The beam quality of an idealized two-dimensional field emitter is evaluated. Under the assumption that the space-charge effects are negligible, a scaling law is constructed for the intrinsic emittance of an isolated emitter. This scaling law takes into account the Fowler–Nordheim (F–N) emission law and the effects of local field enhancement. It is given in terms of the height and width of the emitter, anode–cathode separation and voltage drop, as well as the F–N coefficients A and B.
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Liu et al. (1996) studied this question.