The field emission (FE) properties of carbon nanotube (CNT)-based cathodes have been investigated on nanostructured surfaces grown by plasma enhanced chemical vapor deposition. The FE angular properties and temporal stability of the emergent electron beam have been determined using a dedicated apparatus for cathodes of various architectures and geometries, characterized by scanning electron microscopy and I-V measurements. The angular electron beam divergence and time instability at the extraction stage, which are crucial parameters in order to obtain high brilliance of FE-based-cathode electron sources, have been measured for electrons emitted by several regular architectures of vertically aligned arrays and critically compared to conventional disordered cathodes. The measured divergences strongly depend on the grid mesh. For regular arrays of individual CNT, divergences from 2° to 5° have been obtained; in this specific case, measurements together with ray-tracing simulations suggest that the maximum emission angle is of the order of ±30° about the tube main axis. Larger divergences have been measured for electron beams emitted from honeycomb-structured cathodes (6°) and significantly broader angle distributions (10°) from disordered CNT surfaces. Emission current instabilities of the order of 1% for temporal stability studies conducted across a medium time scale (hours) have been noted for all cathodes consisting of a high number (10$^{4}$ and larger) of aligned CNTs, with the degree of stability being largely independent of the architecture.
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