  Depending on their mechanism of self-propulsion, active particles can exhibit
a time-dependent, often periodic, propulsion velocity. The precise propulsion
velocity profile determines their mean square displacement and their effective
diffusion coefficient at long times. Here we demonstrate that any periodic
propulsion profile results in a larger diffusion coefficient than the
corresponding case with constant propulsion velocity. We investigate in detail
the case of periodic exponentially decaying velocity pulses, expected in
propulsion mechanisms based on sudden absorption of finite amounts of energy.
We show both analytically and with numerical simulations that in these cases
the effective diffusion coefficient can be arbitrarily enhanced with respect to
the case with constant velocity equal to the average speed. Our results may
help interpret in a new light observations on the diffusion enhancement of
active particles.
