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In this paper, 6 ansatzes are investigated for their potential to allow 3-dimensional ideal magnetohydrodynamic (HMD) equilibria. The ansatzes are based on a Clebsch representation for the magnetic field and a generalized Clebsch representation. Three classes of equilibria, all with a straight magnetic axis, were obtained. Equilibria of the first class have a purely poloidal magnetic field of the Clebsch type and include the 3-dimensional equilibria already known. Equilibria of the 2 other classes have a purely toroidal (ie here longitudinal) magnetic field and pressure surfaces which can be chosen such that poloidal sections are closed. Solutions to the second class contain a free function of theta which determines the poloidal sections of the pressure surfaces at, say, z = 0. The behaviour in the toroidal direction is then fixed but not periodic. The equilibria of the third class are similar to those of the second class but contain no free function and field lines are not plane. Finally, 3-dimensional vacuum fields, which exhibit 3-dimensional magnetic surfaces, are presented. They have the same geometry as the equilibria of the third class and, in fact, can be obtained as a certain limit from these equilibria. Possible applications of the equilibria found are mentioned.

Additional information

Authors: KAISER R, Universität Bayreuth, Lehrstuhl für Angewandte Mathematik (DE);SALAT A, Max-Planck-Institut für Plasmaphysik, Garching bei München (DE)
Bibliographic Reference: Report: IPP 6/335 EN (1995) 32pp.
Availability: Available from Max-Planck-Institut für Plasmaphysik, 85748 Garching bei München (DE)
Record Number: 199610158 / Last updated on: 1996-03-01
Original language: en
Available languages: en
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