Cosmic-ray photons of energy >5 × ${10}^{19}$ eV will pair produce in the Earth's magnetic field. The electrons radiate by quantum synchrotron radiation; the produced photons may in turn pair produce and continue the cascade. This electromagnetic cascade interacts with the Earth's atmosphere and produces an extensive air shower. Some implications for determining the photon contribution to the highest-energy cosmic rays are discussed.

• Received 8 June 1981

DOI:https://doi.org/10.1103/PhysRevD.24.2536