  The dynamics of relativistic electrons in the intense laser radiation and
quasi-static electromagnetic fields both along and across to the laser
propagating direction are studied in the 3/2 dimensional Hamiltonian framework.
It is shown that the unperturbed oscillations of the relativistic electron in
these electric fields could exhibit a long tail of harmonics which makes an
onset of stochastic electron motion be a primary candidate for electron
heating. The Poincar\'e mappings describing the electron motions in the laser
and electric fields only are derived from which the criterions for instability
are obtained. It follows that for both transverse and longitudinal electric
fields, there exist upper limits of the stochastic electron energy depending on
the laser intensity and electric field strength. Specifically, these maximum
stochastic energies are enhanced by a strong laser intensity but weak electric
field. Such stochastic heating would be reduced by the superluminal phase
velocity in both cases. The impacts of the magnetic fields on the electron
dynamics are different for these two cases and discussed qualitatively. These
analytic results are confirmed by the numerical simulations of solving the 3/2D
Hamiltonian equations directly.
