The conceptional design of the proposed linear electron-positron collider TESLA is based on 9-cell 1.3 GHz superconducting niobium cavities with an accelerating gradient of ${E}_{\mathrm{acc}}\ensuremath{\ge}25\mathrm{MV}/\mathrm{m}$ at a quality factor ${Q}_{0}\ensuremath{\ge}5\ifmmode\times\else\t...
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