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Effects of External Magnetic Fields on the Multi-mode Rayleigh-Taylor Instability

Xin Bian, Riccardo Betti, Dongxiao Zhao, Hussein Aluie

TL;DR

This study systematically characterizes how external magnetic fields, oriented parallel or perpendicular to the RTI interface, shape the nonlinear evolution of multi‑mode mRTI in 2D and 3D using resistive MHD with explicit viscosity and resistivity. By varying field strength over a broad range and comparing parallel versus vertical orientations, the authors demonstrate that weak parallel fields enhance mixing while strong parallel fields suppress it, whereas vertical fields delay early growth but promote late‑time, self‑similar mixing through altered anisotropy and vorticity. The work attributes these behaviors primarily to magnetic tension in the Lorentz force, which modulates drag, buoyancy, energy transfer, and flow morphology, providing a cohesive framework that reconciles disparate prior results. These insights have implications for inertial confinement fusion and magnetized astrophysical plasmas, and the study outlines future extensions to ablation physics, Biermann battery effects, spatially varying resistivity, and cylindrical geometries to capture additional real‑world effects.

Abstract

The magneto-Rayleigh-Taylor instability (mRTI) is a key process in inertial confinement fusion and is thought to be widespread in the interstellar medium, where it can concentrate plasma into discrete structures. We present resistive MHD simulations of the nonlinear evolution of multi-mode mRTI in both two and three dimensions, examining the effects of uniform external magnetic fields oriented either parallel or perpendicular to the initial interface. In both 2-D and 3-D, weak parallel fields enhance mixing-zone growth, whereas stronger fields suppress it. For perpendicular fields, growth is initially inhibited but becomes enhanced at later times. These behaviors arise from magnetic tension, which modifies flow anisotropy, buoyancy, drag, and vortex dynamics. The interplay of these mechanisms governs the distinct ways in which magnetic fields influence mRTI evolution.

Effects of External Magnetic Fields on the Multi-mode Rayleigh-Taylor Instability

TL;DR

This study systematically characterizes how external magnetic fields, oriented parallel or perpendicular to the RTI interface, shape the nonlinear evolution of multi‑mode mRTI in 2D and 3D using resistive MHD with explicit viscosity and resistivity. By varying field strength over a broad range and comparing parallel versus vertical orientations, the authors demonstrate that weak parallel fields enhance mixing while strong parallel fields suppress it, whereas vertical fields delay early growth but promote late‑time, self‑similar mixing through altered anisotropy and vorticity. The work attributes these behaviors primarily to magnetic tension in the Lorentz force, which modulates drag, buoyancy, energy transfer, and flow morphology, providing a cohesive framework that reconciles disparate prior results. These insights have implications for inertial confinement fusion and magnetized astrophysical plasmas, and the study outlines future extensions to ablation physics, Biermann battery effects, spatially varying resistivity, and cylindrical geometries to capture additional real‑world effects.

Abstract

The magneto-Rayleigh-Taylor instability (mRTI) is a key process in inertial confinement fusion and is thought to be widespread in the interstellar medium, where it can concentrate plasma into discrete structures. We present resistive MHD simulations of the nonlinear evolution of multi-mode mRTI in both two and three dimensions, examining the effects of uniform external magnetic fields oriented either parallel or perpendicular to the initial interface. In both 2-D and 3-D, weak parallel fields enhance mixing-zone growth, whereas stronger fields suppress it. For perpendicular fields, growth is initially inhibited but becomes enhanced at later times. These behaviors arise from magnetic tension, which modifies flow anisotropy, buoyancy, drag, and vortex dynamics. The interplay of these mechanisms governs the distinct ways in which magnetic fields influence mRTI evolution.
Paper Structure (25 sections, 12 equations, 28 figures, 2 tables)

This paper contains 25 sections, 12 equations, 28 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Linear stability analysis
  3. 2D mRTI
  4. 3D parallel magnetic fields
  5. 3D vertical magnetic fields
  6. Numerical simulations
  7. Results and Analysis
  8. mRTI structure
  9. Mixing width and energy evolution
  10. 2D mixing-zone width
  11. 3D mixing width
  12. Effect of initial perturbations
  13. Evolution of kinetic and magnetic energies
  14. Roles of magnetic fields
  15. Effect of Lorentz force
  16. ...and 10 more sections

Figures (28)

  • Figure 1: Visualization of density at $Agt^2/L = 3.9$ (top panels), 10 (middle panels), and 30 (bottom panels) of 2D simulations. Note we have cropped the plots vertically for a better presentation.
  • Figure 2: Visualization of density at $Agt^2/L = 3.9$ (top panels), 8.3 (middle panels) and 14.7 (bottom panels) in 3D hRTI and mRTI with parallel B-fields. Note the plots are cropped for a better presentation.
  • Figure 3: Visualization of density at $Agt^2/L = 3.9$ (top panels), 8.3 (middle panels) and 14.7 (bottom panels) in 3D hRTI and mRTI with vertical B-fields. Note the plots are cropped for a better presentation.
  • Figure 4: Time evolution of the bubble height $(a,d)$, spike height $(b,e)$, and mixing zone width $(c,f)$ for 2D simulations with $\mathrm{Pr}_m=1$. Panels (a–c) illustrate the effects of horizontal magnetic fields, whereas panels (d–f) show the effects of vertical magnetic fields.
  • Figure 5: Time evolution of the bubble height $(a,d)$, spike height $(b,e)$, and mixing zone width $(c,f)$ for 3D simulations with $\mathrm{Pr}_m=1$. Panels (a–c) illustrate the effects of horizontal magnetic fields, whereas panels (d–f) show the effects of vertical magnetic fields.
  • ...and 23 more figures