The sheet model of consecutive charge injection for a rough cathode in an accelerating diode

We consider space-charge-limited (SCL) electron emission from a rough cathode modeled as a fractional object. An analytical model of uniformly spaced charge sheets is developed to calculate the SCL charge density as a function of gap spacing, voltage, pulse separation, number of pulses, and surface roughness. Results show that cathode roughness significantly reduces the maximum SCL charge density, especially under high-voltage, multi-pulse conditions, where classical flat-surface models fail to apply.