Modeling quantum processes in classical molecular dynamics simulations of dense plasmas

We present a method for treating quantum processes in a classical molecular dynamics (MD) simulation. The computational approach, called 'Small Ball' (SB), was originally introduced to model emission and absorption of free-free radiation. Here, we extend this approach to handle ionization/recombination reactions as well as nuclear fusion events. This method exploits the short-range nature of screened-particle interactions in a dense plasma to restrict consideration of quantum processes to a small region about a given ion, and carefully accounts for the effects of the plasma environment on two-particle interaction rates within that region. The use of a reduced set of atomic rates, corresponding to the bottleneck approximation, simplifies their implementation within an MD code. We validate the extended MD code against a collisional-radiative code for model systems under two scenarios: (i) solid-density carbon at conditions encountered in recent experiments, and (ii) high-density Xe-doped hydrogen relevant for laser fusion. We find good agreement for the time-dependent ionization evolution for both systems. We also simulate fast protons stopping in warm, dense carbon plasmas. Here, reasonable agreement with recent experimental data requires contributions from both bound electrons, as modeled by SB in the extended MD code, and free electrons; for the latter, use of the classical random phase approximation (RPA) formula instead of the MD prediction yields better agreement with the experiment, a result that can be attributed to the use of modified Coulomb potentials in MD simulations of electron-ion plasmas. Finally, we confirm that the fusion reaction rate obtained from an MD simulation agrees with analytical expressions for the reaction rate in a weakly screened plasma.