A parameter-space exploration of the Relativistic Discharge Model mapping for which conditions ALOFT’s Flickering Gamma-ray Flashes are produced

During the ALOFT flight campaign, July 2023, a novel type of multi-pulse gamma-ray emission from thunderclouds was systematically recorded. Referred to as flickering gamma-ray flashes (FGFs), this type of emission is not linked with lightning leaders and does not coincide with detectable radio emissions [1].

A promising candidate theory for explaining this phenomenon is the relativistic feedback discharge (RFD) developed by Dr. J. Dwyer and his group [2]. Fully self-consistent 3D Monte-Carlo calculations of RFD [3], which take the field quenching by produced currents into account, are quite computationally intensive. In fact, the full physics of RFD has barely been explored outside Dwyer’s group.

Therefore, we developed an independent numerical model especially made to evaluate the capability of the RFD theory to reproduce FGFs. Despite its simplification into a set of spatially-independent ordinary differential equations (ODEs), it applies the most relevant physics: ionisation, electron dynamics, attachment processes, relativistic runaway electron avalanche (RREA), and feedback akin to Dwyer’s theory. The ODEs that we end up solving are analogous to a complexified Lotka-Volterra model which describes a system with oscillations.

In this presentation, we introduce a 0.5D model (i.e., with indirect account of the spatial size of the RREA region) and demonstrate its ability to reproduce emission light curves very alike FGFs under realistic conditions, given the right set of parameters (see below). Furthermore, we show that the same model also reproduces light curves alike terrestrial gamma-ray flashes (TGFs, both single and multiple pulses) and gamma-ray glows (GRGs) for different sets of parameters but still under realistic conditions, hence proving this model to be even more general than originally intended.

With this, we performed a parameter-space exploration, using our model and systematically applying different values for 1) the initial (background) internal electric field strength of the cloud, 2) the characteristic growth time of the external electric field, 3) the vertical size of the high-field region in the cloud, and 4) the maximum change of the external field. The results, as shown in parameter-space diagrams, are qualitatively as expected. TGFs tend to occur for relatively small high-field regions. For larger high-field regions, the model reproduces GRGs in the case of slowly increasing external fields while FGFs and weak TGFs in the case of rapidly increasing external fields. The amplitude and the number of pulses typically scale with the maximum change of the external field. Finally, increasing the value of the initial internal electric field leads to a decrease in the minimum required change in the external field needed to reproduce FGFs, multi-pulse TGFs and GRGs.

 

References:

[1] 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).

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

[3] Liu, N., Dwyer, D., “Modeling terrestrial gamma ray flashes produced by relativistic feedback discharges”, Journal of Geophysical Research (Space Physics), Vol. 118, no. 5, p. 2359-2376 (2013)