  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. 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 1970's. 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. (abridged)
