Preliminary study of plasma modes and electron-ion collisions in partially magnetized strongly coupled plasmas

Magnetic fields influence ion transport in plasmas. Straightforward comparisons of experimental measurements with plasma theories are complicated when the plasma is inhomogeneous, far from equilibrium, or characterized by strong gradients. To better understand ion transport in a partially magnetized system, we study the hydrodynamic velocity and temperature evolution in an ultracold neutral plasma at intermediate values of the magnetic field. We observe a transverse, radial breathing mode that does not couple to the longitudinal velocity. The inhomogeneous density distribution gives rise to a shear velocity gradient that appears to be only weakly damped. This mode is excited by ion oscillations originating in the wings of the distribution where the plasma becomes non-neutral. The ion temperature shows evidence of an enhanced electron-ion collision rate in the presence of the magnetic field. Ultracold neutral plasmas provide a rich system for studying mode excitation and decay.

Figure 1

(a) Partial energy level diagram for Ca. The number of atoms in the MOT is enhanced by repumping at 424 nm. Less than 1% of the population from the $4s7s{}^{1}P_1$ level is lost to the trap. (b) Energy levels in ${\mathrm{Ca}}^{+}$. To avoid optically pumping, both $\mathrm{\Delta }m=0$ transitions are driven by the 393-nm probe laser light. (c) Timing diagram for the experiment. The MOT laser beams and magnetic field gradient are turned off, and a uniform bias field is turned on 1.4 ms before the ionizing laser pulse arrives. After a time $\mathrm{\Delta }t$, the probe laser beams are turned on and the camera observes the laser-induced fluorescence. (d) Schematic representation of the fluorescence measurement geometry.

Figure 2

Longitudinal UNP expansion in the presence of a magnetic field. The probe laser beam propagates in the $z$ direction, parallel to $\vec{B}$. Black circles: experimental measurements. Error bars indicate $1\sigma$ scatter in repeated measurements. Solid line: one-dimensional expansion model. (a) The scaled hydrodynamic velocity gradient along the magnetic field direction, $\tau {\gamma }_3\left(t\right)$, agrees qualitatively with the asymmetric expansion model. There is no evidence of any oscillation in ${\gamma }_3$. (b) The ion temperature, $T_i$, reveals an additional source of heating beyond disorder-induced heating and electron-ion collisions in Eq. (A2). For this figure, $n_0=3.3\left(2\right)\times {10}^8{\text{cm}}^{-3},{\sigma }_0=1.30\text{mm},T_e=96\text{K},$ and $B=216$ G.

Figure 3

Transverse hydrodynamic velocity measurements. (a) $B=0$ and (b) $B=183\text{G}$. The initial electron temperature, ion density, and rms plasma size are $T_e=100\mathrm{K}, n_0=6.7\times {10}^8{\text{cm}}^{-3}$, and ${\sigma }_0=1.3\mathrm{mm}$. These show the hydrodynamic velocity $2\mu \mathrm{s}$ after the plasma was formed. The magnetic field points in the $z$ direction, and the probe laser propagates in the $+x$ direction, from left to right.

Figure 4

(a) Scaled transverse velocity gradient in the presence of a magnetic field. In contrast to the longitudinal gradient plotted in Fig. 2, pronounced oscillations about zero are observed. The black circles are the experimental data. The solid line is a fit from Eq. (29). (b) Fitted scaled oscillation frequency vs charge imbalance. The symbols are experimental data with conditions listed in Table 1. The solid line indicates the scaled ion plasma frequency at the edge of the electron density distribution, where the plasma becomes non-neutral.

Figure 5

Ion temperature for different initial electron temperatures. (a) As the initial electron temperature increases, the ion temperature decreases. The inset shows the ion temperature during the first 800 ns. (b) Plotting the ion temperature vs scaled time shows the influence of electron-ion collisions and plasma expansion. The legend shows initial electron temperatures in K. The circles and dashed lines show experimental data. Solid lines show predictions from the asymmetric expansion model of Sec. 3 with enhanced values of ${\gamma }_{ei}$ as described in the text. The experimental temperature data are from set 2 in Fig. 4 and Table 1.