MHD Stability

  • Gary Webb
Part of the Lecture Notes in Physics book series (LNP, volume 946)


In this chapter our main concern is the analysis of stability for MHD flows and magnetostatic equilibria. The linear stability of magnetostatic equilibria was investigated in the seminal paper by Bernstein et al. (1958) who derived sufficient conditions for magneto-static equilibria, based on the so-called energy principle. A sufficient, but not necessary condition for magnetostatic equilibria is that the potential energy functional W(ξ, ξ) satisfies δ2W(ξ, ξ) > 0, where ξ is the Lagrangian displacement of the fluid element. A generalization of the energy principle for steady MHD flows was obtained by Frieman and Rotenberg (1960) They noted that for steady flows, the perturbed MHD equations could be written in the form:


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Gary Webb
    • 1
  1. 1.CSPARThe University of Alabama in HuntsvilleHuntsvilleUSA

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