Kelvin–Helmholtz instability under stabilizing parallel magnetic field in nonhomogeneous compressible MHD flows

Peyrichon, G.; El-Rabii, H.; Ripoll, J.-F.; Casner, A.; Michael, A.; Merkin, V. G.; Hurricane, O. A.

doi:10.1063/5.0252162

Kelvin–Helmholtz instability under stabilizing parallel magnetic field in nonhomogeneous compressible MHD flows

Journal Article · Mon Apr 28 00:00:00 EDT 2025 · Physics of Plasmas

DOI:https://doi.org/10.1063/5.0252162· OSTI ID:2585273

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CEA DAM Île-de-France (DIF), Arpajon (France)
Institut Pprime, Poitiers (France)
CEA DAM Île-de-France (DIF), Arpajon (France); Univ. Paris-Saclay (France)
Johns Hopkins Univ., Laurel, MD (United States)
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

We study the Kelvin–Helmholtz instability (KHI) for the general case of a compressible, nonhomogeneous, magnetized plasma flow. The study is limited to a vortex sheet interface with an imposed parallel magnetic field. We introduce a new formalism based on a convective Mach number M_c, a convective Alfvénic Mach number M_Ac, and a total convective Mach number that combines the two. We derive an analytic expression of the KHI growth rate for a homogeneous flow (i.e., zero Atwood number, A=0) that converges toward both the expression for unmagnetized compressible flow and Chandrasekhar's expression for magnetized incompressible flow. Otherwise, the dispersion relation is solved numerically and allows deriving general stability diagrams of magnetized KHI for the triplet (A, M_c, β−plasma) parameters. We show these parameters uniquely define all configurations for a parallel magnetic field. We also construct diagrams with respect to the convective Alfvénic Mach number, the β− plasma parameter, or the magnetic field showing which magnetic field strength is required for stabilizing a given shear flow. The theoretical growth rates are compared with 18 simulations made with the GAMERA code, currently used for 3D magnetospheric simulations. Finally, we apply our results to the analysis of a past KHI experiment performed at the OMEGA laser facility, showing linear theory succeeds to provide accurate estimates of the growth rate at early times. We further discuss how our results can inform future experiments in the high-Mach magnetized regime at the National Ignition Facility. Possible limitations of the study due to resistive, mixing, or turbulence effects are discussed.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 2585273

Report Number(s):: LLNL--JRNL-2002188

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 4 Vol. 32; ISSN 1070-664X; ISSN 1089-7674

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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