Three-dimensional modeling and analysis of a high energy density Kelvin-Helmholtz experiment

Abstract

A recent series of experiments on the OMEGA laser provided the first controlled demonstration of the KelvinHelmholtz instability in a high-energy-density physics context (E. C. Harding, et al., Phys. Rev. Lett., 103, 045005,2009; O. A. Hurricane, et al., Phys. Plasmas, 16, 056305, 2009). We present 3D simulations which resolve previously reported discrepancies between those experiments and the 2D simulation used to design them. Our new simulations reveal a three-dimensional mechanism behind the low density "bubble" structures which appeared in the experimental x-ray radiographs at late times but were completely absent in the 2D simulations. We also demonstrate that the three-dimensional expansion of the walls of the target is sufficient to explain the 20% overprediction by 2D simulation of the late-time growth of the KH rollups. The implications of these results for the design of future experiments is discussed.

Evolution of the magnetic field generated by the Kelvin-Helmholtz instability

“…2-9. This difference stems primarily from different initial conditions for these two quantities in our simulations; these different initial conditions are expected to be rather universal for the KH plasma experiments [5][6][7][8]. At the initial time instant, we take zero magnetic field everywhere in the domain, while vorticity has inevitably a certain non-zero distribution due to the initial velocity profile forming the two counter-flows; see in Fig.…”

“…11: Magnetic field evolution in the simulation with the white noise initial perturbation at time instants t = τ0 (top), t = 2τ0 (middle) and t = 4τ0 (bottom). with the logarithmic scale we see that the magnetic field grows faster for larger wavenumbers of the initial perturbations according to the linear dispersion relation (7). The white noise perturbation produces weaker growth, which can be explained in the following way.…”

“…However, until now, all numerical investigations have been for strongly oversimplified model flows, such as the classical 2D RT instability at an inert interface [21][22][23], which is far away from realistic ICF conditions. Simulations of the KH instability in laser plasma have also been performed, but they did not take into account the magnetic field generation [7]. Only recently, magnetic field generation by the KH instability has been considered in the astrophysical context [24].…”

“…A good deal of experiments have been designed and performed on the Omega Laser Facility focusing on the KH instability, e.g., at the foam-aluminum interface in a layered target with two different substances set in motion by counter-propagating shock waves [8]. The other option was inducing the KH instability by a shock refracted at an interface separating two substances of noticeably different density [5][6][7]. The purpose of these experiments was typically to study generation of vortices and turbulence at the KH unstable interface.…”

Validation of a Turbulent Kelvin-Helmholtz Shear Layer Model Using a High-Energy-Density OMEGA Laser Experiment

“…The second image taken at t = 75 ns shows an even wider mixing layer at the same x-location on the target. The modulations above the layer at late time are the manifestation of an instability resulting from the threedimensional expansion of the foam-Be interface in the foreground/background that are being radiographed [19]. The numerical simulations discussed below show that, at x = 0.15 cm the center of the field of view of the data, immediately after the passage of the ∼ 2 Mbar blastwave [with shock position, X s ∼ (E/ρ) 1/3 t 2/3 , scaling as the classical one-dimensional self-similar Taylor-like solution] the post-shock flow speed spikes to ∼ 45 µm/ns and decays to zero at a distance ∼ 1300 µm behind the shock, thus limiting the extent of the most rapid growth of shear mixing to a region immediately behind the shock.…”