  We analyze the behavior of a relativistic particle moving under the influence
of a uniform magnetic field and a stationary electrostatic wave. We work with a
set of pulsed waves that allows us to obtain an exact map for the system. We
also use a method of control for near-integrable Hamiltonians that consists in
the addition of a small and simple control term to the system. This control
term creates invariant tori in phase space that prevent chaos from spreading to
large regions and make the controlled dynamics more regular. We show
numerically that the control term just slightly modifies the system but is able
to drastically reduce chaos with a low additional cost of energy. Moreover, we
discuss how the control of chaos and the consequent recovery of regular
trajectories in phase space are useful to improve regular particle
acceleration.
