  On the basis of the Lorentz equations of motion, the orbit of a charge driven
by a generic E.M. field with planar symmetry is formulated and analyzed within
the framework of a Lorentzian geometry with a curvature whose order of
magnitude is parametrized by the radiation intensity and frequency. This
reformulation leads to (i) a demonstration of the integrability of the particle
motion in a plane-wave field as a result of the vanishing of the curvature,
(ii) a manifestation of the parametric dependence of the dynamical response of
the particle orbit to the E.M. field on the impulse factor in terms of local
stability and the occurrence of parametric resonance and (iii) a mathematically
precise meaning to the ponderomotive oscillation center of the charge executing
oscillatory motion in a sufficiently low impulsive E.M. field, which is
subsequently used to raise (iv) a discussion of the domain of applicability of
the ponderomotive approximation.
