Modelling of electron transfer from a carbon nanotube cap into the vacuum under high extraction fields

In the present work, we consider a system of a grounded CNT of length L and radius r₀ (the emitter) facing a spherical anode of radius R_a(R_a>>r₀). The anode is placed at some distance away from the emitter´s tip. The CNT is modelled as a two-dimensional (2D) manifold where electrons behave as quasi-free and independent particle. The electrons are bound on the CNT surface by a one-dimensional (1D) potential well, due to the restriction imposed by the cylindrical symmetry. In order to have a full description of the electron behaviour in the whole system, a potential energy in the vacuum region needs also to be defined. To this purpose, the CNT cap is simplified as a grounded conducting sphere of radius r₀ facing the anode on the same symmetry axis. As the emitter-anode distance, d and the anode radius, R_a are much greater than r₀, the electric field in vacuum may be computed using the method of electrostatic images.