  The phenomenon of resonant energization of a relativistic quantum particle,
moving in unison with an intense ElectroMagnetic Wave, is demonstrated in a
semiclassical calculation. The wave nature of the quantum particle is of
essence because the resonant process originates in wave-wave
interaction-between the classical EM wave, and the quantum wave associated with
the particle. When the energy /momentum of the quantum wave satisfy the
resonance condition (the effective phase speeds of the two waves are equal),
the particle, drawing energy directly from the intense EM field, could acquire
extremely high energies Such a direct resonant energy transfer from intense
Electromagnetic waves will constitute a hitherto unexploited mechanism that
could power the most energetic of cosmic rays. Some predictions of the theory
will, hopefully, be tested in the laboratory Laser experiments.
