  To achieve Ampere-class electron beam accelerators the pulse delivery rate
need to be much higher than the typical photo injector repetition rate of the
order of a few kilohertz. We propose here an injector which can, in principle,
generate electron bunches at the same rate as the operating RF frequency. A
conduction-cooled superconducting radio frequency (SRF) cavity operating in the
CW mode and housing a field emission element at its region of high axial
electric field can be a viable method of generating high repetition-rate
electron bunches. In this paper, we report the development and experiments on a
conduction-cooled Nb3Sn cavity with a niobium rod intended as a field emitter
support. The initial experiments demonstrate 0.4 MV/m average accelerating
gradient, which is equivalent of peak gradient of 3.2 MV/m. The measured RF
cavity quality factor is 1.4 x 108 slightly above our goal. The achieved field
gradient is limited by the relatively low input RF power and by the poor
coupling between the external power supply and the RF cavity. With ideal
coupling the field gradient can be as high as 0.6 MV/m still below our goal of
about 1 MV/m.
