Relaxation to Nonequilibrium in Expanding Ultracold Neutral Plasmas

We investigate the strongly correlated ion dynamics and the degree of coupling achievable in the evolution of freely expanding ultracold neutral plasmas. We demonstrate that the ionic Coulomb coupling parameter ${\Gamma }_i$ increases considerably in later stages of the expansion, reaching the strongly coupled regime despite the well known initial drop of ${\Gamma }_i$ to order unity due to disorder-induced heating. Furthermore, we formulate a suitable measure of correlation and show that ${\Gamma }_i$ calculated from the ionic temperature and density reflects the degree of order in the system if it is sufficiently close to a quasisteady state. At later times, however, the expansion of the plasma cloud becomes faster than the relaxation of correlations, and the system does not reach thermodynamic equilibrium anymore.

Figure 1

Ion temperature from the H-MD simulation of a plasma of ${10}^6$ Sr ions with initial peak density ${\rho }_0(0)=2\times {10}^9{\mathrm{cm}}^{-3}$ and electron temperature $T_e(0)=38\mathrm{K}$ (solid line), compared to experimental results (dots) [20]. The fact that the experimental ion number is about a factor of 10 larger than in our calculation does not affect the time evolution of the ionic temperature, since there is no significant adiabatic ion cooling on the time scale considered in Fig. 1.

Figure 2

Ionic Coulomb coupling parameter for a plasma with $N_i(0)=5\times {10}^4$, ${\overline{\rho }}_i(0)=1.1\times {10}^9{\mathrm{cm}}^{-3}$, and $T_e(0)=50\mathrm{K}$. The solid line shows the CCP calculated from the average temperature and density; the dashed line marks the CCP extracted from pair correlation functions (see text). Inset: blowup of the short-time behavior.

Figure 3

“Pair correlation functions” of the plasma of Fig. 2 at four different times $\tau =0.54$, $\tau =1.1$, $\tau =10$, and $\tau =60.7$. The ${\tilde{\Gamma }}_i$ indicated in the figure is obtained by fitting the distribution of scaled interionic distances (dots) with pair correlation functions for a homogeneous plasma given in 25 (solid line).

Figure 4

${\tau }_{\Gamma }^{*}$ as a function of ${\tau }_{\exp }^3$ for different initial conditions: $N_i=5\times {10}^4$, ${\overline{\rho }}_i=1.1\times {10}^9{\mathrm{cm}}^{-3}$, $T_e=50\mathrm{K}$; $N_i=4\times {10}^4$, ${\overline{\rho }}_i=3\times {10}^9{\mathrm{cm}}^{-3}$, $T_e=45\mathrm{K}$; $N_i=5\times {10}^4$, ${\overline{\rho }}_i={10}^9{\mathrm{cm}}^{-3}$, $T_e=33.3\mathrm{K}$; $N_i=8\times {10}^4$, ${\overline{\rho }}_i={10}^9{\mathrm{cm}}^{-3}$, $T_e=38\mathrm{K}$; $N_i={10}^5$, ${\overline{\rho }}_i=1.3\times {10}^9{\mathrm{cm}}^{-3}$, $T_e=33.3\mathrm{K}$ (left to right). The solid line is a linear fit. Error bars show the range of 2% to 8% relative deviation between ${\Gamma }_i$ and ${\tilde{\Gamma }}_i$ for determining ${\tau }_{\Gamma }^{*}$.