  Colloidal heat engines extract power out of a fluctuating bath by
manipulating a confined tracer. Considering a self-propelled tracer surrounded
by a bath of passive colloids, we optimize the engine performances based on the
maximum available power. Our approach relies on an adiabatic mean-field
treatment of the bath particles which reduces the many-body description into an
effective tracer dynamics. It leads us to reveal that, when operated at
constant activity, an engine can only produce less maximum power than its
passive counterpart. In contrast, the output power of an isothermal engine,
operating with cyclic variations of the self-propulsion without any passive
equivalent, exhibits an optimum in terms of confinement and activity. Direct
numerical simulations of the microscopic dynamics support the validity of these
results even beyond the mean-field regime, with potential relevance to the
design of experimental engines.
