Superconducting radio-frequency cavities are commonly used in modern particle accelerators for applied and fundamental research. Such cavities are typically made of high-purity, bulk Nb and are cooled by a liquid helium bath at a temperature of ~2 K. The size, cost and complexity of operating a particle accelerator with a liquid helium refrigerator makes the current cavity technology not favorable for use in industrial-type accelerators. We developed a multi-metallic 1.495~GHz elliptical cavity conductively cooled by a cryocooler. The cavity has a ~2 $mu$m thick layer of Nb$_3$Sn on the inner surface, exposed to the rf field, deposited on a ~3 mm thick bulk Nb shell and a bulk Cu shell, of thickness $geqslant 5$ mm deposited on the outer surface by electroplating. A bolt-on Cu plate 1.27 cm thick was used to thermally connect the cavity equator to the second stage of a Gifford-McMahon cryocooler with a nominal capacity of 2 W at 4.2 K. The cavity was tested initially in liquid helium at 4.3 K and reached a peak surface magnetic field of ~36 mT with a quality factor of $2times 10^9$. The cavity cooled by the crycooler achieved a peak surface magnetic field of ~29 mT, equivalent to an accelerating gradient of 6.5 MV/m, and it was able to operate in continuous-wave with as high as 5 W dissipation in the cavity for 1 h without any thermal breakdown. This result represents a paradigm shift in the technology of superconducting accelerator cavities.
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