Normalized intrinsic emittance of cold emission cathodes

We determine the normalized intrinsic emittance associated with a cold emission cathode. While, in principle, we are primarily motivated by carbon nanotube (CNT) cathodes, our approach is applicable to any type of cold cathode. Its essence relies on the evaluation of the initial momentum as the particles tunnel through the Schottky-Nordheim barrier based on the spectral radiance function. Next, the momentum distribution is integrated over the geometry, providing, along with well-known Fowler-Nordheim current, an integral expression for the emittance. An analytic approximation solution shows that the normalized emittance of a single emitter is proportional to the normalized Fermi velocity β F = v F / c of the emitter material, transverse dimension of the emitter, and the square root of the applied local electric field. In the case of an array of such emitters, dependency on the latter virtually vanishes. According to our theoretical results and based on experimental data for CNT emitters available in the literature, we predict that practical cold emission cathodes may provide a normalized intrinsic emittance comparable or even superior to that of conventional photo-emission cathodes used in state-of-the-art electron sources.