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Title: The effect of sheared axial flow on the interchange mode in a hard-core Z pinch

Abstract

It is well known that a static (i.e., v=0) closed field line configuration, such as a levitated dipole, or a hard-core Z pinch, can be stabilized against ideal magnetohydrodynamic (MHD) interchange modes when the edge pressure gradient is sufficiently weak. The stabilizing effect is provided by plasma compressibility. However, many laboratory plasmas exhibit a sheared velocity flow (i.e., n{center_dot}{nabla}v{ne}0), and this flow may affect the marginal stability boundary. The present work addresses this issue by an analysis of the effect of axially sheared flow on interchange stability in a hard-core Z pinch, a cylindrical model for the levitated dipole configuration. Specifically, the goal is to learn whether sheared flow is favorable, unfavorable, or neutral with respect to MHD stability. Analytic calculations of marginal stability for several idealistic velocity profiles show that all three options are possible depending on the shape of the shear profile. This variability reflects the competition between the destabilizing Kelvin-Helmholtz effect and the fact that shear makes it more difficult for interchange perturbations to form. Numerical calculation are also presented for more realistic experimental profiles and compared with the results for the idealized analytic profiles.

Authors:
; ;  [1]
  1. Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139 (United States)
Publication Date:
OSTI Identifier:
20960102
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 1; Other Information: DOI: 10.1063/1.2423014; (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; BOUNDARY LAYERS; COMPRESSIBILITY; CYLINDRICAL CONFIGURATION; DIPOLES; MAGNETOHYDRODYNAMICS; NUMERICAL ANALYSIS; PLASMA; PLASMA INSTABILITY; PLASMA PRESSURE; PRESSURE GRADIENTS; STABILITY; VELOCITY

Citation Formats

Kouznetsov, A., Freidberg, J. P., and Kesner, J.. The effect of sheared axial flow on the interchange mode in a hard-core Z pinch. United States: N. p., 2007. Web. doi:10.1063/1.2423014.
Kouznetsov, A., Freidberg, J. P., & Kesner, J.. The effect of sheared axial flow on the interchange mode in a hard-core Z pinch. United States. doi:10.1063/1.2423014.
Kouznetsov, A., Freidberg, J. P., and Kesner, J.. Mon . "The effect of sheared axial flow on the interchange mode in a hard-core Z pinch". United States. doi:10.1063/1.2423014.
@article{osti_20960102,
title = {The effect of sheared axial flow on the interchange mode in a hard-core Z pinch},
author = {Kouznetsov, A. and Freidberg, J. P. and Kesner, J.},
abstractNote = {It is well known that a static (i.e., v=0) closed field line configuration, such as a levitated dipole, or a hard-core Z pinch, can be stabilized against ideal magnetohydrodynamic (MHD) interchange modes when the edge pressure gradient is sufficiently weak. The stabilizing effect is provided by plasma compressibility. However, many laboratory plasmas exhibit a sheared velocity flow (i.e., n{center_dot}{nabla}v{ne}0), and this flow may affect the marginal stability boundary. The present work addresses this issue by an analysis of the effect of axially sheared flow on interchange stability in a hard-core Z pinch, a cylindrical model for the levitated dipole configuration. Specifically, the goal is to learn whether sheared flow is favorable, unfavorable, or neutral with respect to MHD stability. Analytic calculations of marginal stability for several idealistic velocity profiles show that all three options are possible depending on the shape of the shear profile. This variability reflects the competition between the destabilizing Kelvin-Helmholtz effect and the fact that shear makes it more difficult for interchange perturbations to form. Numerical calculation are also presented for more realistic experimental profiles and compared with the results for the idealized analytic profiles.},
doi = {10.1063/1.2423014},
journal = {Physics of Plasmas},
number = 1,
volume = 14,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}
  • A linear analysis of the ideal magnetohydrodynamic (MHD) stability of the Z-pinch is presented in which plasma flows are included in the equilibrium. With sheared axial flows it is found that substantial stabilization of internal modes is possible for some equilibrium profiles. For this to occur equilibria with a change in fluid velocity across the pinch radius of about Mach 2 are required. However, this ignores the surrounding vacuum and for the more realistic free boundary modes flows of about Mach 4 are required to stabilize all global MHD modes. This stabilization of MHD modes is not observed for allmore » equilibria however. This fact, combined with the supersonic flow speeds required for stability, make it unlikely that a Z-pinch could in practice be stabilized by the introduction of sheared flow. {copyright} {ital 1996 American Institute of Physics.}« less
  • The effect of sheared axial flow on the Z-pinch sausage instability has been examined with two-dimensional magnetohydrodynamic simulations. Diffuse Bennett equilibria in the presence of axial flows with parabolic and linear radial profiles have been considered, and a detailed study of the linear and nonlinear development of small perturbations from these equilibria has been performed. The consequences of both single-wavelength and random-seed perturbations were calculated. It was found that sheared flows changed the internal m=0 mode development by reducing the linear growth rates, decreasing the saturation amplitude, and modifying the instability spectrum. High spatial frequency modes were stabilized to smallmore » amplitudes and only long wavelengths continued to grow. Full stability was obtained for supersonic plasma flows.« less
  • 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,more » 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.« less
  • The ZaP Flow Z-Pinch project is experimentally studying the effect of sheared flows on Z-pinch stability. It has been shown theoretically that when dV{sub z}/dr exceeds 0.1kV{sub A} the kink (m=1) mode is stabilized. [U. Shumlak and C. W. Hartman, Phys. Rev. Lett. 75, 3285 (1995).] Z pinches with an embedded axial flow are formed in ZaP with a coaxial accelerator coupled with a 1 m assembly region. Long-lived, quiescent Z pinches are generated throughout the first half cycle of the current. During the initial plasma acceleration phase, the axial motion of the current sheet is consistent with snowplow models.more » Magnetic probes in the assembly region measure the azimuthal modes of the magnetic field. The amplitude of the m=1 mode is proportional to the radial displacement of the Z-pinch plasma current. The magnetic mode levels show a quiescent period which is over 2000 times the growth time of a static Z pinch. The axial velocity is measured along 20 chords through the plasma and deconvolved to provide a radial profile. Using data from multiple pulses, the time evolution of the velocity profile is measured during formation, throughout the quiescent period, and into the transition to instability. The evolution shows that a sheared plasma flow develops as the Z pinch forms. Throughout the quiescent period, the flow shear is greater than the theoretically required threshold for stability. As the flow shear decreases, the magnetic mode fluctuations increase. The coaxial accelerator provides plasma throughout the quiescent period and may explain the evolution of the velocity profile and the sustainment of the flow Z pinch.« less
  • A holographic interferometer is used to determine the radial electron number density profile of a sheared-flow Z pinch. Chord-integrated density information is recorded during a plasma pulse using the expanded beam of a pulsed ruby laser and holographic techniques. An Interactive Data Language (IDL) computer routine that requires only minimal user interaction is used to measure the resulting fringe shift in the reconstructed interferogram. This chord-integrated density information is inverted using an Abel inversion to determine the radial electron density profile. The density profiles obtained show a radially symmetric plasma column with an electron density of 10{sup 16}-10{sup 17} cm{supmore » -3} above the background plasma density. Holographic measurements are made at different times on separate plasma pulses to track the evolution of the density profile over time. These measurements are corroborated by time-dependent measurements made using a He-Ne interferometer.« less