  The higher efficiency of superconducting radio-frequency (SRF) cavities
compared to normal-conducting ones enables the development of high-energy
continuous-wave linear accelerators (linacs). Recent progress in the
development of high-quality Nb$_3$Sn film coatings along with the availability
of cryocoolers with high cooling capacity at 4 K makes it feasible to operate
SRF cavities cooled by thermal conduction at relevant accelerating gradients
for use in accelerators. A possible use of conduction-cooled SRF linacs is for
environmental applications, requiring electron beams with energy of $1 - 10$
MeV and 1 MW of power. We have designed a 915 MHz SRF linac for such an
application and developed a prototype single-cell cavity to prove the proposed
design by operating it with cryocoolers at the accelerating gradient required
for 1 MeV energy gain. The cavity has a $\sim 3$ $\mu$m thick Nb$_3$Sn film on
the inner surface, deposited on a $\sim4$ mm thick bulk Nb substrate and a bulk
$\sim7$ mm thick Cu outer shell with three Cu attachment tabs. The cavity was
tested up to a peak surface magnetic field of 53 mT in liquid He at 4.3 K. A
horizontal test cryostat was designed and built to test the cavity cooled with
three Gifford-McMahon cryocoolers. The rf tests of the conduction-cooled
cavity, performed at General Atomics, achieved a peak surface magnetic field of
50 mT and stable operation was possible with up to 18.5 W of rf heat load. The
peak frequency shift due to microphonics was 23 Hz. These results represent the
highest peak surface magnetic field achieved in a conduction-cooled SRF cavity
to date and meet the requirements for a 1 MeV energy gain.
