The Laser Driven Vacuum Photodiode

A vacuum photodiode is constructed in the form of a parallel plate capacitor with plate separation d. A battery maintains constant potential V between the plates. A short laser pulse illuminates that cathode at time t = 0 with energy sufficient to liberate all of the surface charge density. This charge moves across the capacitor gap as a sheet until it is collected at the anode at time T . Then another laser pulse strikes the cathode, and the cycle repeats. Estimate the average current density 〈j〉 that flows onto the anode from the battery, ignoring the recharing of the cathode as the charge sheet moves away. Then calculate the current density and its time average when this effect is included. Compare with Child’s Law for steady current flow. You may suppose that the laser photon energy is equal to the work function of the cathode, so the electrons leave the cathode with zero velocity.