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The LOFAR radio telescope measures air showers in the energy range 1017 to 1018 eV. For each measured shower, the depth of shower maximum Xmax is reconstructed by simulating the radio signal for an ensemble of showers using Corsika and CoREAS. Fitting their radio ‘footprints’ on the ground to the measured radio data yields an Xmax estimate to a precision of about 20 g/cm2 . Compared to previous works, we have improved the method in several ways. Local atmospheric data and refractive index profiles are now included into the simulations. The energy estimate and the fitting procedure are now done using the radio signals only, thus limiting systematic uncertainties due to the particle detector array (LORA). Using selection criteria from a more elaborate characterisation of the radio and particle detection, we reduce a composition bias in the Xmax reconstruction. A possible residual bias has been bounded from above. Thus, the systematic uncertainties on hXmaxi have been lowered, reducing an important limiting factor for composition studies at any level of statistics.

The LOw-Frequency ARray (LOFAR) measures radio emission from extensive air showers. Precise knowledge of the electric field at each antenna in the 30 − 80 MHz range is obtained using a newly developed, frequency-dependent calibration built on knowledge of the Galactic emission and a detailed model of the signal chain. The energy fluence for each event is then determined, allowing for the calculation of the radiation energy of the air shower. The radiation energy, corrected for geometrical effects, scales quadratically with the energy contained in the electromagnetic component of the air shower. These measurements, combined with predictions that rely only on first-principle electrodynamics, provide an energy estimate for the primary particle. In this contribution we present the radio-based energy scale of cosmic rays detected with LOFAR, and compare it to particle-based energy measurements made using the scintillator array located at the LOFAR core.

Estimating the depth of shower maximum Xmax with high precision is of great interest for the study of primary particle composition. One of the systematic uncertainties in reconstructing Xmax from the radio emission of air showers is the limited knowledge of the atmospheric parameters like humidity, pressure, temperature and the index-of refraction. Using the Global Data Assimilation System (GDAS), a global atmospheric model, we have implemented time-dependent realistic atmospheric profiles in the air shower simulation codes CORSIKA and the radio plug-in CoREAS. This program is now available within CORSIKA and flexible to be adapted for different air shower experiments. We have analyzed the LOFAR cosmic ray data with dedicated simulations for each detected air shower with event specific GDAS atmospheres and investigated the effects of pressure and humidity on the reconstructed Xmax. This study shows that for bulk of the events, where the ground pressure is close to US standard atmosphere values, there is a small systematic shift in Xmax that is less than 2 g/cm2 and for very low pressure values the shift is up to 15 g/cm2 .

The detection of astrophysical neutrinos by IceCube has opened a new window for the observation of our universe. The use of antennas for detecting astroparticles has been proven useful and accurate after many years of radio cosmic-ray detections, and will be a valuable asset for increasing the statistics for the detection of neutrinos < 10PeV and reaching out to the highest energies. The radio technique requires realistic and precise simulations of the electric field created after the neutrino interacts with the detector volume, how it propagates through media, and what measurable signal it produces in the detector. With the goal of providing accurate, fast simulations of neutrino-induced electric fields, we have created the NuRadioMC code. It builds on the experience of software used for current radio neutrino and cosmic ray experiments.

Preface 2019 (Instead of an Abstract) On this day, 23 years ago, I received my PhD in astronomy based on this thesis. By a time when the term ‘astroparticle physics’ didn’t even exist, the purpose of this work was to lay down the fundamentals of the propagation of very- and ultra-high energy cosmic rays in photon environments as they are found in extragalactic space (e.g., the cosmic microwave background), but also in the vicinity of potential sources of such cosmic rays. It contains a (by this time) state-of-the-art treatment of photohadronic and photonuclear interactions, plus an attempt to find a simplified description of the stochastic processes governing the propagation of each individual cosmic ray. The idea behind this was to extend the simple continuous differential-equation approach common at these times to a continuous description of moments describing probability distributions, essentially an approximate solution to the Boltzmann-equation governing cosmic ray transport. From today's perspective, I think it is fair to say that my thesis work never reached its main goal, (a) because the intended mathematical description has never been developed to a stage that it became usable, and (b) because the rapid development in computer power has rendered any mathematical approximation to stochastic processes obsolete – nowadays, as anything else, cosmic ray transport is treated in Monte-Carlo simulations. In that respect, immersion into statistics had essentially auto-didactic value, or, as Neil Armstrong didn’t say 50 years ago: a big leap for me, a small step for mankind. For the latter, a much bigger step this thesis had contributed to was that its detailed results on the interaction physics of cosmic ray protons and nuclei have strongly influenced and partly even triggered the development of todays leading Monte-Carlo codes for cosmic-ray interactions and propagation, i.e., SOPHIA [Mücke et al., CoPhC 124 p.290, 2000] and, based on this, CRPropa [Alves Batista et al., JCAP 05 (2016) 038, and references therein]. The reason for making it now, 23 years after its original small-batch publication, part of the Zenodo “Astronomy Thesis Collection” is (i) to honor the special meaning of the number 23 [Rachen & Gahlings, arXiv:1303.7476], (ii) because I feel that it had enough impact on science to belong there, and (iii) because it still contains some interesting approximate treatments of problems where Monte-Carlo methods haven’t gone yet, like photodisintegration of cosmic ray nuclei during Fermi-acceleration in a non-thermal photon-background. I therefore hope that, opened now to a wider audience, it may still catch the interest of the one or other working in astroparticle physics, and if it is only to check out how things were done in the old times. Jörg Rachen, on September 11, 2019