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

Title: Coupling of sausage, kink, and magneto-Rayleigh-Taylor instabilities in a cylindrical liner

Abstract

This paper analyzes the coupling of magneto-Rayleigh-Taylor (MRT), sausage, and kink modes in an imploding cylindrical liner, using ideal MHD. A uniform axial magnetic field of arbitrary value is included in each region: liner, its interior, and its exterior. The dispersion relation is solved exactly, for arbitrary radial acceleration (-g), axial wavenumber (k), azimuthal mode number (m), liner aspect ratio, and equilibrium quantities in each region. For small k, a positive g (inward radial acceleration in the lab frame) tends to stabilize the sausage mode, but destabilize the kink mode. For large k, a positive g destabilizes both the kink and sausage mode. Using the 1D-HYDRA simulation results for an equilibrium model that includes a pre-existing axial magnetic field and a preheated fuel, we identify several stages of MRT-sausage-kink mode evolution. We find that the m = 1 kink-MRT mode has a higher growth rate at the initial stage and stagnation stage of the implosion, and that the m = 0 sausage-MRT mode dominates at the main part of implosion. This analysis also sheds light on a puzzling feature in Harris' classic paper of MRT [E. G. Harris, Phys. Fluids 5, 1057 (1962)]. An attempt is made to interpret the persistence of the observedmore » helical structures [Awe et al., Phys. Rev. Lett. 111, 235005 (2013)] in terms of non-axisymmetric eigenmode.« less

Authors:
; ; ;  [1]; ; ;  [2]
  1. Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, Michigan 48109-2104 (United States)
  2. Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States)
Publication Date:
OSTI Identifier:
22408218
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; ACCELERATION; ASPECT RATIO; COMPUTERIZED SIMULATION; CYLINDRICAL CONFIGURATION; DISPERSION RELATIONS; EXACT SOLUTIONS; IMPLOSIONS; KINK INSTABILITY; LINERS; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; RAYLEIGH-TAYLOR INSTABILITY; THERMONUCLEAR FUELS

