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.
Highlights
For accelerators and electron devices, the usefulness of a high brightness electron beam is constrained by its emittance [1], of which that portion due to the cathode, known as “intrinsic emittance,” is of increasing importance
Krasilnikov [38] generalizes the 2D sinusoidal variation of a surface to 3D, as well as examines the Lorenztian model of Lau [39], to conclude that the increased electric field on the surface can lead to an increase in thermal emittance comparable to 30%, and argues that space charge effects increase it; his conclusions are supported by the present work
Realistic thermionic and photoemission surfaces have surface features varying in size and randomly placed, and field emitters can be made in triangular arrays rather than on a square lattice, for the analytic model, assume that first, the M2 protrusions are uniformly sized; second, that the protrusions are located on a square array with a pitch of l so that the area of the array is 1⁄2ðM − 1Þl2 ≡ L2; and third, that l is sufficiently large that to a good approximation, the trajectories of a single boss are unaffected by its neighbors
Summary
For accelerators and electron devices, the usefulness of a high brightness electron beam is constrained by its emittance [1], of which that portion due to the cathode, known as “intrinsic emittance,” is of increasing importance. For field and photoemission sources, is complicated by emission nonuniformity and geometric effects. For field and photoemission, emittance is strongly coupled to space charge effects. Numerical estimates of a geometrical array of emitters is considered, as is the manner in which the methodology may be extended to wirelike (carbon fiber) field emitters. A discussion of how the methodology may be modified to treat the consequences of space charge forces due to the emitted current, with respect to beam optics codes, is given
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