Electronic Resource
[S.l.]
:
American Institute of Physics (AIP)
Physics of Plasmas
5 (1998), S. 1354-1359
ISSN:
1089-7674
Source:
AIP Digital Archive
Topics:
Physics
Notes:
The eigenfunctions of the equation ∇×bn=λnbn are the solutions of a Sturm-Liouville operator and form an orthonormal basis for the expansion of magnetic fields on any closed domain. Equilibria can be formed by summing individual eigenfunctions bn. The so-called Taylor state is a member of the general class of equilibria consisting entirely of a single mode with the lowest eigenvalue. It is interesting to note that the more general configurations formed by sums of these eigenfunctions are not necessarily zero pressure, nor are they necessarily stable. Physical insight can be gained from decomposition in this way. Stability calculations are greatly simplified in this choice of basis functions, especially for incompressible modes with ∇⋅ξ=0. The magnetohydrodynamic (MHD) δW equation can be written as a bilinear form δW=an*Wnmam, where the Wnm matrix can be composed from the integrated scalar triple products of the m=0 equilibrium basis curl-eigenfunction states and the forward and adjoint curl-eigenfunction magnetic perturbations. The problem of ideal MHD stability in simple geometries (but general equilibria) becomes tractable for PC solutions. The general procedure for stability analysis in arbitrary geometries is given, and detailed calculations for spherical equilibria are given. © 1998 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.872795
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