Modeling and electrostatic focusing for a field emission electron source

Summary form only given. Because 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 interaction structures, require a focused electron beam to be transported over distances many orders of magnitude larger than the typical field emitter´s 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. 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 which involves emission from the multiple energy states that are either discretely or continuously distributed within the bandgap. The bandgap spread can be caused by various kinds of imperfections, intentional or accidental, such as lattice defects, dislocations, phase and chemical impurities, doping, and surface treatment. We implemented these new model concepts with the MICHELLE [2] particle optics code. We also discuss the calculated particles transverse energy distributions, intrinsic emittance and brightness threshold including the thermal effects, 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 terahe- tz periodic structure for extended beam-wave interaction with no magnetic field for focusing.