  We study the effect of the flux noise on the Cooper pair current and pumping.
We generalize the definition of the current in order to take into account the
contribution induced by the environment. It turns out that this dissipative
current vanishes for charge noise but it is finite in general for noise
operators that do not commute with the charge operator. We discuss in a generic
framework the effect of flux noise and present a way to engineer it by coupling
the system to an additional external circuit. We calculate numerically the
pumped charge through the device by solving the master equation for the reduced
density matrix of the system and show how it depends on the coupling to the
artificial environment.
