Scaling law for temporal dispersion of a short electron pulse across a diode in space-charge regime

The space-charge phenomenon in the diode of a photoinjector induces simultaneously temporal and spatial dispersions of the electrons burst in pulsed regime. They are higher when the initial pulse duration is shortened. Here, we present the results of temporal dispersion obtained by computer simulation and we give a simple scaling law accounting for it. This law can be used to compare durations of electron pulses at the cathode and anode in any well-defined operation set, in space-charge regime.