pulse if they pass the sample plane within an annular boundary, shown in figure 7(a). The direction and strength of the electric field in the xy plane (mutually perpendicular to the z-axis along which the electron pulse propagates) is indicated by the arrows. The shaded region is the annulus, opaque to electrons, so could be considered thick as compared to the mean free path of the electrons.

![image](fig7.jpg){width="\textwidth"}

The influence of both the opaque region and localized electric field is shown in figure 7(b), where the point of arrival of the macroparticles at the detector plane are indicated by a point. The green points are the field free case, and the red points indicate the modified trajectories caused by a scattering field $E_{scat}$ = 10 MV/m.

Following the notation convention in figure 7, the geometry of the annuluses from i=1 to i=5 in the format outer radius (nm):inner radius (nm) shown in figure 7(c) are (i = 1) 200:100, (i = 2) 100:50, (i = 3) 50:25, (i = 4) 20:10 and (i = 5) 10:5. The macroparticles representing the electron pulse are propagated though the fs-TEM where they encounter the geometry shown in figure 7(c) and fields shown in 