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We investigate the concept of a standard map for the interaction ofrelativistic particles and electrostatic waves of arbitrary amplitudes, underthe action of external magnetic fields. The map is adequate for physicalsettings where waves and particles interact impulsively, and allows for aseries of analytical result to be exactly obtained. Unlike the traditional formof the standard map, the present map is nonlinear in the wave amplitude anddisplays a series of peculiar properties. Among these properties we discuss therelation involving fixed points of the maps and accelerator regimes.

Standard map in magnetized relativistic systems: fixed points and regular acceleration