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.
Ruiz, D. E.. "On a variational formulation of the weakly nonlinear magnetic Rayleigh–Taylor instability." Physics of Plasmas, vol. 27, no. 2, Dec. 2019. https://doi.org/10.1063/1.5132750
Ruiz, D. E. (2019). On a variational formulation of the weakly nonlinear magnetic Rayleigh–Taylor instability. Physics of Plasmas, 27(2). https://doi.org/10.1063/1.5132750
Ruiz, D. E., "On a variational formulation of the weakly nonlinear magnetic Rayleigh–Taylor instability," Physics of Plasmas 27, no. 2 (2019), https://doi.org/10.1063/1.5132750
@article{osti_1605728,
author = {Ruiz, D. E.},
title = {On a variational formulation of the weakly nonlinear magnetic Rayleigh–Taylor instability},
annote = {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.},
doi = {10.1063/1.5132750},
url = {https://www.osti.gov/biblio/1605728},
journal = {Physics of Plasmas},
issn = {ISSN 1070-664X},
number = {2},
volume = {27},
place = {United States},
publisher = {American Institute of Physics (AIP)},
year = {2019},
month = {12}}
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 223, Issue 1154, p. 348-360https://doi.org/10.1098/rspa.1954.0120