Emittance, surface structure, and electron emission

Abstract

The emittance of high brightness electron sources, particularly field emitters and photocathodes but also thermionic sources, is increased by surface roughness on the emitter. Such structure causes local field enhancement and complicates both the prediction of emittance and the underlying emission models on which such predictions depend. In the present work, a method to find the emission trajectories near regions of high field enhancement is given and applied to emittance predictions for field, photo, and thermal emission for an analytically tractable hemispherical model. The dependence of the emittance on current density, spatial variation, and acceleration close to the emission site is identified and the impact of space charge discussed. The methodology is extensible to field emission from close-spaced wirelike structures, in particular, and extensions to that configuration are discussed. The models have application to electron sources for high frequency vacuum electronics, high power microwave devices, and free-electron lasers.

Schottky’s conjecture, field emitters, and the point charge model

“…Yet, as Miller, et al, clearly point out, 9 that conjecture is largely unproven except for special cases (e.g., the 2D rectilinear geometries considered by Miller, et al, using conformal mapping techniques), even as it is an essential component in explaining causes of field emission or dark current, 10 has bearing on the putatively low emission fields suggested to be evinced for otherwise planar emitters (but which, as Forbes, et al, 11 argue, is more complex), or suggested by similar studies. 12 Yet some assessment of the conjecture's applicability, particularly to the conical and / or wire-like emitters of contemporary design, is needed to justify its usage in beam optics codes [13][14][15] in the modeling of those field emitters. Such modeling is essential in the design of high power microwave devices, 16,17 amplifiers, 18 and particle accelerators.…”

“…Such a model is sought to account for the microscale structure of carbon fiber field emitters, as evidenced in Figure 1, so as to enable their simulation in particle-in-cell codes. [13][14][15] The conjecture therefore has a very pragmatic side. In contrast to past treatments of the PCM, the present treatment is rendered analytically, thereby giving insight into how Schottky's conjecture unfolds.…”

2D/3D image charge for modeling field emission

“…The next step is to develop a modified tip current model accounting for the effects of prolate spheroidal geometries on total current per tip models in a manner analogous to previous efforts using the planar image charge approximation. 10 …”

“…A simple correction to accommodate curvature effects into the estimate of total current is to incorporate the image charge associated with a hemispherical shape (a staple boundary value problem in electrodynamics textbooks 19,20 and elsewhere 5,21 ) characterized by a tip radius a, by redefining the work function by U a ¼ U þ ðQ=2aÞ in the Fowler-Nordheim equation 5,22 (although important, the modifications to the transmission probability accounting for trajectory curvature effects which increase the tunneling barrier an electron encounters are not part of the present analysis, although they can be included 10,23,24 2 Þ as a function of 1/F in the Fowler-Nordheim representation of data] but also the power that F is raised to in the coefficient (2 -) and the interceptÃ.…”

Delayed photo-emission model for beam optics codes

“…Such surface and/or geometric variations result in the detailed beam distribution immediately taking on a fully 3D nature, for example, in a 3D simulation, and the code calculates and predicts this effect. Finally, a remaining multidimensional effect, that of transverse momentum components during emission, 25,26 becomes important when emittance is treated, and is considered separately.…”