Electron Temperature of Ultracold Plasmas

We study the evolution of ultracold plasmas by measuring the electron temperature. Shortly after plasma formation, competition between heating and cooling mechanisms drives the electron temperature to a value within a narrow range regardless of the initial energy imparted to the electrons. In agreement with theory predictions, plasmas exhibit values of the Coulomb coupling parameter $\Gamma$ less than 1.

Figure 1

Self-consistently calculated electron potentials shown as a function of position along the applied electric field direction, for $F=1.5\mathrm{V}/\mathrm{m}$ (solid line) and $3\mathrm{V}/\mathrm{m}$ (dashed line) applied electric fields. The relevant plasma parameters are $N_{\mathrm{ion}}={10}^6$, $N_{\mathrm{electron}}=0.95N_{\mathrm{ion}}$, $\sigma =0.53\mathrm{mm}$, and $T=40\mathrm{K}$. The value of the parameter $E_{\mathrm{cut}}(F)$ used in the calculation of the fraction of electrons spilled is determined from the saddle point as indicated.

Figure 2

MCP signal (solid line) showing a typical plasma evolution and spilling signal (region indicated in oval). The inset shows the spilling part of the curve in more detail. The magnitude of the applied electric field is also plotted (dashed line).

Figure 3

Fraction of electrons spilled ($f$) versus $E_{\mathrm{cut}}$ for a typical set of data (solid circles). Fits using the model based on Eq. (1) are shown for the temperatures that are indicated, where the 35 K curve is the best fit curve and the other two are shown for comparison. Note that the value of $T$ is determined primarily from the curvature of $f$ versus $E_{\mathrm{cut}}$.

Figure 4

(a) Measured temperatures versus plasma evolution time for different values of $\Delta E/k_B$ as indicated in the legend. These data have $N_{\mathrm{ion}}\sim {10}^6$, $0.4\mathrm{mm}\le \sigma \le 0.6\mathrm{mm}$ for $\Delta E/k_B\le 100\mathrm{K}$, and $0.4\mathrm{mm}\le \sigma \le 0.7\mathrm{mm}$ for $\Delta E/k_B>100\mathrm{K}$. This size range was chosen because it corresponds to the plasma evolution time just after the initial electrons have escaped from the plasma. Times $0.5–2\mu \mathrm{s}$ earlier (depending on ${\Delta }_E$) and a few microseconds later were also measured. The error bars show only the statistical uncertainty. (b) Corresponding $\Gamma$ for the data shown in Fig. 4a. The $\Delta E/k_B=100\mathrm{K}$ data do not continue to increase but rather level out at later evolution times.