$<$ 10 nm), the DC electric field is relatively constant over the first ten nanometres, causing near-constant acceleration. Between 10 nm $<$ z $<$ 100 $\mu$m, the electric field transitions between being governed by the NSMT to the parallel plate case. This is shown in figure 1(d), by the tendency for the different V cases to converge to a constant value at z $>$ 100 $\mu$m. Examination of the flatness of the contours in figure 1(a) around z $>$ 100 $\mu$m, the linearity of the electric field E$_z$ in figure 1(d) and the linear increase of velocity with z position in figure 1(f) indicates the completion of the transition between NSMT-influenced acceleration and parallel plate acceleration. Upon exit of the anode the electrons reach their final velocity of $v_z \approx$ 0.48c ($\lambda_{e} \approx $ 4.5 pm), as indicated in figure 1(f).

The total flight time of the electron pulse from the NSMT to the anode is shown in figure 1(g). The significant DC field gradient at the apex of the tip means that the electron pulse accelerates dramatically in the first 10 nm, which is a key consideration when trying to mitigate the influence of space charge. The transnational behaviour 