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Measuring the radio emission from cosmic ray particle cascades has proven to be a very efficient method to determine their properties such as the mass composition. Efficient modeling of the radio emission from air showers is crucial in order to extract the cosmic ray physics parameters from the measured radio emission. MGMR3D is a fast semi-analytic code that calculates the complete radio footprint, i.e.\ intensity, polarization, and pulse shapes, for a parametrized shower-current density and can be used in a chi-square optimization to fit a given radio data. It is many orders of magnitude faster than its Monte Carlo counterparts. We provide a detailed comparative study of MGMR3D to Monte Carlo simulations, where, with improved parametrizations, the shower maximum $\Xmax$ is found to have very strong agreement with a small dependency on the incoming zenith angle of the shower. Another interesting feature we observe with MGMR3D is sensitivity to the shape of the longitudinal profile in addition to $\Xmax$. This is achieved by probing the distinguishable radio footprint produced by a shower having a different longitudinal profile than usual. Furthermore, for the first time, we show the results of reconstructing shower parameters for LOFAR data using MGMR3D, and obtaining a $\Xmax$ resolution of 22 g/cm$^2$ and energy resolution of 19\%.

The current generation of air shower radio arrays has demonstrated that the atmospheric depth of the shower maximum Xmax can be reconstructed with high accuracy. These experiments are now contributing to mass composition studies in the energy range where a transition from galactic to extragalactic cosmic-ray sources is expected. However, we are still far away from an unambiguous interpretation of the data. Here we propose to use radio measurements to derive a new type of constraint on the mass composition, by reconstructing the shower length L. The low-frequency part of the Square Kilometer Array will have an extremely high antenna density of roughly 60.000 antennas within one square kilometer, and is the perfect site for high-resolution studies of air showers. In this contribution, we discuss the impact of being able to reconstruct L, and the unique contribution that SKA can make to cosmic-ray science., Comment: Proceedings 9th International Workshop on Acoustic and Radio EeV Neutrino Detection Activities - ARENA2022, 7-10 June 2022, Santiago de Compostela, Spain (8 pages)

Analysis of radio signals from cosmic-ray induced air showers has been shown to be a reliable method to extract shower parameters such as primary energy and depth of shower maximum. The required detailed air shower simulations take 1 to 3 days of CPU time per shower for a few hundred antennas. With nearly $60,000$ antennas envisioned to be used for air shower studies at the Square Kilometre Array (SKA), simulating all of these would come at unreasonable costs. We present an interpolation algorithm to reconstruct the full pulse time series at any position in the radio footprint, from a set of antennas simulated on a polar grid. Relying on Fourier series representations and cubic splines, it significantly improves on existing linear methods. We show that simulating about 200 antennas is sufficient for high-precision analysis in the SKA era, including e.g. interferometry which relies on accurate pulse shapes and timings. We therefore propose the interpolation algorithm and its implementation as a useful extension of radio simulation codes, to limit computational effort while retaining accuracy., Comment: 21 pages, 14 figures. Accepted for publication in JINST (Journal of Instrumentation)

We explore the possibilities of measuring the longitudinal profile of individual air showers beyond $X_{\rm max}$ when using very dense radio arrays such as SKA. The low-frequency part of the Square Kilometre Array, to be built in Australia, features an enormous antenna density of about $50,000$ antennas in the inner core region of radius 500 m, with a frequency band from 50 to 350 MHz. From CoREAS simulations, a SKA-Low antenna model plus noise contributions, and adapted LOFAR analysis scripts, we obtain a resolution in the shower maximum $X_{\rm max}$ and energy that is considerably better than at LOFAR. Already from this setup, we show that at least one additional parameter of the longitudinal profile can be measured. This would improve mass composition analysis by measuring an additional composition-dependent quantity. Moreover, it would offer an opportunity to discriminate between the different predictions of hadronic interaction models, hence contributing to hadronic physics at energy levels beyond man-made accelerators., Comment: 8 pages, 6 figures. Presented at ARENA Conference 2022, Santiago de Compostela, Spain

We present an updated cosmic-ray mass composition analysis in the energy range $10^{16.8}$ to $10^{18.3}$ eV from 334 air showers measured with the LOFAR radio telescope, and selected for minimal bias. In this energy range, the origin of cosmic rays is expected to shift from galactic to extragalactic sources. The analysis is based on an improved method to infer the depth of maximum $X_{\rm max}$ of extensive air showers from radio measurements and air shower simulations. We show results of the average and standard deviation of $X_{\rm max}$ versus primary energy, and analyze the $X_{\rm max}$-dataset at distribution level to estimate the cosmic ray mass composition. Our approach uses an unbinned maximum likelihood analysis, making use of existing parametrizations of $X_{\rm max}$-distributions per element. The analysis has been repeated for three main models of hadronic interactions. Results are consistent with a significant light-mass fraction, at best fit $23$ to $39$ $\%$ protons plus helium, depending on the choice of hadronic interaction model. The fraction of intermediate-mass nuclei dominates. This confirms earlier results from LOFAR, with systematic uncertainties on $X_{\rm max}$ now lowered to 7 to $9$ $\mathrm{g/cm^2}$. We find agreement in mass composition compared to results from Pierre Auger Observatory, within statistical and systematic uncertainties. However, in line with earlier LOFAR results, we find a slightly lower average $X_{\rm max}$. The values are in tension with those found at Pierre Auger Observatory, but agree with results from other cosmic ray observatories based in the Northern hemisphere., Comment: 24 pages, 14 figures. Accepted for publication in Phys. Rev. D

