  We investigate the properties of a hybrid single electron transistor,
involving a small superconducting island sandwiched between normal metal leads,
which is driven by dc plus ac voltages. In order to describe its properties we
derive from the microscopic theory a set of coupled equations. They consist of
a master equation for the probability to find excess charges on the island,
with rates depending on the distribution of non-equilibrium quasiparticles.
Their dynamics follows from a kinetic equation which accounts for the
excitation by single-electron tunneling as well as the relaxation and eventual
recombination due to the interaction with phonons. Our low-temperature results
compare well with recent experimental findings obtained for ac-driven hybrid
single-electron turnstiles.
