Classical scaling and the correspondence between the coupled rate equation and molecular dynamics models for the evolution of ultracold neutral plasma

Abstract

Coupled rate equation calculations demonstrate that the variational rate theory models for the three-body electron–electron–ion scattering dynamics associated with ultracold plasma evolution scale with density in accordance with the classical mechanics of a Coulomb system. Completeness of scaling requires a broad domain of Rydberg levels over which a quasi-equilibrium can be established. For given initial conditions, the predicted evolution of electron temperature with time changes with the choice of nmax, i.e. the highest Rydberg orbital populated by three-body recombination. But, if the criterion that defines nmax scales with density, then the results scale. Molecular dynamics calculations distinguish bound Rydberg states by an electron–ion distance criterion, Rmax, which is represented in scaled coordinates by Rmax = rmaxaws, where aws represents the Wigner–Seitz radius and rmax is chosen arbitrarily. The rate equation calculations best conform with the output of molecular dynamics simulations for values of nmax defined by a thermal criterion, . In a hydrogenic limit, the thermal criterion equates with a scaled distance criterion when rmax = Γe/2, where Γe = e2/4πϵ0awskBTe describes the degree of electron correlation. Molecular dynamics simulations conventionally attenuate the Coulomb potential by means of a term, C, . Reference to rate equation calculations suggests a connection between the soft-core term, C, and nmin, the lowest Rydberg level considered in the relaxation of the plasma to a quasi-steady state.