With LOFAR we have been able to image the development of lightning flashes with meter-scale accuracy and unprecedented detail. We discuss the primary steps behind our most recent lightning mapping method. To demonstrate the capabilities of our technique we show and interpret images of the first few milliseconds of two intra-cloud flashes. In all our flashes the negative leaders propagate in the charge layer below the main negative charge. Among several interesting features we show that in about 2~ms after initiation the Primary Initial Leader triggers the formation of a multitude (more than ten) negative leaders in a rather confined area of the atmosphere. From these only one or two continue to propagate after about 30~ms to extend over kilometers horizontally while another may propagate back to the initiation point. We also show that normal negative leaders can transition into an initial-leader like state, potentially in the presence of strong electric fields. In addition, we show some initial breakdown pulses that occurred during the primary initial leader, and even during two "secondary" initial leaders that developed out of stepped leaders., Comment: Submitted to Journal of geophysics research: Atmospheres

We use the Low Frequency ARray (LOFAR) to probe the dynamics of the stepping process of negatively-charged plasma channels (negative leaders) in a lightning discharge. We observe that at each step of a leader, multiple pulses of VHF (30~--~80 MHz) radiation are emitted in short-duration bursts ($<10\ \mu$s). This is evidence for streamer formation during corona flashes that occur with each leader step, which has not been observed before in natural lightning and it could help explain X-ray emission from lightning leaders, as X-rays from laboratory leaders tend to be associated with corona flashes. Surprisingly we find that the stepping length is very similar to what was observed near the ground, however with a stepping time that is considerably larger, which as yet is not understood. These results will help to improve lightning propagation models, and eventually lightning protection models., Comment: 5 pages

The limited knowledge of atmospheric parameters like humidity, pressure, temperature, and the index of refraction has been one of the important systematic uncertainties in reconstructing the depth of the shower maximum from the radio emission of air showers. Current air shower Monte Carlo simulation codes like CORSIKA and the radio plug-in CoREAS use various averaged parameterized atmospheres. However, time-dependent and location-specific atmospheric models are needed for the cosmic ray analysis method used for LOFAR data. There, dedicated simulation sets are used for each detected cosmic ray, to take into account the actual atmospheric conditions at the time of the measurement. Using the Global Data Assimilation System (GDAS), a global atmospheric model, we have implemented time-dependent, realistic atmospheric profiles in CORSIKA and CoREAS. We have produced realistic event-specific atmospheres for all air showers measured with LOFAR, an event set spanning several years and many different weather conditions. A complete re-analysis of our data set shows that for the majority of data, our previous correction factor performed rather well; we found only a small systematic shift of 2 g/cm$^2$ in the reconstructed $X_{\rm max}$. However, under extreme weather conditions, for example, very low air pressure, the shift can be up to 15 g/cm$^2$. We provide a correction formula to determine the shift in $X_{\rm max}$ resulting from a comparison of simulations done using the US-Std atmosphere and the GDAS-based atmosphere., Comment: Accepted for publication in Astroparticle Physics. arXiv admin note: text overlap with arXiv:1911.02859

Cosmic rays are routinely measured at LOFAR, both with a dense array of antennas and with the LOFAR Radboud air shower Array (LORA) which is an array of plastic scintillators. In this paper, we present two results relating to the cosmic-ray energy scale of LOFAR. First, we present the reconstruction of cosmic-ray energy using radio and particle techniques along with a discussion of the event-by-event and absolute scale uncertainties. The resulting energies reconstructed with each method are shown to be in good agreement, and because the radio-based reconstructed energy has smaller uncertainty on an event-to-event basis, LOFAR analyses will use that technique in the future. Second, we present the radiation energy of air showers measured at LOFAR and demonstrate how radiation energy can be used to compare the energy scales of different experiments. The radiation energy scales quadratically with the electromagnetic energy in an air shower, which can in turn be related to the energy of the primary particle. Once the local magnetic field is accounted for, the radiation energy allows for a direct comparison between the LORA particle-based energy scale and that of the Pierre Auger Observatory. They are shown to agree to within (6$\pm$20)% for a radiation energy of 1 MeV, where the uncertainty on the comparison is dominated by the antenna calibrations of each experiment. This study motivates the development of a portable radio array which will be used to cross-calibrate the energy scales of different experiments using radiation energy and the same antennas, thereby significantly reducing the uncertainty on the comparison.