Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Generalized magnetohydrostatic equilibria


Author: Bhimsen K. Shivamoggi
Journal: Quart. Appl. Math. 44 (1986), 487-491
MSC: Primary 76W05
DOI: https://doi.org/10.1090/qam/860901
MathSciNet review: 860901
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Abstract: This note shows the existence of a generalized class of magnetohydrostatic elliptic equilibria of a perfectly conducting fluid in systems with cylindrical topology for which the surfaces of constant pressure have an elliptic transverse cross section with the eccentricity given by an arbitrary function of the axial distance. Further, it is shown that a change in the parameters characterizing the solution leads to a generalized class of hyperbolic equilibria for which the surfaces of constant pressure have a hyperbolic transverse cross section with the eccentricity given by an arbitrary function of the axial distance. Whereas the first class of equilibria is of interest in a plasma-confinement system, the second class of equilibria is of interest in a magnetic-field-line reconnection system.


References [Enhancements On Off] (What's this?)

  • [1] M. L. Woolley, Generated elliptic equilibria in the magneto-hydrodynamic approximation, J. Plasma Phys. 17, 259-272 (1977)
  • [2] S. R. Habbal and T. F. Tuan, Plane MHD flows in a hyperbolic magnetic field: implications for the problem of magnetic field line reconnection, J. Plasma Phys. 21, 85-91 (1979)
  • [3] C. C. Lin, Note on a class of exact solutions in magnetohydrodynamics, Arch. Rational Mech. Anal. 1 (1958), 391–395. MR 0097939, https://doi.org/10.1007/BF00298016
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DOI: https://doi.org/10.1090/qam/860901
Article copyright: © Copyright 1986 American Mathematical Society


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