As the laser driven shock travels down the length of the target (from left to right in this diagram), vorticity is generated at the interface since the pressure gradient from the shock and the density gradient at the interface are nearly orthogonal. An unavoidable transmitted shock (shown) and reflected shocks (not shown) are also present, but make smaller contributions to vorticity production than the primary laser driven shock.
Shown is the dimensionless function . The decrease of this function with is a reflection of the fact that the primary shock is less effective at generating vorticity the more nonlinear the initial perturbation is.
Frames of the simulation results show the expected target behavior in a synthetic x-ray image. The simulation shows that the region of the target to the left of is messy, which is why the experiment's diagnostic field of view was chosen to be . At late time, small zero pressure and zero density voids are observed following the primary shock wave—it is unclear whether these voids are the result a numerical error or a cavitationlike effect.
The target package is comprised of a rectangular cross-sectional shock tube (left) and a plasma shield (right). The shock tube is formed by joining two L shaped beryllium parts together enclosing the CRF foam and sandwich of iodinated plastic and polyamide imide. Not visible is the fact that the sinusoidal perturbed interface between the CRF and CH iodine/polyamide imide is match machined so that no air gap is present between the stack-up of materials.
Experimental radiograph at on Omega shot 51097 (left) and the synthetic radiograph from simulation (right) at the same time. The shock in the simulation is slightly ahead of that from the data image, . As expected, the data image shows vortices beginning to form after the passage of the shock wave. With the shock visible in the image we estimate the shock speed to be at this time.
Experimental radiograph at on Omega shot 51086 (left) and the synthetic radiograph from simulation (right) at the same time. Here the left most vortex is in its full development, while the rightmost is just starting to form and is showing a wisp of material at its tip that appears to be getting pulled into the postshock flow. There is qualitative agreement with the simulation, but the cores of simulated vortices are much more filled in than those observed in the data.
Experimental radiograph at on Omega shot 51090 (left) and the synthetic radiograph from simulation (right) at the same time. The left most vortex of the data image shows the arm of high density material “diffusing” away, while the simulated image continues to show a vortex that is filled in with high density material. The data and simulated vortices also show a difference in shape, with the simulation having vortices that are taller than they are wide.
The shows profiles of density in (red curve 0), pressure in Mbar (blue curve 1), material temperature in 10 eV units (magenta curve 2), and velocity along the -direction in (brown curve 3) from the simulation at 25 ns.
Vortex amplitude vs time is shown for the data (red squares with uncertainty bounds), the CALE simulation (blue diamonds), and the line vortex model (purple asterisk). The vortex model result includes the extra vertical stretching that comes from the transmitted shock postshock flow (green triangles).
“Bubbles” of low optical depth are present above each vortex and these bubbles appear to be bigger for the more evolved vortices. These bubble features have the visual character of what one would expect from shocks, but may also be cavities of some other origin. No such features were anticipated by the simulation.
In a figure similar to the above, Dimotakis (Ref. 33) conjectured the formation of a bubblelike “shocklet” as subsonic flow in the convective frame of reference, accelerates becoming transonic as it passes over the crest of the vortex. The supersonic flow is suddenly decelerated as it runs into the subsonic flow of the next vortex, forming a shock front. The picture has a striking resemblance to the bubbles that we observe in the data image of Fig. 10.
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