Measuring High-Energy Cosmic Particles with the SKA

The origin of high-energy cosmic rays remain one of astrophysics' greatest unsolved mysteries. SKA-Low will be able to measure air showers initiated by cosmic rays with unprecedented precision in the PeV - EeV energy range, covering the critical transition region between Galactic and extragalactic sources. SKA-Low's densely instrumented core and broad bandwidth will allow for measurements of individual air showers with a level of detail unmatched by any existing or planned detector. The depth of shower maximum, the primary mass-sensitive observable, will be reconstructed with a resolution of better than 8~g/cm$^2$, a significant improvement over existing methods. Additionally, new reconstruction methods are expected to enable full air shower reconstruction across a wide energy range, down to PeV levels. At these energies, efficient photon/hadron separation may offer an opportunity to measure PeV gamma-ray air showers. Furthermore, SKA-Low opens a window into studying high-energy hadronic interactions, including via the unique channel of anomalous air showers. This combination of measurements provides a unique opportunity to investigate the origins and physics of high-energy cosmic rays. A dedicated particle detector array will provide triggered readout of raw antenna-level voltage buffers, enabling fully commensal cosmic-ray observations alongside regular operations. We outline our science case and discuss the observational strategy, signal properties and detector design underpinning these measurements. We also summarize the accompanying book chapters, which address composition measurements in the Galactic-to-extragalactic transition region, next-generation interferometric reconstruction techniques, hadronic interaction physics through anomalous air showers, the prospects for detecting PeV gamma-rays from Galactic sources, and the related project of imaging lightning using SKA-Low.