NuRadioMC is a framework for the simulation of ultra-high-energy neutrino detectors that measure the radio signal emitted in neutrino-induced particle cascades used in different radio neutrino experiments. We present an extension to the analytic raytracing method for multilayered exponential refractive index models, where the full refractive index profile is described by a set of different single-exponential layers, supporting realistic medium descriptions at various experiment sites while maintaining computational efficiency. This approach also enables a realistic exponential refractive index description of the atmosphere and allows us to model signal propagation over non-smooth changes in the refractive index. This report outlines the fundamentals of the multilayered analytic raytracing method and shows some applied examples.

Double-bump showers are a surprising class of extensive air showers (EAS) predicted by Monte Carlo simulations, which, so far, no experiment has been able to directly detect. They occur when a high-energy secondary particle, the leading particle, travels significantly farther than the rest, creating a distinct double-peaked longitudinal profile. The unique radio footprint of double-bump showers, characterized by multiple pulses in the signals and interference patterns in the frequency spectra, enables reconstruction of longitudinal profiles from radio observations. With its dense antenna array and broad frequency range, SKA-Low will be the first observatory capable of detecting these features, offering a new opportunity to probe hadronic interactions and use the distinctive signatures of elements to provide new mass composition measurements. The goal of this analysis is to take the first steps toward using these radio signatures to reconstruct the relevant parameters of the longitudinal profile of a double-bump shower. We will start by explaining the radio signal of double-bump}showers compared to that of average showers. Then we will create a simple 2-point emission model to explain the interference patterns in the frequency spectra, which can be inverted to obtain rudimentary estimates of atmospheric depth of both peaks. Lastly, we implement a brute-force approach to reconstruct multiple parameters of the double bump.

The identification of the sources and acceleration mechanisms of cosmic rays require precise measurements of their mass composition. Currently, the most reliable method is to measure the atmospheric depth at which cosmic ray air showers in our atmosphere reach their maximum (). However, the hadronic interaction properties that govern the longitudinal development of air showers are not precisely known, which is a major source of systematic uncertainty on the mass composition. SKA-Low will observe cosmic rays in the 10^16 - 10^18 eV energy range with unprecedented resolution and bandwidth. This allows for a much more detailed reconstruction of the longitudinal shower evolution, which can be used to gain better understanding of the hadronic interactions, as well as the primary mass composition. After the first interaction of the cosmic ray with an atom in an air molecule, the secondary particles still carry a significant fraction of the total energy. When one of these particle travels very far before interacting again, it produces a sub-shower that can be recognized as a secondary bump in the longitudinal profile. Simulations have demonstrated that SKA-Low can resolve such double bump profiles by virtue of its high antenna density and broad bandwidth. In this chapter, we demonstrate how double-bump showers and other anomalous longitudinal developments can be used to constrain hadronic interaction properties, and to determine the mass composition of cosmic rays in the Galactic-to-extragalactic transition region.

Current reconstruction techniques for air-shower radio emission generated by cosmic rays have shown great success, having been applied to several radio detectors over the last decade. Nevertheless, they are limited by their high computational cost, simplified approximations, and signal information used for reconstruction. As such, advanced analyses are required to not only be able to perform a holistic reconstruction of all parameters, but also to conduct near-field interferometry of the air shower. This can be achieved through Information Field Theory (IFT), an imaging reconstruction framework based on Bayesian inference that can extract all available information within the signal to infer distributions of field-like quantities. In this chapter, we highlight current novel approaches that use IFT for air shower reconstruction, and the potential of their applicability towards SKA-Low.

Decades of observations inside thunderclouds have failed to measure electric fields large enough to spontaneously initiate a spark. The initiation process of lightning is thus an open question. We present comprehensive observations of the breakdown processes occurring at initiation for several lightning flashes using very high frequency (VHF) radio observations made using the LOFAR radio telescope. We confirm earlier observations that lightning often initiates with a rapidly propagating positive discharge, followed by the formation of a negative leader. The observations show that while the propagation speeds of the positive initiating event (PIE) are nearly constant at about 5×10^6 m/s, both the e-folding rates in VHF-intensity and peak intensities differ significantly and show no correlation with altitude. Additionally, these structures are extremely narrow, with diameters under 0.8 meters, and maintain this confinement over propagation distances exceeding 100 meters. By tracing the tracks of subsequent dart leaders we show the PIE did not form a hot conductive structure.

The radio detection of extensive air showers provides a powerful method for studying the origin of high-energy cosmic rays. The Low-Frequency Array (LOFAR) offers unprecedentedly detailed measurements of the radio emission footprint. However, fully exploiting this information requires advanced reconstruction techniques. In this paper, we introduce a novel framework for air shower reconstruction based on Bayesian inference and Information Field Theory (IFT). Our method is built on a fully differentiable forward model of the radio signal, which incorporates a physical emission parameterization and a precise wavefront model. Additionally, we augment this physical model with Gaussian processes to account for systematic uncertainties in both the signal fluence and arrival timing. By leveraging gradient information, our approach enables efficient (three orders of magnitude acceleration w.r.t. the legacy method) and robust inference of the underlying physical shower parameters, such as primary energy and the depth of shower maximum, X_max. This work provides not only point estimates but also a rigorous quantification of uncertainties. We achieve a resolution in X_max of 25 g/cm^2 and a radiation energy resolution of 12% on simulations for LOFAR.

