Microwave--Driven SET--Box with Superconducting Island

The effect of a high--frequency microwave irradiation on the averaged stationary charge in a single--electron tunneling box (SET--box) with superconducting island is investigated. The resulting $\langle Q\rangle$--$Q_g$ characteristics are modified compared with those from the well--known constant voltage--driven box. It can be shown that there is a cross--over from the 2e--periodic regime in $Q_g$ corresponding to the parity effect to 1e--periodic behavior not only with increasing temperature but also with increasing irradiation amplitude.