  The radiation force on a single electron in an ultraintense plane wave ($a =
eE/mc\omega \sim 1$) is calculated and shown to be proportional to $a^4$ in the
high-$a$ limit for arbitrary waveform and polarization. The cyclotron motion of
an electron in a constant magnetic field and an ultraintense plane wave is
numerically found to be quasiperiodic even in the high-$a$ limit if the
magnetic field is not too strong, as suggested by previous analytical work. A
strong magnetic field causes highly chaotic electron motion and the boundary of
the highly chaotic region of parameter space is determined numerically.
Applications to experiments and astrophysics are briefly discussed.
