Direct Measurement of the Return Current Instability in a Laser-Produced Plasma

Measurements were made of the return current instability growth rate, demonstrating its concurrence with nonlocal transport. Thomson scattering was used to measure a maximum growth rate of $5.1\times {10}^9\mathrm{Hz}$, which was 3 times less than classical Spitzer-Härm theory predicts. The measured plasma conditions indicate the heat flux was nonlocal, and Vlasov–Fokker-Planck simulations that account for nonlocality reproduce the measured growth rates. Furthermore, the threshold for the return current instability was measured (${\delta }_T=0.017\pm 0.002$) to be in good agreement with previous theoretical models.

Figure 1

Ultraviolet beams (blue) were used to heat the plasma, and a 526.5-nm beam (green) was used as a Thomson-scattering probe. This heating configuration produced a hot region (red sphere) surrounded by a cooler region of plasma (blue sphere). Over a series of shots, the Thomson-scattered light was collected at different locations (black spheres). The ion-acoustic waves ($k_{IAW}$, red arrow) probed by Thomson scattering were aligned with the heat flux and return current (purple arrows). The insets show (a) the overlapped heater beam intensity, (b) the spatially resolved electron-plasma wave features measured when the probe beam passed through the center of the plasma, and an example of (c) the temporally resolved blueshifted ion acoustic wave that was driven by RCI ($r=475\mu \mathrm{m}$).

Figure 2

Electron density, blue left axes, and electron temperature, red right axes, as a function of (a) time and (b) radius. Error bars give the uncertainty in the measured plasma conditions. (b) The data were matched with a hyperbolic tangent (dashed curves) to provide continuous functions for calculating the Knudsen number. The shaded regions mark the 90% confidence interval for these fits. Dark red and blue data (circles) were measured in a single spatially resolved spectrum, while the lighter color data (squares) represent the set of temporally resolved spectra taken at different radii over multiple shots.

Figure 3

The ion acoustic wave amplitude (black) at a radius of (a) $475\mu \mathrm{m}$ and (b) $200\mu \mathrm{m}$ are matched with an exponential model (red curve) with a shaded 90% confidence interval. (a) Exponential models with growth rates from the Spitzer-Härm theory (purple) and VFP simulations (blue) are compared to the data. (c) Measured growth rates (red) are compared to growth rates from the Spitzer-Härm theory (purple) and VFP simulations (blue) as a function of radius.

Figure 4

(a) The Knudsen number calculated for individual data points (red circles) is compared with the hyperbolic tangent model (red curve) and its confidence interval (shaded region). A model from Tikhonchuk et al. [31] (green) is compared with the data while a nonlocality threshold is shown in black. (b) The heat flux is normalized to the free streaming limit for the Spitzer-Härm theory (purple), VFP simulations (blue), and the SNB model (orange). Two common flux limiters are shown in black.