Kinetic modeling and molecular dynamics simulation of ultracold neutral plasmas including ionic correlations

A kinetic approach for the evolution of ultracold neutral plasmas including interionic correlations and the treatment of ionization/excitation and recombination/deexcitation by rate equations is described in detail. To assess the reliability of the approximations inherent in the kinetic model, we have developed a hybrid molecular dynamics method. Comparison of the results reveals that the kinetic model describes the atomic and ionic observables of the ultracold plasma surprisingly well, confirming our earlier findings concerning the role of ion-ion correlations [Phys. Rev. A 68, 010703 (2003)]. In addition, the molecular dynamics approach allows one to study the relaxation of the ionic plasma component toward thermodynamical equilibrium.

Figure 1

Electronic temperature $T_e\left(t\right)$ for an expanding plasma of $\mathrm{40\hspace{0.17em}000}$ ions with an initial average density of ${10}^9{\mathrm{cm}}^{-3}$ and an initial electron kinetic energy of $20\mathrm{K}$, obtained from the HMD simulation (a) and the kinetic model (b), with (solid) and without (dotted) the inclusion of ICs. The inset shows the ratio of the electron temperatures obtained from the HMD simulation and the kinetic model.

Figure 2

Number $N_a\left(t\right)$ of recombined atoms obtained from the HMD simulation (a) and the kinetic model (b) for the same parameters as in Fig. 1. The solid line shows the result taking into account the ICs while the dotted line is obtained from the mean-field treatment.

Figure 3

Population of bound Rydberg states with principal quantum number $n$, after $t=1.5\mu \mathrm{s}$ (a), $t=6\mu \mathrm{s}$ (b), and $t=40\mu \mathrm{s}$ (c). The vertical bars represent the HMD calculation, the solid line the kinetic model. The dashed curve in (c) shows the kinetic model neglecting ICs. Initial-state parameters are the same as in Fig. 1.

Figure 4

Spatial densities ${\rho }_i$ (solid) and ${\rho }_a$ (dashed) of the ions and atoms, respectively, at $t=3\mu \mathrm{s}$ (a) and $t=31.3\mu \mathrm{s}$ (b), compared to the Gaussian profile assumed for the kinetic model (dotted). Additionally, ${\rho }_i$ obtained from the particle simulation using the mean-field interaction only is shown as the dot-dashed line in (a). Initial-state parameters are the same as in Fig. 1.

Figure 5

Hydrodynamic velocity $u\left(r\right)$ of ions (full circles) and atoms (open circles) at the same times as in Fig. 4, compared to the straight-line assumption of the kinetic model. The dashed line in (a) shows the result of the particle simulation using a mean-field treatment of the ion-ion interaction.

Figure 6

Distribution of thermal ionic velocities at $t=0.3\mu \mathrm{s}$ sampled from three different regions of the plasma: $r⩽1.3\sigma$ (a), $1.3\sigma <r⩽2\sigma$ (b), and $r>2\sigma$ (c), and from the total plasma volume (d). The solid lines show a fit to a Maxwell-Boltzmann distribution corresponding to the temperatures specified in the figure. Initial-state parameters are the same as in Fig. 1.

Figure 7

Same as Fig. 6, but for $t=1.5\mu \mathrm{s}$.

Figure 8

Average thermal ionic energy as a function of the distance from the plasma center at four different times: $t=0.3\mu \mathrm{s}$ (solid), $t=1.5\mu \mathrm{s}$ (dashed), $t=6.0\mu \mathrm{s}$ (dotted), and $t=25.3\mu \mathrm{s}$ (dot-dashed). Initial-state parameters are the same as in Fig. 1.

Figure 9

Correlation energy (solid line, HMD simulation; dot-dashed, kinetic result) and thermal ion kinetic energy (dashed, HMD; dotted, kinetic). Initial-state parameters are the same as in Fig. 1. The inset shows the ion thermal energy in the early stage of the relaxation process with its characteristic transiently oscillatory behavior.