Citation Formats

Weis, M. R., Zhang, P., Lau, Y. Y., E-mail: yylau@umich.edu, Gilgenbach, R. M., Schmit, P. F., Peterson, K. J., and Hess, M. Coupling of sausage, kink, and magneto-Rayleigh-Taylor instabilities in a cylindrical liner. United States: N. p., 2015. Web. doi:10.1063/1.4915520.
Weis, M. R., Zhang, P., Lau, Y. Y., E-mail: yylau@umich.edu, Gilgenbach, R. M., Schmit, P. F., Peterson, K. J., & Hess, M. Coupling of sausage, kink, and magneto-Rayleigh-Taylor instabilities in a cylindrical liner. United States. doi:10.1063/1.4915520.
Weis, M. R., Zhang, P., Lau, Y. Y., E-mail: yylau@umich.edu, Gilgenbach, R. M., Schmit, P. F., Peterson, K. J., and Hess, M. Sun . "Coupling of sausage, kink, and magneto-Rayleigh-Taylor instabilities in a cylindrical liner". United States. doi:10.1063/1.4915520.
@article{osti_22408218,
title = {Coupling of sausage, kink, and magneto-Rayleigh-Taylor instabilities in a cylindrical liner},
author = {Weis, M. R. and Zhang, P. and Lau, Y. Y., E-mail: yylau@umich.edu and Gilgenbach, R. M. and Schmit, P. F. and Peterson, K. J. and Hess, M.},
abstractNote = {This paper analyzes the coupling of magneto-Rayleigh-Taylor (MRT), sausage, and kink modes in an imploding cylindrical liner, using ideal MHD. A uniform axial magnetic field of arbitrary value is included in each region: liner, its interior, and its exterior. The dispersion relation is solved exactly, for arbitrary radial acceleration (-g), axial wavenumber (k), azimuthal mode number (m), liner aspect ratio, and equilibrium quantities in each region. For small k, a positive g (inward radial acceleration in the lab frame) tends to stabilize the sausage mode, but destabilize the kink mode. For large k, a positive g destabilizes both the kink and sausage mode. Using the 1D-HYDRA simulation results for an equilibrium model that includes a pre-existing axial magnetic field and a preheated fuel, we identify several stages of MRT-sausage-kink mode evolution. We find that the m = 1 kink-MRT mode has a higher growth rate at the initial stage and stagnation stage of the implosion, and that the m = 0 sausage-MRT mode dominates at the main part of implosion. This analysis also sheds light on a puzzling feature in Harris' classic paper of MRT [E. G. Harris, Phys. Fluids 5, 1057 (1962)]. An attempt is made to interpret the persistence of the observed helical structures [Awe et al., Phys. Rev. Lett. 111, 235005 (2013)] in terms of non-axisymmetric eigenmode.},
doi = {10.1063/1.4915520},
journal = {Physics of Plasmas},
number = 3,
volume = 22,
place = {United States},
year = {Sun Mar 15 00:00:00 EDT 2015},
month = {Sun Mar 15 00:00:00 EDT 2015}
}
  • Cited by 10
  • The development and use of a single-fluid two-temperature approximated 2-D Magneto-Hydrodynamics code is reported. Z-pinch dynamics and the evolution of Magneto-Rayleigh-Taylor (MRT) instabilities in a gas jet type Extreme Ultraviolet (EUV) source are investigated with this code. The implosion and stagnation processes of the Z-pinch dynamics and the influence of initial perturbations (single mode, multi- mode, and random seeds) on MRT instability are discussed in detail. In the case of single mode seeds, the simulation shows that the growth rates for mm-scale wavelengths up to 4 mm are between 0.05 and 0.065 ns{sup −1}. For multi-mode seeds, the mode couplingmore » effect leads to a series of other harmonics, and complicates MRT instability evolution. For perturbation by random seeds, the modes evolve to longer wavelengths and finally converge to a mm-scale wavelength approximately 1 mm. MRT instabilities can also alter the pinch stagnation state and lead to temperature and density fluctuations along the Z axis, which eventually affects the homogeneity of the EUV radiation output. Finally, the simulation results are related to experimental results to discuss the mitigations of MRT instability.« less
  • A two-dimensional computational methodology has been developed that uses a phenomenological representation of initial perturbations to model the evolution of magnetically driven Rayleigh{endash}Taylor instabilities in a hollow Z pinch. The perturbed drive current waveform and x-ray output obtained from the two-dimensional models differ qualitatively from the results of unperturbed (one-dimensional) models. Furthermore, the perturbed results reproduce the principle features measured in a series of capacitor bank-driven pulsed power experiments. In this paper we discuss the computational approach and the computational sensitivity to initial conditions (including the initial perturbations). Representative examples are also presented of instability evolution during implosions, and themore » results are compared with experimentally measured current waveforms and visible framing camera images of perturbed implosions. Standard magnetohydrodynamic modeling, which includes instability growth in two dimensions, is found to reproduce the features seen in experiments. {copyright} {ital 1996 American Institute of Physics.}« less
  • We study the linear stability of an arbitrary number N of cylindrical concentric shells undergoing a radial implosion or explosion.We derive the evolution equation for the perturbation {eta}{sub i} at interface i; it is coupled to the two adjacent interfaces via {eta}{sub i{+-}1}. For N=2, where there is only one interface, we verify Bell's conjecture as to the form of the evolution equation for arbitrary {rho}{sub 1} and {rho}{sub 2}, the fluid densities on either side of the interface. We obtain several analytic solutions for the N=2 and 3 cases. We discuss freeze-out, a phenomenon that can occur in allmore » three geometries (planar, cylindrical, or spherical), and ''critical modes'' that are stable for any implosion or explosion history and occur only in cylindrical or spherical geometries. We present numerical simulations of possible gelatin-ring experiments illustrating perturbation feedthrough from one interface to another. We also develop a simple model for the evolution of turbulent mix in cylindrical geometry and define a geometrical factor G as the ratio h{sub cylindrical}/h{sub planar} between cylindrical and planar mixing layers. We find that G is a decreasing function of R/R{sub o}, implying that in our model h{sub cylindrical} evolves faster (slower) than h{sub planar} during an implosion (explosion).« less
  • The instability of a radially accelerated cylindrical shell in a magnetic field has been investigated. It was assumed thai the shell was of infinitesimal thickness. For perturbations which do not bend the lines of the magnetic field, the growth rate was found to be w= (gk) 1/2, where g is the acceleration of the shell and k is the wavenumber. This growth rate is independent of the shell thickness. Perturbations which do bend the lines of the field were also found to be unstable. From a supplementary calculation, it was concluded that these instabilities were effective only for wavelengths greatermore » than 8 pi a where 2a is the shell thickness.« less