duration by no more than an order of magnitude over the z-axis range we consider. Nonetheless, it is clear that propagating an electron pulse containing 100 electrons will be very challenging if we want to react a duration of below ten femtoseconds.

For the 1 fs pulse the extreme longitudinal confinement coupled with radial confinement (spatial focus) causes a rapid explosion in time. As the convergence angle is decreased from 10 mrad to 1 mrad, the duration is seen to increase more rapidly with increasing z. Furthermore, for low convergence foci and 10 and 100e pulses, the duration is observed to be distorted over a far larger distance as compared to the high convergence foci.

With an eye to design criteria (2 & 3) (see Methods), we find that an electron pulse containing around 10 electrons, with an initial duration of 10 fs provides a good balance between minimisation spatial focus induced temporal distortion and charge per pulse. Indeed, such a pulse repeatedly passing through foci would undergo most temporal distortion after the first focus, followed by successively reducing distortions as the duration further increases. As seen later, a pulse with a duration of high tens of femtoseconds is compressible 