  A Zevatron is an accelerator scheme envisaged to accelerate particles to ZeV
energies (1 ZeV = $10^{21}$ eV). Schemes, most notably the internal shock
model, have been proposed to explain the acceleration of ultra-high-energy
cosmic-ray (UHECR) particles that have been sporadically detected reaching
Earth since 1962. Here, the cyclotron auto-resonance acceleration (CARA)
mechanism is tailored and used to demonstrate possible acceleration of
particles ejected as a result of violent astrophysical processes such as the
merger of a binary system or a supernova explosion. Such events result in
emission of highly-energetic particles and ultra-intense beamed radiation. In
the simultaneous presence of a super-strong magnetic field, the condition for
cyclotron auto-resonance may be met. Thus CARA can act like a {\it booster} for
particles pre-accelerated inside their progenitor by shock waves, possibly
among other means. As examples, it is shown that nuclei of hydrogen, helium,
and iron-56, may reach ZeV energies by CARA, under which conditions the
particles, while gyrating around the lines of an ultra-strong magnetic field,
also surf on the waves of a super-intense radiation field. When
radiation-reaction is taken into account, it is shown that the ZeV energy
gained by a particle can fall off by less than an order-of-magnitude if the
resonance condition is missed by roughly less than 20\%.
