The origin and nature of the highest energy cosmic ray events is currently the subject of intense investigation by giant air shower arrays and fluorescent detectors. These particles reach energies well beyond what can be achieved in ground-based particle accelerators and hence they are fundamental probes for particle physics as well as astrophysics. One of the main topics today focuses on the high energy end of the spectrum and the potential for the production of high-energy neutrinos. Above about 10 20 eV cosmic rays from extragalactic sources are expected to be severely attenuated by pion photoproduction interactions with photons of the cosmic microwave background. Investigating the shape of the cosmic ray spectrum near this predicted cut-off will be very important. In addition, a significant high-energy neutrino background is naturally expected as part of the pion decay chain which also contains much information. Because of the scarcity of these high-energy particles, larger and larger ground-based detectors have been built. The new generation of digital radio telescopes may play an important role in this, if properly designed. Radio detection of cosmic ray showers has a long history but was abandoned in the 1970s. Recent experimental developments together with sophisticated air shower simulations incorporating radio emission give a clearer understanding of the relationship between the air shower parameters and the radio signal, and have led to resurgence in its use. Observations of air showers by the SKA could, because of its large collecting area, contribute significantly to measuring the cosmic ray spectrum at the highest energies. Because of the large surface area of the moon, and the expected excellent angular resolution of the SKA, using the SKA to detect radio Cherenkov emission from neutrino-induced cascades in lunar regolith will be potentially the most important technique for investigating cosmic ray origin at energies above the photoproduction cut-off.
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