| 20 May 2026
Relativistic runaway electron avalanches: unified density-dependent scaling and transport
Abstract. Relativistic runaway electron avalanches (RREA) play a key role in producing high-energy radiation in thunderstorm environments, yet their quantitative description remains largely empirical, with limited validation across atmospheric conditions. In this work, we develop a unified framework that consistently describes both avalanche development within the electric field and particle propagation beyond it, using CORSIKA simulations at four high-altitude stations spanning a wide range of atmospheric densities. We show that the classical relation for avalanche length requires revision: the empirical coefficient K is not universal but varies systematically with atmospheric density. Introducing density-dependent scaling yields a consistent description of avalanche growth across all sites. At the same time, we identify an effective energy-partition coefficient, calibrated at a characteristic propagation scale of 100 m, which remains stable across all stations and reflects the available propagation after exiting a strong acceleration field. The results demonstrate that RREA can be described as a two-stage physical system that links density-dependent avalanche growth with density-dependent particle transport via a universal energy-partition mechanism. This framework provides a compact and physically transparent basis for interpreting high-energy atmospheric phenomena across altitudes.
The manuscript addresses a central problem in high-energy atmospheric physics: how relativisticrunaway electron avalanches develop in thunderstorm electric fields and how the resulting particlespropagate after leaving the acceleration region. Its focus is on obtaining a compact, density-awaredescription of RREA growth and linking it to post-field particle transport in a single simulation-basedframework.
The specific contribution of the paper is a CORSIKA-based empirical framework that treats twoconnected stages together: avalanche multiplication inside the electric field and subsequent particletransport below the field region. This integrated treatment is a useful organizing idea.
The strongest result is the proposed density-dependent correction to the avalanche-length scaling.Within the author’s simulations, this correction substantially reduces the scatter between different high-altitude stations and gives a more consistent description of avalanche development across differentatmospheric densities. The second important result is the calibration of an effective electron–gammaenergy-partition parameter for the transport stage, which links the particle spectra at the fieldboundary to the detector level.
The main achievement is therefore practical unification: the paper provides a simple parameterizationfor altitude- and density-dependent avalanche growth, coupled to a compact estimate of post-fieldtransport. This is much simpler than constructing a full storm-field model and may be useful for first-order interpretation of high-altitude TGE or gamma-ray glow observations and exploratory modeling.The trade-off is that such simplicity inevitably reduces event-specific accuracy, especially when the goalis to reconstruct the actual source geometry, infer the detailed electric-field structure, or interpretindividual observed spectra quantitatively.
The main limitation is that the degree of universality remains insufficiently demonstrated. The resultsare based on four high-altitude station configurations, one simulation framework, idealized verticallyuniform electric-field layers, and a fixed post-field propagation distance. These assumptions arereasonable for a controlled scaling study, but they are much simpler than real thunderstormenvironments, where electric fields are nonuniform, time-dependent, and often organized in complexmulti-cell structures.
Several additions would considerably strengthen the result: comparison with other Monte Carlo tools,more explicit uncertainty estimates for the fitted parameters, sensitivity tests to field geometry andfitting range, analysis of different post-field gap lengths, and validation against observed TGE orgamma-ray glow spectra. Such checks would make the proposed scaling more robust, better calibrated,and more clearly positioned relative to existing RREA parameterizations.
A minor stylistic point is that the manuscript is written by a single author but frequently uses collectiveformulations such as “we show” and “we develop.” Replacing these phrases with passive constructionsor formulations such as “this work shows” would improve stylistic clarity.
Overall, this is a useful parameterization study with two clear strengths: it links avalanche growth andparticle transport within a single framework, and it explicitly accounts for the role of atmosphericdensity in the avalanche-length scaling. Its main vulnerability is that the fitted relations are stilldemonstrated mainly within a controlled CORSIKA setup. The paper would be stronger if the proposeddensity correction and transport coefficient were tested across broader geometries, propagationdistances, simulation tools, and observational constraints.