Periodic Reporting for period 4 - LOFAR (Searching for The Origin of Cosmic Rays and Neutrinos with LOFAR) Reporting period: 2019-12-01 to 2020-11-30 Summary of the context and overall objectives of the project The origin of cosmic rays remains one of the largest mysteries in astrophysics. Innovative and accurate radiomeasurements of cosmic rays and neutrinos with LOFAR promise to provide new answers.It is generally believed that ultra-high-energy cosmic rays are produced in extragalactic sources like gamma-raybursts or active galactic nuclei, while the lower energy cosmic rays come from our own Galaxy. At whatenergy this transition takes place is still unknown. Here we focus on disentangling Galactic and extragalacticcomponents by studying the mass composition between 10^17 and 10^18 eV, a regime that is also crucial forunderstanding the origin of the extraterrestrial neutrinos detected by IceCube.We do this with LOFAR, the first radio telescope that can detect individual cosmic rays with hundreds ofantennas. This incredible level of detail allowed us to finally understand the complicated radiation mechanismand to perform the first-ever accurate mass analysis based on radio measurements. Our first data reveal a strongproton component below 1018 eV, suggesting an early transition to an extragalactic component. With upgradesto our detector and techniques we will be able to improve our sample size by an order of magnitude, resolvemore mass components, and identify the origin of high-energy cosmic rays and neutrinos.The technique may be scaled up to higher energies, measured at the Pierre Auger Observatory, where massinformation is needed to correlate cosmic rays with their astrophysical sources and to confirm the nature of thecutoff at ~10^19.6 eV.We can even search for particles beyond the GZK limit. With the Westerbork telescope we have alreadyset the best limit on cosmic rays and neutrinos above 10^23 eV. With LOFAR we will achieve a much bettersensitivity at lower energies, also probing for new physics, like the decays of cosmic strings predicted bysupersymmetric theories. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far We have performed the first high-precision radio measurements of the mass composition of cosmic rays. The mixed composition is indicative of a complicated transition from galactic to extragalactic origin, that can for example be explained with supernova explosions of very massive stars or re-acceleration of cosmic rays at the galactic wind termination shock.In order to increase the accuracy of this analysis we have improved several aspects. A realistic treatment of the local atmosphere, including weather effects such as air pressure, humidity and index of refraction, was implemented in the air shower simulation code. This allows more precise reconstruction of the atmospheric depth of the shower maximum, which is the key parameter for cosmic-ray composition studies. In addition, an expansion and upgrade to the LORA particle detector array at the LOFAR central core facility was designed and its performance was simulated. The installation is currently in progress. Finally, A thorough re-calibration of the LOFAR low-band antennas using the galactic background low-frequency radio emission was performed. This reduces the uncertainties in the antenna frequency response, and will allow the inclusion of spectral information in the cosmic-ray composition fit.The highest energy particles can be observed by searching for short radio flashes resulting from particles interactions with the Moon. We have developed a real-time GPU-based observation pipeline to search for the ultrashort radio flashes of cosmic rays and neutrinos hitting the Moon. First observations have been performed.To study the origin of the cosmic particles, a cosmic ray acceleration module was implemented in the simulation package CRPropa in order to study the interpretation of cosmic-ray composition measurements. In a first study, we demonstrated how first-order Fermi acceleration can be invoked to explain composition measurements at the highest energies. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) The method that was used to measure the composition of cosmic rays is based on a full two-dimensional treatment of the radio footprint that we developed to make complete use of the information embedded in the complicated radio emission emitted by air showers. Earlier methods did not achieve sufficient accuracy to allow for mass composition analysis. Our method achieves a resolution that is at least as good as the more traditional technique of fluorescence detection. Our publication is Nature represents the first high-accuracy measurement of the cosmic-ray composition based on the radio technique.Improvements on all aspects of the experiment: detector layout, trigger schemes, reconstruction algorithms, and composition analysis are currently ongoing. By the end of the project we will have a more accurate composition measurement based on a larger sample of showers.Our new antenna calibration is based on a calibration on the background noise itself, produced by our Galaxy. This method is completely different from traditional calibration techniques in radio astronomy and offers possibilities to achieve higher accuracy with array-type radio observatories like LOFAR and the future SKA.We have started LOFAR observations of the Moon to search for ultra-high energy particle impacts on the lunar surface. Our search is the first that uses a real-time GPU algorithm and will either produce the most constraining upper limits on cosmic rays and neutrinos ate the highest energies, or a first lunar detection. LOFAR observation of an air shower. A simulation is superimposed on a arial view of the LOFAR core.