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Related Experiment Videos

Viscous, resistive magnetohydrodynamic stability computed by spectral techniques.

R B Dahlburg1, T A Zang, D Montgomery

  • 1College of William and Mary, Williamsburg, Virginia 23185.

Proceedings of the National Academy of Sciences of the United States of America
|September 1, 1983
PubMed
Summary
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This study investigates magnetohydrodynamic quasiequilibria stability using Chebyshev polynomials. Instability is linked to current profile inflection points, suggesting potential for nonlinear 3D instabilities.

Area of Science:

  • Plasma Physics
  • Fluid Dynamics
  • Magnetohydrodynamics (MHD)

Background:

  • Magnetohydrodynamic (MHD) quasiequilibria are fundamental in plasma physics.
  • Understanding their linear stability is crucial for predicting plasma behavior.
  • Finite resistivity and viscosity significantly influence plasma dynamics.

Purpose of the Study:

  • To analyze the linear stability of one-dimensional MHD quasiequilibria.
  • To investigate the role of finite resistivity and viscosity in stability.
  • To explore the relationship between current profiles and instability.

Main Methods:

  • Utilized Chebyshev polynomial expansions for stability analysis.
  • Modeled the method on Orszag's approach for the Orr-Sommerfeld equation.

Related Experiment Videos

  • Defined stability boundaries using two Reynolds-like numbers.

    • Main Results:

    • Stability boundaries are governed by the geometric mean of two Reynolds-like numbers.
    • Marginal stability curves and growth rates were computed.
    • Instability was numerically associated with inflection points in the current profile.

    Conclusions:

    • Instability in MHD quasiequilibria is linked to current profile inflection points.
    • Further research may reveal nonlinear subcritical three-dimensional instabilities.
    • The findings have implications for understanding plasma confinement and behavior.