  We investigate the concept of a standard map for the interaction of
relativistic particles and electrostatic waves of arbitrary amplitudes, under
the action of external magnetic fields. The map is adequate for physical
settings where waves and particles interact impulsively, and allows for a
series of analytical result to be exactly obtained. Unlike the traditional form
of the standard map, the present map is nonlinear in the wave amplitude and
displays a series of peculiar properties. Among these properties we discuss the
relation involving fixed points of the maps and accelerator regimes.