Lightning is a surprisingly poorly understood phenomena. It consists of a wide variety of complex processes such as initiation, propagation, connection to ground, even emission of high-energy radiation. However, due to the extreme challenges in observing lightning at fast time scales, small spatial scales, and behind obscuring clouds, these processes are not well understood. In the past, interferometers such as the LOFAR radio telescope have provided unique insight and discoveries into the physics of lightning. The new SKA-LOW being built in western Australia will provide unrivaled spectral bandwidth and sensitivity, which will be combined with high resolution resulting from large antenna baselines. We will use SKA-LOW to observe lightning in order to explore its fundamental plasma physics, such as how it initiates and propagates. SKA's high bandwidth will allow us to test how lightning emits VHF radiation, giving tremendous insight into precisely how the plasma behaves. SKA's sensitivity will allow us to explore extremely faint lightning processes, such as the very first radio emission from a lightning flash. Here, we detail the lightning physics that can be explored with SKA, as well as the observation strategy needed explore such physics.

The origin of high-energy cosmic rays remain one of astrophysics' greatest unsolved mysteries. SKA-Low will be able to measure air showers initiated by cosmic rays with unprecedented precision in the PeV - EeV energy range, covering the critical transition region between Galactic and extragalactic sources. SKA-Low's densely instrumented core and broad bandwidth will allow for measurements of individual air showers with a level of detail unmatched by any existing or planned detector. The depth of shower maximum, the primary mass-sensitive observable, will be reconstructed with a resolution of better than 8 g/cm^2, a significant improvement over existing methods. Additionally, new reconstruction methods are expected to enable full air shower reconstruction across a wide energy range, down to PeV levels. At these energies, efficient photon/hadron separation may offer an opportunity to measure PeV gamma-ray air showers. Furthermore, SKA-Low opens a window into studying high-energy hadronic interactions, including via the unique channel of anomalous air showers. This combination of measurements provides a unique opportunity to investigate the origins and physics of high-energy cosmic rays. A dedicated particle detector array will provide triggered readout of raw antenna-level voltage buffers, enabling fully commensal cosmic-ray observations alongside regular operations. We outline our science case and discuss the observational strategy, signal properties and detector design underpinning these measurements. We also summarize the accompanying book chapters, which address composition measurements in the Galactic-to-extragalactic transition region, next-generation interferometric reconstruction techniques, hadronic interaction physics through anomalous air showers, the prospects for detecting PeV gamma-rays from Galactic sources, and the related project of imaging lightning using SKA-Low.

The Radio Neutrino Observatory-Greenland (RNO-G, at Summit Station) experiment comprises an extensive fat-dipole antenna array deployed into ice boreholes over an eventual area of approximately 35 km2. Since the RNO-G experimental sensitivity depends on the radio-frequency properties of the firn, which are known to vary laterally on sub-km distance scales and vertically on sub-meter distance scales, a technique for quickly extracting information on firn ice properties with depth ( $n(z)$) during drilling and deployment is desirable. Given that a dipole's resonant wavelength is fixed by geometry, the resonant frequency $f_{res}$ (measured as an S-parameter reflection coefficient [' $S_{11}$'] minimum) scales inversely with the local refractive index, allowing a translation of a depth-dependent $S_{11}$(z) profile into $n(z)$. $S_{11}$(z) data were initially taken in August 2024 using a dipole lowered into a newly drilled 98 +/- 1 mm diameter, 350 m deep borehole at Summit Station, Greenland, approximately 1 km from the site of the original GISP-2 core; improved measurements were subsequently made in May 2025. We conclude that $S_{11}$(z) data can be used to estimate $n(z)$, on 50 cm vertical scales, at the per cent level of accuracy required by experiments such as RN0-G.

While radio measurements of extensive air showers have shown to achieve a high precision of X_max sensitivity, it has been shown that parameters beyond X_max can also be reconstructed. These shape parameters contain additional sensitivity to the hadronic physics in the shower as well as its mass composition. In this work, we showcase a reconstruction framework to recover the full longitudinal profile from realistic radio measurements. The framework is based on Information Field Theory that infers the full profile with a forward-based model, which uses a Gaisser-Hillas profile with weakly informative shower priors, SMIET with a template library to synthesise pulses at any event geometry, and a realistic antenna response and noise level emulating that of SKA-Low. We verify the self-consistency of our framework with ∼ 900 events generated with SMIET with antennas placed on the v⃗× (v⃗×B⃗) axis. The framework recovers the full profile within uncertainty and capture correlations between shower parameters. We yield an X_max resolution of < 9 g cm^-2 as well as resolutions of the width and asymmetry with minimal bias. The profile is also recovered with a bias of < 4