Non-equilibrium classical recombination in the expanding ultracold plasmas

The efficiency of recombination is of crucial importance for the existence of ultracold plasmas (UCP), particularly those formed in the magneto-optical traps. Unfortunately, the equilibrium thermodynamic treatment of the ionization–recombination processes is inappropriate for the evolving UCP clouds, while the straightforward kinetic simulation encounters the problem of the huge difference in the spatial and temporal scales for free and bound motion of the electrons. As a result, only the “virtual” electron–ion pairs are usually reproduced in such modeling, and it is necessary to employ some heuristic criteria to identify them with the recombined atoms. It is the aim of this paper to present the first successful ab initio simulation of the non-equilibrium recombination in the evolving UCP plasmas. We employed a special algorithm, which is based on using the “scalable” reference frame, co-moving with the expanding substance. Then, the recombination events are identified by a series of sharp equidistant peaks in the kinetic and/or potential energies, which are caused by the captured electrons passing near the pericenters of their orbits, and this is confirmed by a detailed inspection of their trajectories. Thereby, we were able to trace the real—rather than “virtual”—electron–ion pairs, and the total efficiency of their formation was found to be about 20%, which is in agreement with the laboratory measurements.