Blast-wave driven Kelvin-Helmholtz shear layers in a laser driven high-energy-density plasma

O.A. Hurricane 0 J.F. Hansen 0 E.C. Harding 0 V.A. Smalyuk 0 B.A. Remington 0 G. Langstaff 0 H.-S. Park 0 H.F. Robey 0 C.C. Kuranz 0 M.J. Grosskopf 0 R.S. Gillespie 0 0 J.F. Hansen General Atomics, 3550 General Atomics Court, San Diego, CA 92121-1122, USA The first successful high energy density KelvinHelmholtz (KH) shear layer experiments (O.A. Hurricane et al. in Phys. Plasmas, 16:056305, 2009; E.C. Harding et al. in Phys. Rev. Lett., 103:045005, 2009) demonstrated the ability to design and field a target that produces, in a controlled fashion, an array of large diagnosable KH vortices. Data from these experiments vividly showed the complete evolution of large (400 m) distinct eddies, from formation to apparent turbulent break-up in the span of about 75 ns. A second set of experiments, in which the density of a key carbon-foam material was varied, was recently performed. The new series showed a great deal of fine-structure that was not as apparent as in the original experiments. In this paper, the results of both experiments will be discussed along with supporting theory and simulation. An attempt is made to connect these observations with some turbulent scale-lengths. Finally, we speculate about the possible connection of these experiments to astrophysical contexts. - In May 2008, our team fielded the first successful highenergy-density-plasma (HEDP) Kelvin-Helmholtz (KH) experiments (Hurricane et al. 2009; Harding et al. 2009) on the Omega laser at the University of Rochester. These experiments demonstrated the conceptual design (Hurricane 2008) that relied upon shock driven baroclinic vorticity production and also showed that vivid high quality data (see Fig. 1) could be obtained on KH in a HEDP environment. The basic configuration consists of a stack of opaque high density plastic and low density foam all of which is contained in a shock tube of rectangular cross-section, made from Be so as to be able to radiograph through it with xrays of a few keV energy (see Fig. 2)details of the target design can be found in Hurricane et al. (2009). Laser energy (4 kJ in a 1 ns pulse for this case) is delivered to an 820 m diameter (FWHM) spot on an ablator covering the low density foam part of the target (on the left of Fig. 2). In this way, a strong shock is launched into the low density foam such that the pressure gradient at the leading edge of the shock would essentially be at right angles to the density gradient at the interface of the two dissimilar materials thus maximizing P . The interface between the two materials is perturbed by a sinusoidal contour with amplitude (a = 30 m) and wavelength ( = 400 m) chosen such that a number of large vortices would develop nonlinear structure in the expected field of view during the experiment. The data from our initial experiments were largely consistent with expectations based upon two-dimensional (2D) simulation. 1.1 Instability growth The images shown in Fig. 1 are simply converted into datum of vortex height versus time (Harding et al. 2009) that can be Fig. 1 From left to right, radiographic data from Omega shots 51097, 51086, and 51090 are shown. These three images show the time development of the KH instability at 25 ns, 45 ns, and 75 ns respectively. In the left frame, the vorticity producing shock wave is visible in the low density (100 mg/cc) carbon foam. Wave crests begin to develop immediately after passage of the shock wave and grow into fully developed vortices (middle frame). At late time (right frame), the spiral arms of the vortices appear to begin to diffuse away presumably the result of the onset of turbulence (figure adapted from Hurricane et al. 2009; Harding et al. 2009) compared with simulation and theory. In Fig. 3 an updated comparison of the vortex height data is shown against a revised simulation result and theory. The data shown in Fig. 3 are identical to those shown in Hurricane et al. (2009), Harding et al. (2009), but the simulation result shown here superceeds that presented previously. Here the simulation used to produce the data shown in Fig. 3 has been corrected to include the actual as-shot Be shock tube thickness of 500 m rather than the 200 m thickness used for the simulations shown in Hurricane et al. (2009), Harding et al. (2009) and a more accurate method of determining the vortex height from the simulation has also been used. The vortex model theory shown in Fig. 3 comes from using the expression for the fluid circulation, , derived in Hurricane (2008) (with values P = 1.62 Mbar, H = 1.43 g/cc, L = 0.1 g/cc, and = 5/3) in combination with the differential equations for the flow field where these differential equations imply vortex growth up to a saturation of the vortex amplitude to a value of ymax = cosh1(3)/2 0.281 (Hurricane 2008; Rikanati et al. 2003) the full vortex height then being hmax = 2ymax. Since (2) trace out the trajectory that a massless particle would follow starting from some initial point (x0, y0) at t = 0, the full vortex height as plotted in Fig. 3 is then twice the value of the envelope of solutions to (2) using the (x, y) locations that trace out the initial interface (see Fig. 4). An attempt to include the added complication of flow in the direction of vortex growth, due to the effect the transmitted shock, is shown in Fig. 3 as the stretched vortex model and is arrived at by adding a constant y-velocity of 2 m/ns (from simulation) to the vortex model solution. At late-time, the simulation and the stretched vortex model (which uses simulation derived values) both over predict the data. The simulation does exhibit the same change in growth rate at around t = 38 ns that the data show. Inspection of the simulation at t = 38 ns indicates that this is the time at which a shock traveling in the y direction, that was reflected from the top of the Be shock tube, impacts the chain of vortices slightly compressing them. The late-time over-prediction of the simulation is likely explained by the fact that the simulation is 2D, while the target itself is 3D. That is in 2D, the simulation the post-shock expansion of the shock-tube would under-estimate the real decay in the post-shock flow that results from the shocktube expanding in 3D. Circumstantial evidence that supports this 3D shock-tube expansion hypothesis, is that the earlier 2D simulation Hurricane et al. (2009) that uses a thinner Be shock-tube wall thickness than the simulation presented here is closer to the data at late time. An actual 3D simulation would be necessary to fully prove this hypothesis and some effort in that direction is underway. Another possible reason for the over-prediction of the simulation is that the monotonic-Q (an artificial dissipation term needed to stabilize the simulation against shocks is known to over-deposit vorticitya tensor-Q would be needed to alleviate this numeric problem. 2 Second campaign of experiments A second series of experiments was performed at the Omega las (...truncated)