  The Tera Electronvolt Superconducting Linear Accelerator TESLA is the only
linear electron-positron collider project based on superconductor technology
for particle acceleration. In the first stage with 500 GeV center-of-mass
energy an accelerating field of 23.4 MV/m is needed in the superconducting
niobium cavities which are operated at a temperature of 2 K and a quality
factor Q0 of 10 to the 10. This performance has been reliably achieved in the
cavities of the TESLA Test Facility (TTF) accelerator. The upgrade of TESLA to
800 GeV requires accelerating gradients of 35 MV/m. Using an improved cavity
treatment by electrolytic polishing it has been possible to raise the gradient
to 35 - 43 MV/m in single cell resonators. Here we report on the successful
transfer of the electropolishing technique to multi-cell cavities. Presently
four nine-cell cavities have achieved 35 MV/m, and a fifth cavity could be
excited to 39 MV/m. In two high-power tests it could be verified that
EP-cavities preserve their excellent performance after welding into the helium
cryostat and assembly of the high-power coupler. One cavity has been operated
for 1100 hours at the TESLA-800 gradient of 35 MV/m and 57 hours at 36 MV/m
without loss in performance.
