Strong-field ionization in particle-in-cell simulations

The inclusion of the process of multiple ionization of atoms in high-intensity electromagnetic fields into particle-in-cell (PIC) codes applied to the simulation of laser-plasma interactions is a challenging task. In this paper, we first revisit ionization rates as given by the Smirnov-Chibisov and Perelomov-Popov-Terent'yev formulas within the paradigm of sequential tunnel ionization. We analyze the limit of validity and possible inconsistencies of this approach. We show that a strongly limiting factor to a precise description of ionization is the competing contribution of different sequential ionization processes. To solve this an algorithm is proposed that allows one to find the dominant nonsequential path of tunnel ionization and significantly improves the precision in simulations. This procedure is implemented in the PIC code SMILEI, and includes the dependence of the ionization rates on the magnetic quantum number of the level. The sensitivity to variations in the ionization model is studied via full simulations of the ionization of an argon target by an incident high-intensity laser pulse. Finally, we analyze generalizations of the Perelomov-Popov-Terent'yev rate developed to describe the barrier suppression ionization in high fields and discuss the necessity and possibility of including these extensions in PIC simulations.