Thermionic Emission of Electrons from Metal Surfaces in the Warm Dense Matter Regime

Thermionic emission of electrons is a process fundamental to our understanding of laser–matter interactions in the ultra-short pulse regime. Charge collected from an emission process, as well the secondary radiation generated by their collective motion, provides avenues for diagnosing and verifying existing laser–solid interaction models. Laser fluences (∼104 J/m2) are of particular interest as they heat the surface electrons to temperatures on the order of a few electron volts (eV), placing it in the warm dense matter regime where much underlying physics is yet to be fully understood. However, even at such moderate fluences the conventional Richardson–Dushman formula for the emission rate becomes invalid. We consider an additional barrier potential on the surface that appears due to space-charge effects, which then limits the thermionic emission. This provides feedback leading to a self-consistent solution with the emission rate. Unlike the work function, this barrier dynamically evolves during the emission process. Here, we present the first calculation of the barrier potential on the surface, along with analytical expression, from a one-dimensional electrostatic model. The result is a generalization of the Richardson–Dushman picture to moderate laser fluences. The potential barrier has been incorporated into a two-temperature model for thermionic emission from an Al target irradiated by a femtosecond laser. The collisional and transport data for Al have been obtained using an average atom model.