Fig. 4: Spatial power spectra of the turbulent zone.

Spatial power spectrum (a), temporal evolution of the knee position (b) and bump morphology (c). a Typical radial power spectrum of the turbulent plasma obtained, at different times after the laser drive, compared to a reference case, non-shocked foam. The “low” spectrum evolved as a power law consistent with turbulence theory: a fiducial with a −5/3 coefficient is marked by dashes. The middle zone follows a power law with a much higher coefficient (nearly −6.6 in the 60 ns spectrum). The spatial frequency corresponding to the ion inertial range at 50 ns, f_i, is marked by the dash-dot line and is near the inflexion of the spectrum. The bump is highlighted by the grey zone, and is abnormal considering classical turbulence theory. The nearly flat spectrum, for spatial frequency above the bump, corresponds to the resolution limit of our diagnostic. b Evolution of the knee position as a function of time. The data points correspond to the mean values of our data set with a standard deviation as error bars. The dashed fiducial corresponds to a t^−1/4 evolution. The dotted line corresponds to the simulated Kolmogorov scale (as calculated in Table 2 for the hydrodynamic mono-mode case) time of 10⁴. The green dash-dotted line to the theoretical ion inertial range. c Comparison of the bump morphology at different times. The greyed zone highlights the bump position. The red arrow marks the phase contrast wavelength measured on grids.