  High-repetition-rate sources of bright electron bunches have a wide range of
applications. They can directly be employed as probes in electron-scattering
setups, or serve as a backbone for the generation of radiation over a broad
range of the electromagnetic spectrum. This paper describes the development of
a compact sub-Mega-electronvolt (sub-MeV) electron-source setup capable of
operating at MHz repetition rates and forming sub-picosecond electron bunches
with transverse emittance below 20~nm. The setup relies on a conduction-cooled
superconducting single-cell resonator with its geometry altered to enhance the
field at the surface of the emitter. The system is designed to accommodate
cooling using a model a $2$~W at 4.2 K pulse tube cryogen-free cryocooler.
Although we focus on the case of a photoemitted electron bunch, the scheme
could be adapted to other emission mechanisms.
