Space charge effects on the short pulse beam profile

Space charge effects play an important role in restricting the development of free electron beam based electronics, such as high-power vacuum devices and ultrafast atomic resolution electron imaging and diffraction technologies [1], [2]. Child-Langmuir (CL) law provides the classical current density limit that may be drawn from a vacuum diode with a continuous electron beam [3]. Both theoretical and experimental findings suggest that this CL limit may be significantly exceeded for electron pulses with pulse durations that are much shorter than the diode gap transit time [4].