On a variational formulation of the weakly nonlinear magnetic Rayleigh–Taylor instability

Ruiz, D. E.

doi:10.1063/1.5132750

Title: On a variational formulation of the weakly nonlinear magnetic Rayleigh–Taylor instability

Journal Article · 31 December 2019 · Physics of Plasmas

DOI: https://doi.org/10.1063/1.5132750 · OSTI ID:1605728

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Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

The magnetic-Rayleigh–Taylor (MRT) instability is a ubiquitous phenomenon that occurs in magnetically-driven Z-pinch implosions. It is important to understand this instability since it can decrease the performance of such implosions. In this work, I present a theoretical model for the weakly nonlinear MRT instability. I obtain such a model by asymptotically expanding an action principle, whose Lagrangian leads to the fully nonlinear MRT equations. After introducing a suitable choice of coordinates, I show that the theory can be cast as a Hamiltonian system, whose Hamiltonian is calculated up to the sixth order in a perturbation parameter. The resulting theory captures the harmonic generation of MRT modes. It is shown that the amplitude at which the linear magnetic-Rayleigh–Taylor instability exponential growth saturates depends on the stabilization effect of the magnetic-field tension. Overall, the theory provides an intuitive interpretation of the weakly nonlinear MRT instability and provides a systematic approach for studying this instability in more complex settings.

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Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

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

Grant/Contract Number:: AC04-94AL85000; NA0003525

OSTI ID:: 1605728

Report Number(s):: SAND--2020-2688J; 684470

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 2 Vol. 27; ISSN 1070-664X

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

Country of Publication:: United States

Language:: English

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Title: On a variational formulation of the weakly nonlinear magnetic Rayleigh–Taylor instability

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