An electron is placed at rest in the middle of this electric field (due to a parallel-plate capacitor). There is a vacuum between the plates. What can we say will happen to the electron while it is in this electric field

This allows for a higher voltage rating than an air dielectric using a smaller total volume.

Explanation:

capacitors store the energy of the electrons in the form of an electrical charge on the plates the larger the plates and/or smaller their separation the greater will be the charge that the capacitor holds for any given voltage across its plates.

Electrons do not flow through a capacitor. They accumulate (as conduction band electrons) on the negative plate and deplete on the positive plate. This process continues as long as the voltage is applied and tapers off as the electric charge between the plates approaches the applied voltage.

In a capacitor, you have an electric field between the plates. This passes AC, but blocks DC, all without allowing electrons to pass between the plates ... Indeed, at a high enough temperature (ballpark of 1000K) thermal energy alone is enough to 'cast' electrons out into the vacuum