skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Finite Larmor radius magnetohydrodynamic analysis of the Rayleigh-Taylor instability in Z pinches with sheared axial flow

Abstract

The Rayleigh-Taylor (RT) instability in Z pinches with sheared axial flow (SAF) is analyzed using finite Larmor radius (FLR) magnetohydrodynamic theory, in whose momentum equation the FLR effect (also referred to as the effect of gyroviscosity) is introduced through an anisotropic ion (FLR) stress tensor. A dispersion relation is derived for the linear RT instability. Both analytical and numerical solutions of the dispersion equation are given. The results indicate that the short-wavelength modes of the RT instability can be stabilized by a sufficient FLR, whereas the long-wavelength modes can be stabilized by a sufficient SAF. In the small-wavenumber region, for normalized wavenumber K<2.4, the hybrid RT/KH (Kelvin-Helmholtz) instability is shown to be the most difficult to stabilize. However the synergistic effect of the SAF and gyroviscosity can mitigate both the RT instability in the large-wavenumber region (K>2.4) and the hybrid RT/KH instability in the small-wavenumber region. In addition, this synergistic effect can compress the RT instability to a narrow wavenumber region. Even the thorough stabilization of the RT instability in the large-wavenumber region is possible with a sufficient SAF and a sufficient gyroviscosity.

Authors:
; ;  [1]
  1. Southwestern Institute of Physics, P. O. Box 432, Chengdu 610041 (China)
Publication Date:
OSTI Identifier:
20974870
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 3; Other Information: DOI: 10.1063/1.2717583; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANISOTROPY; DISPERSION RELATIONS; DISPERSIONS; EQUATIONS; HELMHOLTZ INSTABILITY; IONS; LARMOR RADIUS; MAGNETOHYDRODYNAMICS; NUMERICAL SOLUTION; PLASMA; RAYLEIGH-TAYLOR INSTABILITY; SHEAR; STABILIZATION; STRESSES; TENSORS; WAVELENGTHS

Citation Formats

Qiu, X. M., Huang, L., and Jian, G. D. Finite Larmor radius magnetohydrodynamic analysis of the Rayleigh-Taylor instability in Z pinches with sheared axial flow. United States: N. p., 2007. Web. doi:10.1063/1.2717583.
Qiu, X. M., Huang, L., & Jian, G. D. Finite Larmor radius magnetohydrodynamic analysis of the Rayleigh-Taylor instability in Z pinches with sheared axial flow. United States. doi:10.1063/1.2717583.
Qiu, X. M., Huang, L., and Jian, G. D. Thu . "Finite Larmor radius magnetohydrodynamic analysis of the Rayleigh-Taylor instability in Z pinches with sheared axial flow". United States. doi:10.1063/1.2717583.
@article{osti_20974870,
title = {Finite Larmor radius magnetohydrodynamic analysis of the Rayleigh-Taylor instability in Z pinches with sheared axial flow},
author = {Qiu, X. M. and Huang, L. and Jian, G. D.},
abstractNote = {The Rayleigh-Taylor (RT) instability in Z pinches with sheared axial flow (SAF) is analyzed using finite Larmor radius (FLR) magnetohydrodynamic theory, in whose momentum equation the FLR effect (also referred to as the effect of gyroviscosity) is introduced through an anisotropic ion (FLR) stress tensor. A dispersion relation is derived for the linear RT instability. Both analytical and numerical solutions of the dispersion equation are given. The results indicate that the short-wavelength modes of the RT instability can be stabilized by a sufficient FLR, whereas the long-wavelength modes can be stabilized by a sufficient SAF. In the small-wavenumber region, for normalized wavenumber K<2.4, the hybrid RT/KH (Kelvin-Helmholtz) instability is shown to be the most difficult to stabilize. However the synergistic effect of the SAF and gyroviscosity can mitigate both the RT instability in the large-wavenumber region (K>2.4) and the hybrid RT/KH instability in the small-wavenumber region. In addition, this synergistic effect can compress the RT instability to a narrow wavenumber region. Even the thorough stabilization of the RT instability in the large-wavenumber region is possible with a sufficient SAF and a sufficient gyroviscosity.},
doi = {10.1063/1.2717583},
journal = {Physics of Plasmas},
number = 3,
volume = 14,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
  • 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