  A Tevatron is an accelerator capable of imparting TeV energies to particles
like a proton (1 TeV = $10^{12}$ eV). By analogy, a Zevatron is an accelerator
scheme envisaged to accelerate particles to ZeV energies (1 ZeV = $10^{21}$
eV). Zevatron schemes have been proposed to explain the acceleration of
ultra-high-energy-cosmic-ray (UHECR) particles detected on Earth since 1962.
Here we show that nuclei of hydrogen, helium, and iron-56, may be accelerated
to ZeV energies, if injected along the common direction of an existing
ultra-strong magnetic field and a super-intense radiation field. This can
happen if the injection speed, the magnetic field strength, the charge-to-mass
ratio of the nucleus, and the radiation field frequency, are such that an
auto-resonance condition is fulfilled, whereby the cyclotron frequency of the
particle, around the magnetic field lines, matches the Doppler-shifted
frequency of the radiation field.
