  The proposed linear electron-positron collider TESLA is based on 1.3 GHz
superconducting niobium cavities for particle acceleration. For a
centre-of-mass energy of 500 GeV, an accelerating field of 23.4 MV/m is
required which is reliably achieved with a niobium surface preparation by
chemical etching. An upgrade of the collider to 800 GeV requires an improved
cavity preparation technique. In this paper, results are presented on
single-cell cavities which demonstrate that fields of up to 40 MV/m are
accessible by electrolytic polishing of the inner surface of the cavity.
