Vacuum electron sources exploiting field emission are generally operated in direct current (DC) mode. The development of nanosecond and sub-nanosecond pulsed power supplies facilitates the emission of compact bunches of electrons of high density. The breakdown level is taken as the highest value of the voltage avoiding the thermo-emission instability. The effect of such ultra-fast pulses on the breakdown voltage and the emitted electron current is discussed as a result of the thermo-emission modelling applied to a significant protrusion. It is found that pulsing very rapidly the vacuum breakdown occurs at higher voltage values than for the DC case, because it rises faster than the heat diffusion. In addition, the electron emission current increases significantly regardless of the theoretical approach is used. A comparative study of this theoretical work is discussed for several different forms of the protrusion (elliptic and hyperbolic) and different metals (hence varying the melting point), particularly refractory (tungsten) versus conductor (titanium). Pulsed mode operation can provide an increase on breakdown voltage (up to 18%) and a significant increase (up to 330%) of the electron extracted current due to its high non-linear dependency with the voltage, for the case for the case with a hyperbolic protrusion.