Electron-Temperature Evolution in Expanding Ultracold Neutral Plasmas

We have used the free expansion of ultracold neutral plasmas as a time-resolved probe of electron temperature. A combination of experimental measurements of the ion expansion velocity and numerical simulations characterize the crossover from an elastic-collision regime at low initial ${\Gamma }_e$, which is dominated by adiabatic cooling of the electrons, to the regime of high ${\Gamma }_e$ in which inelastic processes drastically heat the electrons. We identify the time scales and relative contributions of various processes, and we experimentally show the importance of radiative decay and disorder-induced electron heating for the first time in ultracold neutral plasmas.

Figure 1

Expansion velocity (a) and electron temperature (b) for low ${\Gamma }_e$ showing little or no electron heating effects. (a) The initial peak densities and sizes are $n_0=3.5\times {10}^{15}{\mathrm{m}}^{-3}$ and $\sigma (0)=1\mathrm{mm}$. The self-similar analytic solution (dark solid line) provides an excellent fit of the data, with fitted $T_e(0)$ indicated in the legend. The full numerical simulation (dashed line) describes the data with no adjustable parameters. (b) Electron-temperature evolutions [Eq. (3)] are determined from parameters of the fits to $v_{i,\mathrm{rms}}$ or by numerical simulation. For $2E_e/3k_B=25\mathrm{K}$, the analytic solution fit and numerical simulation for $T_e(t)$ deviate significantly, showing the importance of inelastic collision effects.

Figure 2

(a) Expansion velocity and (b) electron temperature for moderate initial ${\Gamma }_e=0.2$ [$2E_e/3k_B=14\mathrm{K}$, $\sigma (0)=0.9\mathrm{mm}$, and $n_0(0)=7\times {10}^{15}{\mathrm{m}}^{-3}$]. (a) A fit of the expansion to the analytic solution [Eq. (2), solid line] yields $T_e(0)=34\mathrm{K}$, which reflects much faster expansion than expected for elastic-collisional dynamics with $2E_e/3k_B=14\mathrm{K}$ (dotted line). Only including TBR and REC in the simulation (dot-dashed line) overestimates the heating. Including RD as well (dashed line) brings theory into good agreement with experiment. Including DIH increases the initial electron temperature by about 3 K, but has little effect on the velocity fit. (b) The fit $T_e(0)$ approximately equals the maximum of the actual $T_e(t)$ obtained with simulation.

Figure 3

(a) Ion velocity and (b) electron temperature for ${\Gamma }_e\sim 1$ [$2E_e/3k_B=4\mathrm{K}$, $n_0(0)=8\times {10}^{15}{\mathrm{cm}}^{-3}$, $\sigma (0)=1.0\mathrm{mm}$]. (a) The numerical simulation including all heating effects matches the data with no adjustable parameters. For this relatively high density, the initial heating from DIH slows TBR and REC enough to produce an observable effect. The analytic solution fit is poor, but yields $T_e(0)=49\pm 2\mathrm{K}$. (b) The electron temperature shows drastic heating at early times and $T_e(0)$ no longer provides a good estimate of $T_{e,\max }$.

Figure 4

Electron heating summary. The plasma dynamics are parametrized well by ${\Gamma }_e(n_0,E_e)$. $T_{e,\max }$ is the maximum electron temperature attained during the evolution. The heating is negligible in the elastic-collisional regime (${\Gamma }_e<0.1$ [18] ), and $T_{e,\max }/(2E_e/3k_B)\approx 1$. In the inelastic collisional regime, the heating becomes significant and increases with increasing density and decreasing $2E_e/3k_B$. Beyond ${\Gamma }_e\approx 1$, the expansion ceases to be self-similar.