Synopsis of the Method

  • Frances Bauer
  • Octavio Betancourt
  • Paul Garabedian

Abstract

We consider a formulation of the variational principle of magnetohydrodynamics that enables us to calculate equilibrium and stability without recourse to the full equations of motion [3, 37]. Denote the magnetic field by B, the fluid pressure by p and the mass density by p. We assume an equation of state of the form p = pγ where γ is the gas constant. Let
$${E_p} = \smallint \smallint \smallint \left[ {\frac{{{B^2}}}{2} + \frac{p}{{\gamma - 1}}} \right]dxdydz$$
stand for the potential energy of a torus of plasma and let
$${E_v} = \smallint \smallint \smallint \frac{{{B^2}}}{2}dxdydz$$
stand for the potential energy of the magnetic field in a vacuum region surrounding the plasma. The normal component of B is supposed to vanish at the free boundary separating the plasma from the vacuum. Subject to constraints on B, p and p that will be formulated presently, the variational principle asserts that equilibrium is characterized by a stationary value of the Hamiltonian
$$\nabla .B = 0$$

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Copyright information

© Springer-Verlag New York Inc. 1984

Authors and Affiliations

  • Frances Bauer
    • 1
  • Octavio Betancourt
    • 1
  • Paul Garabedian
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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