Recent technological advances have generated interest in using a field emission cathode in a radio-frequency (RF) electron gun. One of the necessary steps towards the realization of this concept is to establish a comprehensive understanding of the electron distribution produced by such a cathode, and the goal of this work is to expand this body of knowledge. For the specific case of ungated field emitter arrays, we investigate aspects of the temporal and transverse electron distribution, as well as the relationship between emission timing and the ensuing acceleration of the electrons.

We show that an upper bound can be placed on the magnitude of the transverse momentum imparted to the electrons by the nonlinear accelerating forces that exist close to the emitter tips. This establishes a limit on the cathode's intrinsic emittance, an important determining factor for beam quality. We examine the consequences of this result in the context of relevant theoretical and experimental studies reported in the literature. This is followed by a series of calculations based on a simple emitter model, which are used to study specific aspects of the transverse momentum distribution. Our focus then shifts to the longitudinal beam dynamics. An examination of the on-axis trajectories demonstrates that it is possible to design a gun such that essentially all of the field-emitted current reaches the exit of the cavity. This indicates a source of this type may be capable of producing high average beam power. In the final chapter, the properties of ungated field emission cathodes are compared with the properties of cathodes that are typically used in RF guns. This gives some insight into how the field emission cathode might perform in this setting.