  Employing a two-parameter model for representing the radiation field, the
theory of cosmic-ray acceleration by cyclotron autoresonance is analytically
generalized here to include any state of polarization. The equations are
derived rigorously and used to investigate the dynamics of the nuclides
$_1$H$^1$, $_2$He$^4$, $_{26}$Fe$^{56}$, and $_{28}$Ni$^{62}$, in severe
astrophysical conditions. Single-particle calculations and many-particle
simulations show that these nuclides can reach ZeV energies ($1 ~ZeV = 10^{21}$
eV) due to interaction with superintense radiation of wavelengths $\lambda=1~$
and $10~ \mu$m, and $\lambda=50$ pm, and magnetic fields of strengths at the
mega- and gigatesla levels. Examples employing radiation intensities in the
range $10^{32}-10^{42}$ W/m$^2$ are discussed.

High Energy Astrophysical Phenomena