Understanding the implications of the data from recent high-energy-density Kelvin-Helmholtz shear layer experiments

The first successful high energy density Kelvin-Helmholtz (KH) shear layer experiments (O.A. Hurricane, et al., Phys. Plasmas, 16, 056305, 2009; E.C. Harding, et al., Phys. Rev. Lett., 103, 045005, 2009) demonstrated the ability to design and field a target that produces an array of large diagnosable KH vortices in a controlled fashion. Data from these experiments vividly showed the complete evolution of large distinct eddies, from formation to apparent turbulent break-up. Unexpectedly, low-density bubbles/cavities comparable to the vortex size (∼ 300− 400 μm) appeared to grow up in the free-stream flow above the unstable material interface. In this paper, the basic principles of the experiment will be discussed, the data reviewed, and the progress on understanding the origin of the above bubble structures through theory and simulation will be reported on. (IFSA 1.10.096) In May 2009, our team fielded the first successful high-energy-density-physics (HEDP) KelvinHelmholtz (KH) experiments [1, 2] on the Omega laser at the University of Rochester. These experiments proved out the unique conceptual design [3] 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 x-rays of a few keV energy (see Fig. 2) – details of the target design can be found in [1]. Laser energy (4 kJ in a 1 ns pulse for this case) is delivered to an 820 μm diameter 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 ×∇ρ. The interface between the two materials is perturbed by a sinusoidal contour with amplitude (a = 30 μm) and wavelength (λ = 400 μm) chosen such that a number of large vortices would develop nonlinear structure in the expected field of view during the experiment. By in large, the data from our May 2008 experiments were consistent with expectations based upon two-dimensional (2D) simulation using the CALE [4] code. The Sixth International Conference on Inertial Fusion Sciences and Applications IOP Publishing Journal of Physics: Conference Series 244 (2010) 042007 doi:10.1088/1742-6596/244/4/042007 c © 2010 IOP Publishing Ltd 1 Figure 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 crest begin to develope immediately after passage of the shock wave and grow into full blown vortices (middle frame). At late time (right frame), the spiral arms of the vortices appear to begin to diffuse away presumably the result of turbulence onset. The images shown in Fig. 1 are simply converted into datum of vortex height versus time [2] that can be 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 Ref. [1, 2], 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 μm rather than the 200 μm thickness used for the simulations shown in [1, 2] and a more accurate method of determining the vortex height from the simulation has also been used. Figure 2. Left: A simulated radiograph result of a simulation of the target performance is shown at t = 80 ns. The materials that compose the target are annotated in the image. The field-of-view (FOV) accessible in the actual experiment is shown as the dashed red circle. Right: an annotated picture of the actual target. Note that the Be tube sides are 200 μ m thick, while the top and bottom sections of the Be tube are 500 μ m thick. The vortex model theory shown in Fig. 3 comes from using the expression for the fluid circulation, Γ, derived in Ref. [3] (with values P = 1.62 Mbar, ρH = 1.43 g/cc, ρL = 0.1 g/cc, The Sixth International Conference on Inertial Fusion Sciences and Applications IOP Publishing Journal of Physics: Conference Series 244 (2010) 042007 doi:10.1088/1742-6596/244/4/042007