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Title: Formation of large-scale structures with sharp density gradient through Rayleigh-Taylor growth in a two-dimensional slab under the two-fluid and finite Larmor radius effects

Abstract

Two-fluid and the finite Larmor effects on linear and nonlinear growth of the Rayleigh-Taylor instability in a two-dimensional slab are studied numerically with special attention to high-wave-number dynamics and nonlinear structure formation at a low β-value. The two effects stabilize the unstable high wave number modes for a certain range of the β-value. In nonlinear simulations, the absence of the high wave number modes in the linear stage leads to the formation of the density field structure much larger than that in the single-fluid magnetohydrodynamic simulation, together with a sharp density gradient as well as a large velocity difference. The formation of the sharp velocity difference leads to a subsequent Kelvin-Helmholtz-type instability only when both the two-fluid and finite Larmor radius terms are incorporated, whereas it is not observed otherwise. It is shown that the emergence of the secondary instability can modify the outline of the turbulent structures associated with the primary Rayleigh-Taylor instability.

Authors:
;  [1]; ; ;  [2];  [3]
  1. Graduate University for Advanced Studies (SOKENDAI), 322-6 Oroshi, Toki, Gifu 509-5292 (Japan)
  2. National Institute for Fusion Science, 322-6 Oroshi, Toki, Gifu 509-5292 (Japan)
  3. (SOKENDAI), 322-6 Oroshi, Toki, Gifu 509-5292 (Japan)
Publication Date:
OSTI Identifier:
22423776
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 22; Journal Issue: 3; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; COMPUTERIZED SIMULATION; LARMOR RADIUS; MAGNETOHYDRODYNAMICS; NONLINEAR PROBLEMS; RAYLEIGH-TAYLOR INSTABILITY; SLABS; TWO-DIMENSIONAL SYSTEMS

Citation Formats

Goto, R., Hatori, T., Miura, H., E-mail: miura.hideaki@nifs.ac.jp, Ito, A., Sato, M., and Graduate University for Advanced Studies. Formation of large-scale structures with sharp density gradient through Rayleigh-Taylor growth in a two-dimensional slab under the two-fluid and finite Larmor radius effects. United States: N. p., 2015. Web. doi:10.1063/1.4916061.
Goto, R., Hatori, T., Miura, H., E-mail: miura.hideaki@nifs.ac.jp, Ito, A., Sato, M., & Graduate University for Advanced Studies. Formation of large-scale structures with sharp density gradient through Rayleigh-Taylor growth in a two-dimensional slab under the two-fluid and finite Larmor radius effects. United States. doi:10.1063/1.4916061.
Goto, R., Hatori, T., Miura, H., E-mail: miura.hideaki@nifs.ac.jp, Ito, A., Sato, M., and Graduate University for Advanced Studies. 2015. "Formation of large-scale structures with sharp density gradient through Rayleigh-Taylor growth in a two-dimensional slab under the two-fluid and finite Larmor radius effects". United States. doi:10.1063/1.4916061.
@article{osti_22423776,
title = {Formation of large-scale structures with sharp density gradient through Rayleigh-Taylor growth in a two-dimensional slab under the two-fluid and finite Larmor radius effects},
author = {Goto, R. and Hatori, T. and Miura, H., E-mail: miura.hideaki@nifs.ac.jp and Ito, A. and Sato, M. and Graduate University for Advanced Studies},
abstractNote = {Two-fluid and the finite Larmor effects on linear and nonlinear growth of the Rayleigh-Taylor instability in a two-dimensional slab are studied numerically with special attention to high-wave-number dynamics and nonlinear structure formation at a low β-value. The two effects stabilize the unstable high wave number modes for a certain range of the β-value. In nonlinear simulations, the absence of the high wave number modes in the linear stage leads to the formation of the density field structure much larger than that in the single-fluid magnetohydrodynamic simulation, together with a sharp density gradient as well as a large velocity difference. The formation of the sharp velocity difference leads to a subsequent Kelvin-Helmholtz-type instability only when both the two-fluid and finite Larmor radius terms are incorporated, whereas it is not observed otherwise. It is shown that the emergence of the secondary instability can modify the outline of the turbulent structures associated with the primary Rayleigh-Taylor instability.},
doi = {10.1063/1.4916061},
journal = {Physics of Plasmas},
number = 3,
volume = 22,
place = {United States},
year = 2015,
month = 3
}
  • The effects of compressibility on the Rayleigh-Taylor (RT) instability in a finite Larmor radius (FLR) plasma of magnetic field acceleration are studied by means of FLR magnetohydrodynamic (MHD) theory. FLR effects are introduced in the momentum equation of MHD theory through an anisotropic ion stress tensor. The linear mode equation which includes main equilibrium quantities and their high-order differential terms is derived. The dispersion equation is solved numerically. The main results indicate that in the compressible FLR plasma the growth rate of the RT instability displays faster growing and broader wavenumber range; and a new branch of low-frequency and long-wavelengthmore » instability, whose real frequency is positive (opposite from the negative real frequency of the RT instability), is found in the compressible FLR plasma. That is, plasma compressibility is a destabilizing factor for both the FLR stabilized RT instability and the new branch of instability.« less
  • The evolution of the Rayleigh{endash}Taylor instability is studied using finite Larmor radius (FLR) magnetohydrodynamic (MHD) theory. Finite Larmor radius effects are introduced in the momentum equation through an anisotropic ion stress tensor. Roberts and Taylor [Phys. Rev. Lett. {bold 3}, 197 (1962)], using fluid theory, demonstrated that FLR effects can stabilize the Rayleigh{endash}Taylor instability in the short-wavelength limit ({ital kL}{sub {ital n}}{gt}1, where {ital k} is the wave number and {ital L}{sub {ital n}} is the density gradient scale length). In this paper a linear mode equation is derived that is valid for arbitrary {ital kL}{sub {ital n}}. Analytic solutionsmore » are presented in both the short-wavelength ({ital kL}{sub {ital n}}{gt}1) and long-wavelength ({ital kL}{sub {ital n}}{lt}1) regimes, and numerical solutions are presented for the intermediate regime ({ital kL}{sub {ital n}}{approximately}1). The long-wavelength modes are shown to be the most difficult to stabilize. More important, the nonlinear evolution of the Rayleigh{endash}Taylor instability is studied using a newly developed two-dimensional (2-D) FLR MHD code. The FLR effects are shown to be a stabilizing influence on the Rayleigh{endash}Taylor instability; the short-wavelength modes are the easiest to stabilize, consistent with linear theory. In the nonlinear regime, the FLR effects cause the {open_quote}{open_quote}bubbles and spikes{close_quote}{close_quote} that develop because of the Rayleigh{endash}Taylor instability to convect along the density gradient and to tilt. Applications of this model to space and laboratory plasma phenomena are discussed. {copyright} {ital 1996 American Institute of Physics.}« less
  • A diffusion model for turbulent mix [C. Cherfils and K. O. Mikaelian, Phys. Fluids {bold 8}, 522 (1996)] is compared with recent two-dimensional magnetohydrodynamic simulations by Huba [Phys. Plasmas {bold 3}, 2523 (1996)]. The model accounts for density gradient stabilization and for finite Larmor radius stabilization, thus suppressing the Rayleigh{endash}Taylor mixing width to below its classical value. The model, which has no free parameters, appears to be in good agreement with Huba`s numerical simulations. {copyright} {ital 1997 American Institute of Physics.}