ultrafast electron pulses through magnetic lenses
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As shown in the fs-TEM schematic in figure 2, the electron pulses are sent through four spatial foci before interaction with the sample, therefore qualification of any resulting spatio-temporal distortion is necessary [@Weninger2012]. As the pulse passes through a spatial focus, the beam dimensions and hence severity of temporal expansion depend on the incident pulse duration, number of electrons and convergence angle. We demonstrate this in figure 3, which shows the influence of convergence angle and electron pulse charge on temporal duration. Rather than consider the full fs-TEM as shown in figure 2, in the case of figure 3, we start a collimated electron pulse at z = 0 with an average energy of 70 keV and[@Schneider2014] a bandwidth of 0.5 eV. The 2$\sigma$(r) radius of the electron pulse is 50 $\mu$m, comparable to that found in figure 2.

![Temporal action of a range of magnetic lens strengths on a 70 keV electron pulse of varying initial duration and charge. Note this electron pulse is generated at z = 0 at 70 keV unlike all other figures. The magnetic lens is at z = 0.1 m (solid line) and forms foci at z 