1This paper presents theory and analysis of single-tip field emission and electron beam propagation in the electrostatic focusing fields. It is shown that two gate apertures with a focusing anode allow transport of narrow electron beams over long distances without need for a confining magnetic field. Physical mechanisms of the beam formation, transport, field emission energy distributions, the effects of the emission properties, and parametric studies are discussed, emission current formula is derived, and new concept and model of the bandgap-spread multilevel field emission is given.
I. INTRDUCTIONBecause of their small emitting area and high emission current density, tip-based field emitters produce beams of low intrinsic emittance and high-brightness. Most prospective applications, such as high-resolution X-ray imaging, free electron lasers, and high-frequency TWT and terahertz periodic structures, require a focused electron beam to be transported over distances many orders of magnitude larger than the typical field emitting geometry transverse dimensions. This paper presents theory, simulations, and analysis that describe focusing and transport of the electron beam from a field emission tip in the electrostatic field produced by two gate apertures and a focusing anode. The idea of two gates was considered first by W. B. Hermannsfeldt [1] and further investigated by others [2][3]. However, the two-gate concept does not allow sufficiently long focused electron beams. We introduced a focusing anode into the geometry and obtained optimized configurations that provide the desired long aspect ratio focusing and beam transport. For more adequate description of the field emission, we derive an emission model with higher order corrections to the Fowler-Nordheim theory and suggest a new concept of bandgap-spread multilevel field emission. We also discuss the calculated particles transverse energy distributions, consider effects of the emission parameters on the beam properties, and show an example of a multiple-beam field * emission source that could be integrated with a terahertz periodic structure for extended beam-wave interaction with no magnetic field for focusing.