Signal model for the radio emission of inclined cosmic-ray air-showers and energy reconstruction of event candidates for GRAND

Ultra-high-energy cosmic rays (UHECRs) originate from the most energetic and mysterious environments in the Universe. When UHECRs reach Earth, they collide with nuclei in the atmosphere, and induce massive particle cascades. Due to their rarity, we can only measure them with large surface detectors. The Giant Radio Array for Neutrino Detection (GRAND) will, next to its main goal of measuring UHE neutrinos, also be especially sensitive to inclined air showers induced by UHECRs. I use CoREAS simulations of the radio emission of inclined air-showers to adapt a previously developed signal model for this phenomenon in the 30–80 MHz frequency band to the 50–200 MHz band used by GRAND. I tune the model for the site of the GRAND prototypes GRAND@Auger, located at the Pierre Auger Observatory in Argentina, and GRANDProto300 (GP300) in the Gansu province of China. I reconstruct the geomagnetic radiation energy by fitting a lateral distribution function to the radially symmetric distribution of the energy deposited in the ground. After I correct for the air-density and geomagnetic field dependence, I correlate the radiation energy with the electromagnetic shower energy. The radio emission of air-showers changes significantly depending on parameters like frequency, geomagnetic field, and observation altitude. With the modifications I introduce to the model, I expect it to be viable for any configuration of the geomagnetic field, as well as lower and higher frequency bands by simply retuning the model parameters. With this work, I provide the first end-to-end event reconstruction for GRAND, including the reconstruction of the electric field from measured data, as well as a solid basis for the analysis of future GRAND measurements. The reconstruction achieves an intrinsic energy resolution better than 5% for the sites of GRAND@Auger and GP300. I benchmark the reconstruction by simulating the sparse antenna layouts of GP300 and GRAND10k, a future stage of GRAND with a 10,000 km2 detection area. Under realistic measurement conditions, the reconstruction achieves an excellent energy resolution of 7% with vanishing biases for both detectors. The reconstruction shows no inherent dependence on the cosmic-ray primary particle. I successfully apply the energy reconstruction to six of the first GRAND cosmic-ray event candidates, measured by a partial configuration of GP300. The reconstructed energies agree with expectations. Furthermore, I study the detection efficiency of GP300 and GRAND10k. I estimate for both detectors the rate of detected and reconstructed cosmic ray events. I expect GP300 and GRAND10k, respectively, to measure about 2000 and 85,000 cosmic-ray events with energies > 1018 eV within one year of exposure time. I predict that a detector like GRAND10k will detect at least 10 UHECR events with energies > 1019.75 eV within the same time period.