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Title: Effects of compressibility on the magneto-Rayleigh-Taylor instability in Z-pinch implosions with sheared axial flows

Abstract

A linear analysis of the ideal magnetohydrodynamic (MHD) stability of the compressible Z-pinch plasma with axial flow is presented. Comparing with results of incompressible models, compressibility can reduce the growth rate of the magneto-Rayleigh-Taylor (MRT)/Kelvin-Helmholtz (KH) instability and allow sheared axial flows to mitigate the MRT instability far more effectively. The effect of magnetic field, which cannot be detected in an incompressible model, is also investigated. The result indicates that the mitigation effect of magnetic field on the MRT instability becomes significant as the perturbation wave-number increases. Therefore, with the cooperation of sheared axial flow, magnetic field, and plasma compressibility, the stability of the Z-pinch plasma is improved remarkably. In addition, the analysis also suggests that in an early stage of the implosion, because the plasma temperature is relatively low, the compressible model is much more suitable than the incompressible one based on the framework of MHD theory.

Authors:
;  [1];  [2]
  1. Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088 (China)
  2. (China) and CCAST (World Laboratory), P.O. Box 8730, Beijing 100080 (China)
Publication Date:
OSTI Identifier:
20782510
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 13; Journal Issue: 2; Other Information: DOI: 10.1063/1.2167912; (c) 2006 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; COMPRESSIBILITY; COOPERATION; ELECTRON TEMPERATURE; HELMHOLTZ INSTABILITY; IMPLOSIONS; ION TEMPERATURE; LINEAR Z PINCH DEVICES; LONGITUDINAL PINCH; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; PLASMA; RAYLEIGH-TAYLOR INSTABILITY; SHEAR; STABILITY

Citation Formats

Zhang Yang, Ding Ning, and Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088. Effects of compressibility on the magneto-Rayleigh-Taylor instability in Z-pinch implosions with sheared axial flows. United States: N. p., 2006. Web. doi:10.1063/1.2167912.
Zhang Yang, Ding Ning, & Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088. Effects of compressibility on the magneto-Rayleigh-Taylor instability in Z-pinch implosions with sheared axial flows. United States. doi:10.1063/1.2167912.
Zhang Yang, Ding Ning, and Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088. Wed . "Effects of compressibility on the magneto-Rayleigh-Taylor instability in Z-pinch implosions with sheared axial flows". United States. doi:10.1063/1.2167912.
@article{osti_20782510,
title = {Effects of compressibility on the magneto-Rayleigh-Taylor instability in Z-pinch implosions with sheared axial flows},
author = {Zhang Yang and Ding Ning and Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088},
abstractNote = {A linear analysis of the ideal magnetohydrodynamic (MHD) stability of the compressible Z-pinch plasma with axial flow is presented. Comparing with results of incompressible models, compressibility can reduce the growth rate of the magneto-Rayleigh-Taylor (MRT)/Kelvin-Helmholtz (KH) instability and allow sheared axial flows to mitigate the MRT instability far more effectively. The effect of magnetic field, which cannot be detected in an incompressible model, is also investigated. The result indicates that the mitigation effect of magnetic field on the MRT instability becomes significant as the perturbation wave-number increases. Therefore, with the cooperation of sheared axial flow, magnetic field, and plasma compressibility, the stability of the Z-pinch plasma is improved remarkably. In addition, the analysis also suggests that in an early stage of the implosion, because the plasma temperature is relatively low, the compressible model is much more suitable than the incompressible one based on the framework of MHD theory.},
doi = {10.1063/1.2167912},
journal = {Physics of Plasmas},
number = 2,
volume = 13,
place = {United States},
year = {Wed Feb 15 00:00:00 EST 2006},
month = {Wed Feb 15 00:00:00 EST 2006}
}
  • The stabilizing effect of different axial flow profiles on the magneto-Rayleigh-Taylor (MTR) instability in Z-pinch implosions is investigated with a compressible skin-current model. The numerical results show that the mitigation effect of the axial flow on the MRT instability is caused by the radial velocity shear, and it is highly susceptible to the shear value nearby the plasma outer surface. By adjusting the flow profile, the mitigation effect can be improved markedly.
  • 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 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, formore » 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.« less
  • Large radius Z-pinches are inherently susceptible to the magnetic Rayleigh-Taylor (RT) instability because of their relatively long acceleration path. This has been reflected in a significant reduction of the argon K-shell yield as was observed when the diameter of the load was increased from 2.5 to >4 cm. Recently, an approach was demonstrated to overcome the challenge with a structured gas puff load that mitigates the RT instability, enhances the energy coupling, and leads to a high compression, high yield Z-pinch. The novel load consists of a 'pusher', outer region plasma that carries the current and couples energy from themore » driver, a 'stabilizer', inner region plasma that mitigates the RT growth, and a ''radiator,'' high-density center jet plasma that is heated and compressed to radiate. In 3.5-MA, 200-ns, 12-cm initial diameter implosions, the Ar K-shell yield has increased by a factor of 2, to 21 kJ, matching the yields obtained on the same accelerator with 100-ns, 2.5-cm-diam implosions. Further tests of such structured Ar gas load on {approx}6 MA, 200-ns accelerators have achieved >80 kJ. From laser diagnostics and measurements of the K-shell and extreme ultraviolet emission, initial gas distribution and implosion trajectories were obtained, illustrating the RT suppression and stabilization of the imploding plasma, and identifying the radiation source region in a structured gas puff load. Magnetohydrodynamic simulations, started from actual initial density profiles, reproduce many features of the measurements both qualitatively and quantitatively.« less
  • Recently, a new approach for efficiently generating K-shell x-rays in large-diameter, long-implosion time, structured argon gas Z-pinches has been demonstrated based on a 'pusher-stabilizer-radiator' model. In this paper, direct observations of the Rayleigh-Taylor instability mitigation of a 12-cm diameter, 200-ns implosion time argon Z-pinch using a laser shearing interferometer (LSI) and a laser wavefront analyzer (LWA) are presented. Using a zero-dimensional snowplow model, the imploding plasma trajectories are calculated with the driver current waveforms and the initial mass distributions measured using the planar laser induced fluorescence method. From the LSI and LWA images, the plasma density and trajectory during themore » implosion are measured. The measured trajectory agrees with the snowplow calculations. The suppression of hydromagnetic instabilities in the ''pusher-stabilizer-radiator'' structured loads, leading to a high-compression ratio, high-yield Z-pinch, is discussed. For comparison, the LSI and LWA images of an alternative load (without stabilizer) show the evolution of a highly unstable Z-pinch.« less