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Small-scale fluctuating magnetic fields of order nG to muG are observed in supernova shocks and galaxy clusters, where amplifications of the field are likely caused by the Biermann battery mechanism induced through curved shock vorticity. However, these fields cannot be amplified further without the presence of the turbulent dynamo mechanism, which generates large-scale magnetic energy through the stretching and compression of magnetic flux lines. Thus, we present here novel three-dimensional magnetohydrodynamic (MHD) simulations of a laser-driven shock propagating into a stratified, multiphase medium, with a small-scale seed magnetic field, to investigate the post-shock turbulent magnetic field amplification via the fluctuating dynamo. The test configuration used here is currently being tested in the shock tunnel facility at the National Ignition Facility (NIF). In order to probe the statistical properties of the post-shock turbulent region, we use tracer trajectories to track its evolution through the Lagrangian framework, thus providing a high-fidelity analysis of the shocked medium. Our simulations indicate that the growth of the magnetic field, which accompanies the near-Saffman power-law kinetic energy decay in the absence of turbulence driving, exhibits fundamentally different characteristics as compared to periodic box simulations. Seemingly no distinct phases exist in its evolution. Yet, the growth rates are still consistent with those expected for compressive driving in subsonic, compressible turbulence. Phenomenological understanding of the dynamics of the magnetic and velocity fields are also elucidated via second-order Lagrangian frequency spectrums, which yield the expected inertial range scalings in the Lagrangian bridge relations. |
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