THE UNICITY OF THE ISODYNAMIC TOROIDAL CONFIGURATIONS
We consider the general case of the toroidal isodynamic magneto-hydrostatic equilibrium (MHS). The reference system is constituted by the magnetic surfaces (MS) and, on these, by the magnetic lines and their orthogonal trajectories. Both these families of lines are in general ergodic on the MS. The problem is therefore somewhat more complex than in the case of the Stellarator. By means of the Maxwell's equations, together with the equilibrium equation and the condition of isodynamicity (B = const. on each MS), the metric tensor is consistently simplified. Again it is possible to find an integral of the six GAUSS and CODAZZI-MAINARDI equations. Making use of this integral, by simple geometric considerations, it is easy to show that each MS is a surface of revolution, so that the configuration is axisymmetric. So the axisymmetric isodynamic equilibrium previously determined by one of us (D.P.) is the only toroidal isodynamic equilibrium.
Bibliographic Reference: SEDUTA DELL'ACCADEMIA DELLE SCIENZE, PALERMO (ITALY), APRIL 26, 1984 WRITE TO CEC LUXEMBOURG, DG XIII/A2, POB 1907 MENTIONING PAPER E 31510 ORA
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Record Number: 1989122074800 / Last updated on: 1987-01-01
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