Compression of turbulent plasma can amplify the turbulent kinetic energy, if the compression is fast compared to the viscous dissipation time of the turbulent eddies. A sudden viscous dissipation mechanism is demonstrated, whereby this amplified turbulent kinetic energy is rapidly converted into thermal energy, suggesting a new paradigm for fast ignition inertial fusion.Introduction.-Unprecedented densities and temperatures are now reached by compressing plasma using lasers or magnetic fields, with the objective of reaching nuclear fusion, prodigious x-ray production, or new regimes of materials. The plasma motion in these compressions can be turbulent, whether magnetically driven [1][2][3][4] or laser driven [5,6]. However, rapid compression of this turbulent plasma, where the viscosity is highly sensitive to temperature, is demonstrated here to exhibit unusual behavior, where the turbulent kinetic energy (TKE) abruptly switches from growing to rapidly dissipating. This behavior occurs in plasma, but is not predicted by studies of neutral gas compression [7][8][9][10][11][12][13]. In fact, it was observations of the dominant effect of the TKE in Zpinches, both in pressure balance [4] and in radiation balance [2,4], that stimulated the present study.Compression is rapid if the rate of compression is fast compared to the turbulent timescale τ = k/ with k the TKE and the viscous dissipation rate. In the initially rapid plasma compressions here, the viscous dissipation eventually grows such that the turbulent timescale τ shortens, and the plasma TKE suddenly dissipates. This dissipation is sudden in that it occurs over a time interval that is small compared to the overall compression time.This sudden dissipation mechanism now suggests a new fast ignition paradigm. Imagine an initially turbulent fusion fuel plasma where the majority of the energy is in the turbulent motion. This plasma is then rapidly compressed, causing both the TKE and thermal energy to grow, while the TKE retains most of the energy, as observed in certain Z-pinch experiments [1][2][3][4]. Since radiation losses (both synchrotron and bremsstrahlung) and nuclear fusion are dependent on thermal energy but not the TKE, those processes are minimized under such compression, since the plasma stays comparatively cool. However, late in the compression, the TKE suddenly dissipates viscously into thermal energy, thereby igniting the plasma without having undergone large radiation losses.In neutral gas, upon rapid compression, the TKE grows. In an isotropic 3D compression, it grows as 1/L 2 , where L is the (time dependent) side length of a box that is compressing with the mean flow along each axis. This is true for both the zero Mach case [7], where the TKE is solenoidal, as well as in the finite Mach case, where the TKE has both solenoidal and dilational components, which each grow in energy as 1/L 2 [12]. This is the same

Classical density functional theory ͑DFT͒ of fluids is a valuable tool to analyze inhomogeneous fluids. However, few numerical solution algorithms for three-dimensional systems exist. Here we present an efficient numerical scheme for fluids of charged, hard spheres that uses O͑N log N͒ operations and O͑N͒ memory, where N is the number of grid points. This system-size scaling is significant because of the very large N required for three-dimensional systems. The algorithm uses fast Fourier transforms ͑FFTs͒ to evaluate the convolutions of the DFT Euler-Lagrange equations and Picard ͑iterative substitution͒ iteration with line search to solve the equations. The pros and cons of this FFT/Picard technique are compared to those of alternative solution methods that use real-space integration of the convolutions instead of FFTs and Newton iteration instead of Picard. For the hard-sphere DFT, we use fundamental measure theory. For the electrostatic DFT, we present two algorithms. One is for the "bulk-fluid" functional of Rosenfeld ͓Y. Rosenfeld, J. Chem. Phys. 98, 8126 ͑1993͔͒ that uses O͑N log N͒ operations. The other is for the "reference fluid density" ͑RFD͒ functional ͓D. Gillespie et al., J. Phys.: Condens. Matter 14, 12129 ͑2002͔͒. This functional is significantly more accurate than the bulk-fluid functional, but the RFD algorithm requires O͑N 2 ͒ operations.

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Turbulent plasma flow, amplified by rapid 3D compression, can be suddenly dissipated under continuing compression. This effect relies on the sensitivity of the plasma viscosity to the temperature, µ ∼ T 5/2 . The plasma viscosity is also sensitive to the plasma ionization state. We show that the sudden dissipation phenomenon may be prevented when the plasma ionization state increases during compression, and demonstrate the regime of net viscosity dependence on compression where sudden dissipation is guaranteed. Additionally, it is shown that, compared to cases with no ionization, ionization during compression is associated with larger increases in turbulent energy, and can make the difference between growing and decreasing turbulent energy.