  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 $2\times 10^9$. 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.
