  We have developed a quantitative theory of Cooper pair pumping in gated
one-dimensional arrays of Josephson junctions. The pumping accuracy is limited
by quantum tunneling of Cooper pairs out of the propagating potential well and
by direct supercurrent flow through the array. Both corrections decrease
exponentially with the number N of junctions in the array, but give a serious
limitation of accuracy for any practical array. The supercurrent at resonant
gate voltages decreases with N only as sin(v/N)/N, where v is the Josephson
phase difference across the array.
