a significant role in these phenomena.

 

Here we present a new relativistic fluid model based on the same principles but expanded to include the non-uniformity along the vertical axis, allowing us to explore the effects of more realistic space charge distributions as well as simulating and comparing hard radiation signals from high-field regions with both negative and positive polarities. In addition to solving continuity equations for RRE and ions (as the 0.5D model did), this model also includes equations for positrons as well as upward- and downward-propagating photons, making it possible to estimate the flux of positrons compared to electrons as well as mimicking gamma-ray light-curves directly from the simulated photon density. While the 0.5D model provides excellent qualitative results regarding hard-radiation produced with (or without) the help of RFD, we expect this new model to give better quantitative results, for instance a better idea regarding the minimum charge layer separation distance needed to reproduce ALOFT’s FGFs. With this model, we should also be capable of forward-modelling radio and optical signals, which will make it easier to distinguish (multi-pulse) terrestrial gamma-ray flashes (TGFs) from FGFs. That could ultimately also give us a better insight into whether TGFs could be produced solely by RFD.

 

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[1] Ø. H. Færder, N. Lehtinen, D. Sarria, M. Marisaldi, N. Østgaard, I. Bjørge-Engeland, and A. Mezentsev. Numerical parameter-space studies of various types of thundercloud gamma-ray emissions. ESS Open Archive eprints, 776:essoar.175578737, Aug. 2025. doi:10.22541/essoar.175578737.77602064/v2.

[2] Dwyer, J. R., “Relativistic breakdown in planetary atmospheres,” Physics of Plasmas, vol. 14, no. 4, p. 042901 (2007).

[3] Østgaard, N., Mezentsev, A., Marisaldi, M., Grove, J. E., Quick, M., Christian, H., Cummer, S., Pazos, M., Pu, Y., Stanley, M., et al., “Flickering gamma-ray flashes, the missing link between gamma glows and TGFs”, Nature (2023).