The lightning flashes used in this work were mapped using data from the LO-FAR (LOw Frequency ARray) radio telescope. Due to its effective lightning protection system, LOFAR is able to continue to operate during thunderstorm activity[1]. The Dutch LOFAR stations consist of 38 (24 core + 14 remote) stations spread over 3200 km 2 in the northern Netherlands. The largest baseline between core stations is about 3 km, the largest baseline between remote stations is about 100 km. From each station we use 6 dual-polarized low band dipole antennas (LBA), sampled at 200 MHz, to observe the 30-80 MHz band. The raw time series data were saved to the transient buffer boards, which continuously buffer the last 5 s of data from a maximum of 48 dual-polarized antennas per station. The resulting relative timing accuracy is better than 1 ns. See [2] for more details on LOFAR. When a lightning flash occurs within the area enclosed by the Dutch LOFAR stations, as observed by www.lightningmaps.org, the transient buffer boards are stopped and the data is read to disk. The method we used to map each lightning flash has three major steps. In the first step we fitted plane-waves to the time of pulses received by individual LOFAR stations. Note that the LOFAR stations are less than 100 m in diameter and the lighting is many kilometers from the closest LOFAR station, so that a plane-wave approximation is very good for individual LOFAR stations. These plane-waves were used to identify non-functional antennas, and the intersection of their arrival directions gave a rough first estimate of the flash location, accurate to a few kilometers. Since each station has its own clock and cable delays, in the second step we found the clock offsets between the different LOFAR stations by simultaneously fitting the locations of multiple events and station clock offsets to the measured times of radio pulses, with a Levenberg-Marquardt minimizer. In order to achieve the highest precision, we chose to fit locations of 5 events that created pulses that were strong but not saturating, had a simple structure, and did not change shape significantly across different stations. After fitting, the root-mean-square difference between the modeled and measured arrival times of the radio pulses was around 1 ns. The resulting station clock offsets are consistent with LOFAR station clock calibrations, which are known

The mass composition of cosmic rays contains important clues about their origin. Accurate measurements are needed to resolve longstanding issues such as the transition from Galactic to extraGalactic origin and the nature of the cutoff observed at the highest energies. Composition can be studied by measuring the atmospheric depth of the shower maximum X max of air showers generated by high-energy cosmic rays hitting the Earth's atmosphere. We present a new method to reconstruct X max based on radio measurements. The radio emission mechanism of air showers is a complex process that creates an asymmetric intensity pattern on the ground. The shape of this pattern strongly depends on the longitudinal development of the shower. We reconstruct X max by fitting two-dimensional intensity profiles, simulated with CoREAS, to data from the Low Frequency Array (LOFAR) radio telescope. In the dense LOFAR core, air showers are detected by hundreds of antennas simultaneously. The simulations fit the data very well, indicating that the radiation mechanism is now well understood. The typical uncertainty on the reconstruction of X max for LOFAR showers is 17 g=cm 2 .

4Cosmic rays are the highest energy particles found in nature. Measurements of the mass composition of cosmic rays between 10 17 eV and 10 18 eV are essential to understand whether this energy range is dominated by Galactic or extragalactic sources. It has also been proposed that the astrophysical neutrino signal 1 comes from accelerators capable of producing cosmic rays of these energies 2 . Cosmic rays initiate cascades of secondary particles (air showers) in the atmosphere and their masses are inferred from measurements of the atmospheric depth of the shower maximum, X max 3 , or the composition of shower particles reaching the ground 4 .Current measurements 5 suffer from either low precision, and/or a low duty cycle. Radio detection of cosmic rays 6-8 is a rapidly developing technique 9 , suitable for determination of X max 10, 11 with a duty cycle of in principle nearly 100%. The radiation is generated by the separation of relativistic charged particles in the geomagnetic field and a negative charge excess in the shower front 6, 12 . Here we report radio measurements of X max with a mean precision of 16 g/cm 2 between 10 17 − 10 17.5 eV. Because of the high resolution in X max we can determine the mass spectrum and find a mixed composition, containing a light mass fraction of ∼ 80%. Unless the extragalactic component becomes significant already below 10 17.5 eV, our measurements indicate an additional Galactic component dominating at this energy range.Observations were made with the Low Frequency Array (LOFAR 13 ), a radio telescope consisting of thousands of crossed dipoles, with built-in air shower detection capability 14 . LOFAR records the radio signals from air showers continuously while running astronomical observations simultaneously. It comprises a scintillator array (LORA), that triggers the readout of buffers, stor-5 ing the full waveforms received by all antennas.We have selected air showers from the period June 2011 -January 2015 with radio pulses in at least 192 antennas. The total uptime was ∼150 days, limited by construction and commissioning of the telescope. Showers that occurred within an hour from lightning activity, or have a polarisation pattern that is indicative of influences from atmospheric electric fields are excluded from the sample 15 .Radio intensity patterns from air showers are asymmetric due to the interference between geomagnetic and charge excess radiation. They can be reproduced from first principles by summing the radio contributions of all electrons and positrons in the shower. We use the radio simulation code CoREAS 16 , a plug-in of CORSIKA 17 , which follows this approach.It has been shown that X max can be accurately reconstructed from densely sampled radio measurements 18 . We use a hybrid approach, simultaneously fitting the radio and particle data. The radio component is very sensitive to X max , while the particle component is used for the energy measurement.The fit contains four free parameters: the shower core position (x, y), and scaling factors for the partic...

Abstract. We present LOFAR measurements of radio emission from extensive air showers.We find that this emission is strongly polarized, with a median degree of polarization of nearly 99%, and that the angle between the polarization direction of the electric field and the Lorentz force acting on the particles, depends on the observer location in the shower plane. This can be understood as a superposition of the radially polarized charge-excess emission mechanism, first proposed by Askaryan and the geomagnetic emission mechanism proposed by Kahn and Lerche. We calculate the relative strengths of both contributions, as quantified by the charge-excess fraction, for 163 individual air showers. We find that the measured charge-excess fraction is higher for air showers arriving from closer to the zenith. Furthermore, the measured charge-excess fraction also increases with increasing observer distance from the air shower symmetry axis. The measured values range from (3.3 ± 1.0)% for very inclined air showers at 25 m to (20.3 ± 1.3)% for almost vertical showers at 225 m. Both dependencies are in qualitative agreement with theoretical predictions.

Abstract. The pattern of the radio emission of air showers is finely sampled with the LowFrequency ARray (LOFAR). A set of 382 measured air showers is used to test a fast, analytic parameterization of the distribution of pulse powers. Using this parameterization we are able to reconstruct the shower axis and give estimators for the energy of the air shower as well as the distance to the shower maximum.